From 242c9356f5755d13eceeb2f337bf614ca7f3cff6 Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Thu, 30 Apr 2015 13:44:03 -0400 Subject: [PATCH 1/4] Put off moving math in containers with display:none from the hidden div where they are typeset to their proper locations until AFTER they have been remeasured. Resolves issue #1179. --- unpacked/jax/output/HTML-CSS/jax.js | 19 +++++++++++++------ 1 file changed, 13 insertions(+), 6 deletions(-) diff --git a/unpacked/jax/output/HTML-CSS/jax.js b/unpacked/jax/output/HTML-CSS/jax.js index 9ba4c2b093..fba62bbb4f 100644 --- a/unpacked/jax/output/HTML-CSS/jax.js +++ b/unpacked/jax/output/HTML-CSS/jax.js @@ -539,7 +539,7 @@ }, preTranslate: function (state) { - var scripts = state.jax[this.id], i, m = scripts.length, + var scripts = state.jax[this.id], i, m = scripts.length, n, script, prev, span, div, test, jax, ex, em, scale, maxwidth, relwidth = false, cwidth, linebreak = this.config.linebreaks.automatic, width = this.config.linebreaks.width; if (linebreak) { @@ -590,7 +590,10 @@ // // Determine the scaling factors for each script // (this only requires one reflow rather than a reflow for each equation) + // Record any that need to be hidden (don't move them now, since that + // would cause reflows). // + var hidden = []; for (i = 0; i < m; i++) { script = scripts[i]; if (!script.parentNode) continue; test = script.previousSibling; div = test.previousSibling; @@ -601,8 +604,7 @@ if (relwidth) {maxwidth = cwidth} if (ex === 0 || ex === "NaN") { // can't read width, so move to hidden div for processing - // (this will cause a reflow for each math element that is hidden) - this.hiddenDiv.appendChild(div); + hidden.push(div); jax.HTMLCSS.isHidden = true; ex = this.defaultEx; em = this.defaultEm; cwidth = this.defaultWidth; if (relwidth) {maxwidth = cwidth} @@ -614,6 +616,10 @@ jax.HTMLCSS.cwidth = cwidth/this.em; jax.HTMLCSS.lineWidth = (linebreak ? this.length2em(width,1,maxwidth/this.em) : 1000000); } + for (i = 0, n = hidden.length; i < n; i++) { + this.hiddenDiv.appendChild(hidden[i]); + this.addElement(this.hiddenDiv,"br"); + } // // Remove the test spans used for determining scales and linebreak widths // @@ -676,9 +682,8 @@ } this.restorePreview(script); // - // Put it in place, remove the processing marker, and signal the new math + // Remove the processing marker, and signal the new math pending // - if (jax.HTMLCSS.isHidden) {script.parentNode.insertBefore(div,script)} div.className = div.className.split(/ /)[0] + " MathJax_Processed"; HUB.signal.Post(["New Math Pending",jax.inputID]); // FIXME: wait for this? (i.e., restart if returns uncalled callback) // @@ -732,7 +737,8 @@ for (i = state.HTMLCSSlast, m = state.HTMLCSSeqn; i < m; i++) { script = scripts[i]; if (script && script.MathJax.elementJax) { - script.previousSibling.className = script.previousSibling.className.split(/ /)[0]; + var div = script.MathJax.elementJax.HTMLCSS.div; + div.className = div.className.split(/ /)[0]; if (script.MathJax.preview) {script.MathJax.preview.innerHTML = ""} } } @@ -757,6 +763,7 @@ // jax = script.MathJax.elementJax; this.getMetrics(jax); jax.root.toHTML(jax.HTMLCSS.span,jax.HTMLCSS.div,this.PHASE.III); + if (jax.HTMLCSS.isHidden) script.parentNode.insertBefore(jax.HTMLCSS.div,script); delete jax.HTMLCSS.span; delete jax.HTMLCSS.div; // // The math is now fully processed From 805986318b3ed1f4d499143a1f7c598fe5bf2d20 Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Thu, 30 Apr 2015 15:27:45 -0400 Subject: [PATCH 2/4] Change version numbers. --- unpacked/MathJax.js | 6 +++--- unpacked/jax/output/SVG/config.js | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/unpacked/MathJax.js b/unpacked/MathJax.js index 547ef78f4f..72235a97d2 100644 --- a/unpacked/MathJax.js +++ b/unpacked/MathJax.js @@ -45,9 +45,9 @@ if (window.MathJax) {window.MathJax = {AuthorConfig: window.MathJax}} // MathJax.isPacked = true; // This line is uncommented by the packer. -MathJax.version = "2.5.2"; -MathJax.fileversion = "2.5.2"; -MathJax.cdnVersion = "2.5.2"; // specifies a revision to break caching +MathJax.version = "2.5"; +MathJax.fileversion = "2.5.3"; +MathJax.cdnVersion = "2.5.3"; // specifies a revision to break caching MathJax.cdnFileVersions = {}; // can be used to specify revisions for individual files /**********************************************************/ diff --git a/unpacked/jax/output/SVG/config.js b/unpacked/jax/output/SVG/config.js index 49d4906eb0..a74f365673 100644 --- a/unpacked/jax/output/SVG/config.js +++ b/unpacked/jax/output/SVG/config.js @@ -27,7 +27,7 @@ MathJax.OutputJax.SVG = MathJax.OutputJax({ id: "SVG", - version: "2.5.0", + version: "2.5.3", directory: MathJax.OutputJax.directory + "/SVG", extensionDir: MathJax.OutputJax.extensionDir + "/SVG", autoloadDir: MathJax.OutputJax.directory + "/SVG/autoload", From 72af812dfe4e3e711f94103604be7d11362c0342 Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Thu, 30 Apr 2015 17:13:44 -0400 Subject: [PATCH 3/4] Changed the wrong version number in the previous commit. --- unpacked/jax/output/HTML-CSS/config.js | 2 +- unpacked/jax/output/SVG/config.js | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/unpacked/jax/output/HTML-CSS/config.js b/unpacked/jax/output/HTML-CSS/config.js index d1c47b5ae9..967c1894ca 100644 --- a/unpacked/jax/output/HTML-CSS/config.js +++ b/unpacked/jax/output/HTML-CSS/config.js @@ -27,7 +27,7 @@ MathJax.OutputJax["HTML-CSS"] = MathJax.OutputJax({ id: "HTML-CSS", - version: "2.5.2", + version: "2.5.3", directory: MathJax.OutputJax.directory + "/HTML-CSS", extensionDir: MathJax.OutputJax.extensionDir + "/HTML-CSS", autoloadDir: MathJax.OutputJax.directory + "/HTML-CSS/autoload", diff --git a/unpacked/jax/output/SVG/config.js b/unpacked/jax/output/SVG/config.js index a74f365673..49d4906eb0 100644 --- a/unpacked/jax/output/SVG/config.js +++ b/unpacked/jax/output/SVG/config.js @@ -27,7 +27,7 @@ MathJax.OutputJax.SVG = MathJax.OutputJax({ id: "SVG", - version: "2.5.3", + version: "2.5.0", directory: MathJax.OutputJax.directory + "/SVG", extensionDir: MathJax.OutputJax.extensionDir + "/SVG", autoloadDir: MathJax.OutputJax.directory + "/SVG/autoload", From d7419676e277cb4f5a10f6354b37f3a30cc71288 Mon Sep 17 00:00:00 2001 From: "Davide P. Cervone" Date: Thu, 30 Apr 2015 17:14:37 -0400 Subject: [PATCH 4/4] Repack and recombine --- MathJax.js | 2 +- config/AM_HTMLorMML-full.js | 4 ++-- config/AM_HTMLorMML.js | 2 +- config/Accessible-full.js | 4 ++-- config/Accessible.js | 2 +- config/MML_HTMLorMML-full.js | 4 ++-- config/MML_HTMLorMML.js | 2 +- config/TeX-AMS-MML_HTMLorMML-full.js | 4 ++-- config/TeX-AMS-MML_HTMLorMML.js | 2 +- config/TeX-AMS_HTML-full.js | 4 ++-- config/TeX-AMS_HTML.js | 2 +- config/TeX-MML-AM_HTMLorMML-full.js | 4 ++-- config/TeX-MML-AM_HTMLorMML.js | 2 +- jax/output/HTML-CSS/config.js | 2 +- jax/output/HTML-CSS/jax.js | 2 +- 15 files changed, 21 insertions(+), 21 deletions(-) diff --git a/MathJax.js b/MathJax.js index b4e10f878e..b90b288b4a 100644 --- a/MathJax.js +++ b/MathJax.js @@ -16,4 +16,4 @@ * limitations under the License. */ -if(document.getElementById&&document.childNodes&&document.createElement){if(!(window.MathJax&&MathJax.Hub)){if(window.MathJax){window.MathJax={AuthorConfig:window.MathJax}}else{window.MathJax={}}MathJax.isPacked=true;MathJax.version="2.5.2";MathJax.fileversion="2.5.2";MathJax.cdnVersion="2.5.2";MathJax.cdnFileVersions={};(function(d){var b=window[d];if(!b){b=window[d]={}}var e=[];var c=function(f){var g=f.constructor;if(!g){g=function(){}}for(var h in f){if(h!=="constructor"&&f.hasOwnProperty(h)){g[h]=f[h]}}return g};var a=function(){return function(){return arguments.callee.Init.call(this,arguments)}};b.Object=c({constructor:a(),Subclass:function(f,h){var g=a();g.SUPER=this;g.Init=this.Init;g.Subclass=this.Subclass;g.Augment=this.Augment;g.protoFunction=this.protoFunction;g.can=this.can;g.has=this.has;g.isa=this.isa;g.prototype=new this(e);g.prototype.constructor=g;g.Augment(f,h);return g},Init:function(f){var g=this;if(f.length===1&&f[0]===e){return g}if(!(g instanceof f.callee)){g=new f.callee(e)}return g.Init.apply(g,f)||g},Augment:function(f,g){var h;if(f!=null){for(h in f){if(f.hasOwnProperty(h)){this.protoFunction(h,f[h])}}if(f.toString!==this.prototype.toString&&f.toString!=={}.toString){this.protoFunction("toString",f.toString)}}if(g!=null){for(h in g){if(g.hasOwnProperty(h)){this[h]=g[h]}}}return this},protoFunction:function(g,f){this.prototype[g]=f;if(typeof f==="function"){f.SUPER=this.SUPER.prototype}},prototype:{Init:function(){},SUPER:function(f){return f.callee.SUPER},can:function(f){return typeof(this[f])==="function"},has:function(f){return typeof(this[f])!=="undefined"},isa:function(f){return(f instanceof Object)&&(this instanceof f)}},can:function(f){return this.prototype.can.call(this,f)},has:function(f){return this.prototype.has.call(this,f)},isa:function(g){var f=this;while(f){if(f===g){return true}else{f=f.SUPER}}return false},SimpleSUPER:c({constructor:function(f){return this.SimpleSUPER.define(f)},define:function(f){var h={};if(f!=null){for(var g in f){if(f.hasOwnProperty(g)){h[g]=this.wrap(g,f[g])}}if(f.toString!==this.prototype.toString&&f.toString!=={}.toString){h.toString=this.wrap("toString",f.toString)}}return h},wrap:function(i,h){if(typeof(h)!=="function"||!h.toString().match(/\.\s*SUPER\s*\(/)){return h}var g=function(){this.SUPER=g.SUPER[i];try{var f=h.apply(this,arguments)}catch(j){delete this.SUPER;throw j}delete this.SUPER;return f};g.toString=function(){return h.toString.apply(h,arguments)};return g}})})})("MathJax");(function(BASENAME){var BASE=window[BASENAME];if(!BASE){BASE=window[BASENAME]={}}var CALLBACK=function(data){var cb=function(){return arguments.callee.execute.apply(arguments.callee,arguments)};for(var id in CALLBACK.prototype){if(CALLBACK.prototype.hasOwnProperty(id)){if(typeof(data[id])!=="undefined"){cb[id]=data[id]}else{cb[id]=CALLBACK.prototype[id]}}}cb.toString=CALLBACK.prototype.toString;return cb};CALLBACK.prototype={isCallback:true,hook:function(){},data:[],object:window,execute:function(){if(!this.called||this.autoReset){this.called=!this.autoReset;return this.hook.apply(this.object,this.data.concat([].slice.call(arguments,0)))}},reset:function(){delete this.called},toString:function(){return this.hook.toString.apply(this.hook,arguments)}};var ISCALLBACK=function(f){return(typeof(f)==="function"&&f.isCallback)};var EVAL=function(code){return eval.call(window,code)};var TESTEVAL=function(){EVAL("var __TeSt_VaR__ = 1");if(window.__TeSt_VaR__){try{delete window.__TeSt_VaR__}catch(error){window.__TeSt_VaR__=null}}else{if(window.execScript){EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";window.execScript(code);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}else{EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";var head=(document.getElementsByTagName("head"))[0];if(!head){head=document.body}var script=document.createElement("script");script.appendChild(document.createTextNode(code));head.appendChild(script);head.removeChild(script);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}}TESTEVAL=null};var USING=function(args,i){if(arguments.length>1){if(arguments.length===2&&!(typeof arguments[0]==="function")&&arguments[0] instanceof Object&&typeof arguments[1]==="number"){args=[].slice.call(args,i)}else{args=[].slice.call(arguments,0)}}if(args instanceof Array&&args.length===1){args=args[0]}if(typeof args==="function"){if(args.execute===CALLBACK.prototype.execute){return args}return CALLBACK({hook:args})}else{if(args instanceof Array){if(typeof(args[0])==="string"&&args[1] instanceof Object&&typeof args[1][args[0]]==="function"){return CALLBACK({hook:args[1][args[0]],object:args[1],data:args.slice(2)})}else{if(typeof args[0]==="function"){return CALLBACK({hook:args[0],data:args.slice(1)})}else{if(typeof args[1]==="function"){return CALLBACK({hook:args[1],object:args[0],data:args.slice(2)})}}}}else{if(typeof(args)==="string"){if(TESTEVAL){TESTEVAL()}return CALLBACK({hook:EVAL,data:[args]})}else{if(args instanceof Object){return CALLBACK(args)}else{if(typeof(args)==="undefined"){return CALLBACK({})}}}}}throw Error("Can't make callback from given data")};var DELAY=function(time,callback){callback=USING(callback);callback.timeout=setTimeout(callback,time);return callback};var WAITFOR=function(callback,signal){callback=USING(callback);if(!callback.called){WAITSIGNAL(callback,signal);signal.pending++}};var WAITEXECUTE=function(){var signals=this.signal;delete this.signal;this.execute=this.oldExecute;delete this.oldExecute;var result=this.execute.apply(this,arguments);if(ISCALLBACK(result)&&!result.called){WAITSIGNAL(result,signals)}else{for(var i=0,m=signals.length;i0&&priority=0;i--){this.hooks.splice(i,1)}this.remove=[]}});var EXECUTEHOOKS=function(hooks,data,reset){if(!hooks){return null}if(!(hooks instanceof Array)){hooks=[hooks]}if(!(data instanceof Array)){data=(data==null?[]:[data])}var handler=HOOKS(reset);for(var i=0,m=hooks.length;ig){g=document.styleSheets.length}if(!i){i=document.head||((document.getElementsByTagName("head"))[0]);if(!i){i=document.body}}return i};var f=[];var c=function(){for(var k=0,j=f.length;k=this.timeout){i(this.STATUS.ERROR);return 1}return 0},file:function(j,i){if(i<0){a.Ajax.loadTimeout(j)}else{a.Ajax.loadComplete(j)}},execute:function(){this.hook.call(this.object,this,this.data[0],this.data[1])},checkSafari2:function(i,j,k){if(i.time(k)){return}if(document.styleSheets.length>j&&document.styleSheets[j].cssRules&&document.styleSheets[j].cssRules.length){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},checkLength:function(i,l,n){if(i.time(n)){return}var m=0;var j=(l.sheet||l.styleSheet);try{if((j.cssRules||j.rules||[]).length>0){m=1}}catch(k){if(k.message.match(/protected variable|restricted URI/)){m=1}else{if(k.message.match(/Security error/)){m=1}}}if(m){setTimeout(a.Callback([n,i.STATUS.OK]),0)}else{setTimeout(i,i.delay)}}},loadComplete:function(i){i=this.fileURL(i);var j=this.loading[i];if(j&&!j.preloaded){a.Message.Clear(j.message);clearTimeout(j.timeout);if(j.script){if(f.length===0){setTimeout(c,0)}f.push(j.script)}this.loaded[i]=j.status;delete this.loading[i];this.addHook(i,j.callback)}else{if(j){delete this.loading[i]}this.loaded[i]=this.STATUS.OK;j={status:this.STATUS.OK}}if(!this.loadHooks[i]){return null}return this.loadHooks[i].Execute(j.status)},loadTimeout:function(i){if(this.loading[i].timeout){clearTimeout(this.loading[i].timeout)}this.loading[i].status=this.STATUS.ERROR;this.loadError(i);this.loadComplete(i)},loadError:function(i){a.Message.Set(["LoadFailed","File failed to load: %1",i],null,2000);a.Hub.signal.Post(["file load error",i])},Styles:function(k,l){var i=this.StyleString(k);if(i===""){l=a.Callback(l);l()}else{var j=document.createElement("style");j.type="text/css";this.head=h(this.head);this.head.appendChild(j);if(j.styleSheet&&typeof(j.styleSheet.cssText)!=="undefined"){j.styleSheet.cssText=i}else{j.appendChild(document.createTextNode(i))}l=this.timer.create.call(this,l,j)}return l},StyleString:function(n){if(typeof(n)==="string"){return n}var k="",o,m;for(o in n){if(n.hasOwnProperty(o)){if(typeof n[o]==="string"){k+=o+" {"+n[o]+"}\n"}else{if(n[o] instanceof Array){for(var l=0;l="0"&&p<="9"){f[j]=o[f[j]-1];if(typeof f[j]==="number"){f[j]=this.number(f[j])}}else{if(p==="{"){p=f[j].substr(1);if(p>="0"&&p<="9"){f[j]=o[f[j].substr(1,f[j].length-2)-1];if(typeof f[j]==="number"){f[j]=this.number(f[j])}}else{var k=f[j].match(/^\{([a-z]+):%(\d+)\|(.*)\}$/);if(k){if(k[1]==="plural"){var d=o[k[2]-1];if(typeof d==="undefined"){f[j]="???"}else{d=this.plural(d)-1;var h=k[3].replace(/(^|[^%])(%%)*%\|/g,"$1$2%\uEFEF").split(/\|/);if(d>=0&&d=3){c.push([f[0],f[1],this.processSnippet(g,f[2])])}else{c.push(e[d])}}}}else{c.push(e[d])}}return c},markdownPattern:/(%.)|(\*{1,3})((?:%.|.)+?)\2|(`+)((?:%.|.)+?)\4|\[((?:%.|.)+?)\]\(([^\s\)]+)\)/,processMarkdown:function(b,h,d){var j=[],e;var c=b.split(this.markdownPattern);var g=c[0];for(var f=1,a=c.length;f1?d[1]:""));f=null}if(e&&(!b.preJax||d)){c.nodeValue=c.nodeValue.replace(b.postJax,(e.length>1?e[1]:""))}if(f&&!f.nodeValue.match(/\S/)){f=f.previousSibling}}if(b.preRemoveClass&&f&&f.className===b.preRemoveClass){a.MathJax.preview=f}a.MathJax.checked=1},processInput:function(a){var b,i=MathJax.ElementJax.STATE;var h,e,d=a.scripts.length;try{while(a.ithis.processUpdateTime&&a.i1){d.jax[a.outputJax].push(b)}b.MathJax.state=c.OUTPUT},prepareOutput:function(c,f){while(c.jthis.processUpdateTime&&h.i=0;p--){if((b[p].src||"").match(e)){r.script=b[p].innerHTML;if(RegExp.$2){var s=RegExp.$2.substr(1).split(/\&/);for(var o=0,k=s.length;o=parseInt(x[y])}}return true},Select:function(j){var i=j[c.Browser];if(i){return i(c.Browser)}return null}};var d=h.replace(/^Mozilla\/(\d+\.)+\d+ /,"").replace(/[a-z][-a-z0-9._: ]+\/\d+[^ ]*-[^ ]*\.([a-z][a-z])?\d+ /i,"").replace(/Gentoo |Ubuntu\/(\d+\.)*\d+ (\([^)]*\) )?/,"");c.Browser=c.Insert(c.Insert(new String("Unknown"),{version:"0.0"}),a);for(var u in a){if(a.hasOwnProperty(u)){if(a[u]&&u.substr(0,2)==="is"){u=u.slice(2);if(u==="Mac"||u==="PC"){continue}c.Browser=c.Insert(new String(u),a);var q=new RegExp(".*(Version/| Trident/.*; rv:)((?:\\d+\\.)+\\d+)|.*("+u+")"+(u=="MSIE"?" ":"/")+"((?:\\d+\\.)*\\d+)|(?:^|\\(| )([a-z][-a-z0-9._: ]+|(?:Apple)?WebKit)/((?:\\d+\\.)+\\d+)");var t=q.exec(d)||["","","","unknown","0.0"];c.Browser.name=(t[1]!=""?u:(t[3]||t[5]));c.Browser.version=t[2]||t[4]||t[6];break}}}c.Browser.Select({Safari:function(j){var i=parseInt((String(j.version).split("."))[0]);if(i>85){j.webkit=j.version}if(i>=538){j.version="8.0"}else{if(i>=537){j.version="7.0"}else{if(i>=536){j.version="6.0"}else{if(i>=534){j.version="5.1"}else{if(i>=533){j.version="5.0"}else{if(i>=526){j.version="4.0"}else{if(i>=525){j.version="3.1"}else{if(i>500){j.version="3.0"}else{if(i>400){j.version="2.0"}else{if(i>85){j.version="1.0"}}}}}}}}}}j.webkit=(navigator.appVersion.match(/WebKit\/(\d+)\./))[1];j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);j.noContextMenu=j.isMobile},Firefox:function(j){if((j.version==="0.0"||h.match(/Firefox/)==null)&&navigator.product==="Gecko"){var m=h.match(/[\/ ]rv:(\d+\.\d.*?)[\) ]/);if(m){j.version=m[1]}else{var i=(navigator.buildID||navigator.productSub||"0").substr(0,8);if(i>="20111220"){j.version="9.0"}else{if(i>="20111120"){j.version="8.0"}else{if(i>="20110927"){j.version="7.0"}else{if(i>="20110816"){j.version="6.0"}else{if(i>="20110621"){j.version="5.0"}else{if(i>="20110320"){j.version="4.0"}else{if(i>="20100121"){j.version="3.6"}else{if(i>="20090630"){j.version="3.5"}else{if(i>="20080617"){j.version="3.0"}else{if(i>="20061024"){j.version="2.0"}}}}}}}}}}}}j.isMobile=(navigator.appVersion.match(/Android/i)!=null||h.match(/ Fennec\//)!=null||h.match(/Mobile/)!=null)},Opera:function(i){i.version=opera.version()},MSIE:function(j){j.isIE9=!!(document.documentMode&&(window.performance||window.msPerformance));MathJax.HTML.setScriptBug=!j.isIE9||document.documentMode<9;MathJax.Hub.msieHTMLCollectionBug=(document.documentMode<9);if(document.documentMode<10&&!r.params.NoMathPlayer){try{new ActiveXObject("MathPlayer.Factory.1");j.hasMathPlayer=true}catch(m){}try{if(j.hasMathPlayer){var i=document.createElement("object");i.id="mathplayer";i.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";f.appendChild(i);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");j.mpNamespace=true;if(document.readyState&&(document.readyState==="loading"||document.readyState==="interactive")){document.write('');j.mpImported=true}}else{document.namespaces.add("mjx_IE_fix","http://www.w3.org/1999/xlink")}}catch(m){}}}});c.Browser.Select(MathJax.Message.browsers);if(g.AuthorConfig&&typeof g.AuthorConfig.AuthorInit==="function"){g.AuthorConfig.AuthorInit()}c.queue=g.Callback.Queue();c.queue.Push(["Post",r.signal,"Begin"],["Config",r],["Cookie",r],["Styles",r],["Message",r],function(){var i=g.Callback.Queue(r.Jax(),r.Extensions());return i.Push({})},["Menu",r],r.onLoad(),function(){MathJax.isReady=true},["Typeset",r],["Hash",r],["MenuZoom",r],["Post",r.signal,"End"])})("MathJax")}}; +if(document.getElementById&&document.childNodes&&document.createElement){if(!(window.MathJax&&MathJax.Hub)){if(window.MathJax){window.MathJax={AuthorConfig:window.MathJax}}else{window.MathJax={}}MathJax.isPacked=true;MathJax.version="2.5";MathJax.fileversion="2.5.3";MathJax.cdnVersion="2.5.3";MathJax.cdnFileVersions={};(function(d){var b=window[d];if(!b){b=window[d]={}}var e=[];var c=function(f){var g=f.constructor;if(!g){g=function(){}}for(var h in f){if(h!=="constructor"&&f.hasOwnProperty(h)){g[h]=f[h]}}return g};var a=function(){return function(){return arguments.callee.Init.call(this,arguments)}};b.Object=c({constructor:a(),Subclass:function(f,h){var g=a();g.SUPER=this;g.Init=this.Init;g.Subclass=this.Subclass;g.Augment=this.Augment;g.protoFunction=this.protoFunction;g.can=this.can;g.has=this.has;g.isa=this.isa;g.prototype=new this(e);g.prototype.constructor=g;g.Augment(f,h);return g},Init:function(f){var g=this;if(f.length===1&&f[0]===e){return g}if(!(g instanceof f.callee)){g=new f.callee(e)}return g.Init.apply(g,f)||g},Augment:function(f,g){var h;if(f!=null){for(h in f){if(f.hasOwnProperty(h)){this.protoFunction(h,f[h])}}if(f.toString!==this.prototype.toString&&f.toString!=={}.toString){this.protoFunction("toString",f.toString)}}if(g!=null){for(h in g){if(g.hasOwnProperty(h)){this[h]=g[h]}}}return this},protoFunction:function(g,f){this.prototype[g]=f;if(typeof f==="function"){f.SUPER=this.SUPER.prototype}},prototype:{Init:function(){},SUPER:function(f){return f.callee.SUPER},can:function(f){return typeof(this[f])==="function"},has:function(f){return typeof(this[f])!=="undefined"},isa:function(f){return(f instanceof Object)&&(this instanceof f)}},can:function(f){return this.prototype.can.call(this,f)},has:function(f){return this.prototype.has.call(this,f)},isa:function(g){var f=this;while(f){if(f===g){return true}else{f=f.SUPER}}return false},SimpleSUPER:c({constructor:function(f){return this.SimpleSUPER.define(f)},define:function(f){var h={};if(f!=null){for(var g in f){if(f.hasOwnProperty(g)){h[g]=this.wrap(g,f[g])}}if(f.toString!==this.prototype.toString&&f.toString!=={}.toString){h.toString=this.wrap("toString",f.toString)}}return h},wrap:function(i,h){if(typeof(h)!=="function"||!h.toString().match(/\.\s*SUPER\s*\(/)){return h}var g=function(){this.SUPER=g.SUPER[i];try{var f=h.apply(this,arguments)}catch(j){delete this.SUPER;throw j}delete this.SUPER;return f};g.toString=function(){return h.toString.apply(h,arguments)};return g}})})})("MathJax");(function(BASENAME){var BASE=window[BASENAME];if(!BASE){BASE=window[BASENAME]={}}var CALLBACK=function(data){var cb=function(){return arguments.callee.execute.apply(arguments.callee,arguments)};for(var id in CALLBACK.prototype){if(CALLBACK.prototype.hasOwnProperty(id)){if(typeof(data[id])!=="undefined"){cb[id]=data[id]}else{cb[id]=CALLBACK.prototype[id]}}}cb.toString=CALLBACK.prototype.toString;return cb};CALLBACK.prototype={isCallback:true,hook:function(){},data:[],object:window,execute:function(){if(!this.called||this.autoReset){this.called=!this.autoReset;return this.hook.apply(this.object,this.data.concat([].slice.call(arguments,0)))}},reset:function(){delete this.called},toString:function(){return this.hook.toString.apply(this.hook,arguments)}};var ISCALLBACK=function(f){return(typeof(f)==="function"&&f.isCallback)};var EVAL=function(code){return eval.call(window,code)};var TESTEVAL=function(){EVAL("var __TeSt_VaR__ = 1");if(window.__TeSt_VaR__){try{delete window.__TeSt_VaR__}catch(error){window.__TeSt_VaR__=null}}else{if(window.execScript){EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";window.execScript(code);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}else{EVAL=function(code){BASE.__code=code;code="try {"+BASENAME+".__result = eval("+BASENAME+".__code)} catch(err) {"+BASENAME+".__result = err}";var head=(document.getElementsByTagName("head"))[0];if(!head){head=document.body}var script=document.createElement("script");script.appendChild(document.createTextNode(code));head.appendChild(script);head.removeChild(script);var result=BASE.__result;delete BASE.__result;delete BASE.__code;if(result instanceof Error){throw result}return result}}}TESTEVAL=null};var USING=function(args,i){if(arguments.length>1){if(arguments.length===2&&!(typeof arguments[0]==="function")&&arguments[0] instanceof Object&&typeof arguments[1]==="number"){args=[].slice.call(args,i)}else{args=[].slice.call(arguments,0)}}if(args instanceof Array&&args.length===1){args=args[0]}if(typeof args==="function"){if(args.execute===CALLBACK.prototype.execute){return args}return CALLBACK({hook:args})}else{if(args instanceof Array){if(typeof(args[0])==="string"&&args[1] instanceof Object&&typeof args[1][args[0]]==="function"){return CALLBACK({hook:args[1][args[0]],object:args[1],data:args.slice(2)})}else{if(typeof args[0]==="function"){return CALLBACK({hook:args[0],data:args.slice(1)})}else{if(typeof args[1]==="function"){return CALLBACK({hook:args[1],object:args[0],data:args.slice(2)})}}}}else{if(typeof(args)==="string"){if(TESTEVAL){TESTEVAL()}return CALLBACK({hook:EVAL,data:[args]})}else{if(args instanceof Object){return CALLBACK(args)}else{if(typeof(args)==="undefined"){return CALLBACK({})}}}}}throw Error("Can't make callback from given data")};var DELAY=function(time,callback){callback=USING(callback);callback.timeout=setTimeout(callback,time);return callback};var WAITFOR=function(callback,signal){callback=USING(callback);if(!callback.called){WAITSIGNAL(callback,signal);signal.pending++}};var WAITEXECUTE=function(){var signals=this.signal;delete this.signal;this.execute=this.oldExecute;delete this.oldExecute;var result=this.execute.apply(this,arguments);if(ISCALLBACK(result)&&!result.called){WAITSIGNAL(result,signals)}else{for(var i=0,m=signals.length;i0&&priority=0;i--){this.hooks.splice(i,1)}this.remove=[]}});var EXECUTEHOOKS=function(hooks,data,reset){if(!hooks){return null}if(!(hooks instanceof Array)){hooks=[hooks]}if(!(data instanceof Array)){data=(data==null?[]:[data])}var handler=HOOKS(reset);for(var i=0,m=hooks.length;ig){g=document.styleSheets.length}if(!i){i=document.head||((document.getElementsByTagName("head"))[0]);if(!i){i=document.body}}return i};var f=[];var c=function(){for(var k=0,j=f.length;k=this.timeout){i(this.STATUS.ERROR);return 1}return 0},file:function(j,i){if(i<0){a.Ajax.loadTimeout(j)}else{a.Ajax.loadComplete(j)}},execute:function(){this.hook.call(this.object,this,this.data[0],this.data[1])},checkSafari2:function(i,j,k){if(i.time(k)){return}if(document.styleSheets.length>j&&document.styleSheets[j].cssRules&&document.styleSheets[j].cssRules.length){k(i.STATUS.OK)}else{setTimeout(i,i.delay)}},checkLength:function(i,l,n){if(i.time(n)){return}var m=0;var j=(l.sheet||l.styleSheet);try{if((j.cssRules||j.rules||[]).length>0){m=1}}catch(k){if(k.message.match(/protected variable|restricted URI/)){m=1}else{if(k.message.match(/Security error/)){m=1}}}if(m){setTimeout(a.Callback([n,i.STATUS.OK]),0)}else{setTimeout(i,i.delay)}}},loadComplete:function(i){i=this.fileURL(i);var j=this.loading[i];if(j&&!j.preloaded){a.Message.Clear(j.message);clearTimeout(j.timeout);if(j.script){if(f.length===0){setTimeout(c,0)}f.push(j.script)}this.loaded[i]=j.status;delete this.loading[i];this.addHook(i,j.callback)}else{if(j){delete this.loading[i]}this.loaded[i]=this.STATUS.OK;j={status:this.STATUS.OK}}if(!this.loadHooks[i]){return null}return this.loadHooks[i].Execute(j.status)},loadTimeout:function(i){if(this.loading[i].timeout){clearTimeout(this.loading[i].timeout)}this.loading[i].status=this.STATUS.ERROR;this.loadError(i);this.loadComplete(i)},loadError:function(i){a.Message.Set(["LoadFailed","File failed to load: %1",i],null,2000);a.Hub.signal.Post(["file load error",i])},Styles:function(k,l){var i=this.StyleString(k);if(i===""){l=a.Callback(l);l()}else{var j=document.createElement("style");j.type="text/css";this.head=h(this.head);this.head.appendChild(j);if(j.styleSheet&&typeof(j.styleSheet.cssText)!=="undefined"){j.styleSheet.cssText=i}else{j.appendChild(document.createTextNode(i))}l=this.timer.create.call(this,l,j)}return l},StyleString:function(n){if(typeof(n)==="string"){return n}var k="",o,m;for(o in n){if(n.hasOwnProperty(o)){if(typeof n[o]==="string"){k+=o+" {"+n[o]+"}\n"}else{if(n[o] instanceof Array){for(var l=0;l="0"&&p<="9"){f[j]=o[f[j]-1];if(typeof f[j]==="number"){f[j]=this.number(f[j])}}else{if(p==="{"){p=f[j].substr(1);if(p>="0"&&p<="9"){f[j]=o[f[j].substr(1,f[j].length-2)-1];if(typeof f[j]==="number"){f[j]=this.number(f[j])}}else{var k=f[j].match(/^\{([a-z]+):%(\d+)\|(.*)\}$/);if(k){if(k[1]==="plural"){var d=o[k[2]-1];if(typeof d==="undefined"){f[j]="???"}else{d=this.plural(d)-1;var h=k[3].replace(/(^|[^%])(%%)*%\|/g,"$1$2%\uEFEF").split(/\|/);if(d>=0&&d=3){c.push([f[0],f[1],this.processSnippet(g,f[2])])}else{c.push(e[d])}}}}else{c.push(e[d])}}return c},markdownPattern:/(%.)|(\*{1,3})((?:%.|.)+?)\2|(`+)((?:%.|.)+?)\4|\[((?:%.|.)+?)\]\(([^\s\)]+)\)/,processMarkdown:function(b,h,d){var j=[],e;var c=b.split(this.markdownPattern);var g=c[0];for(var f=1,a=c.length;f1?d[1]:""));f=null}if(e&&(!b.preJax||d)){c.nodeValue=c.nodeValue.replace(b.postJax,(e.length>1?e[1]:""))}if(f&&!f.nodeValue.match(/\S/)){f=f.previousSibling}}if(b.preRemoveClass&&f&&f.className===b.preRemoveClass){a.MathJax.preview=f}a.MathJax.checked=1},processInput:function(a){var b,i=MathJax.ElementJax.STATE;var h,e,d=a.scripts.length;try{while(a.ithis.processUpdateTime&&a.i1){d.jax[a.outputJax].push(b)}b.MathJax.state=c.OUTPUT},prepareOutput:function(c,f){while(c.jthis.processUpdateTime&&h.i=0;p--){if((b[p].src||"").match(e)){r.script=b[p].innerHTML;if(RegExp.$2){var s=RegExp.$2.substr(1).split(/\&/);for(var o=0,k=s.length;o=parseInt(x[y])}}return true},Select:function(j){var i=j[c.Browser];if(i){return i(c.Browser)}return null}};var d=h.replace(/^Mozilla\/(\d+\.)+\d+ /,"").replace(/[a-z][-a-z0-9._: ]+\/\d+[^ ]*-[^ ]*\.([a-z][a-z])?\d+ /i,"").replace(/Gentoo |Ubuntu\/(\d+\.)*\d+ (\([^)]*\) )?/,"");c.Browser=c.Insert(c.Insert(new String("Unknown"),{version:"0.0"}),a);for(var u in a){if(a.hasOwnProperty(u)){if(a[u]&&u.substr(0,2)==="is"){u=u.slice(2);if(u==="Mac"||u==="PC"){continue}c.Browser=c.Insert(new String(u),a);var q=new RegExp(".*(Version/| Trident/.*; rv:)((?:\\d+\\.)+\\d+)|.*("+u+")"+(u=="MSIE"?" ":"/")+"((?:\\d+\\.)*\\d+)|(?:^|\\(| )([a-z][-a-z0-9._: ]+|(?:Apple)?WebKit)/((?:\\d+\\.)+\\d+)");var t=q.exec(d)||["","","","unknown","0.0"];c.Browser.name=(t[1]!=""?u:(t[3]||t[5]));c.Browser.version=t[2]||t[4]||t[6];break}}}c.Browser.Select({Safari:function(j){var i=parseInt((String(j.version).split("."))[0]);if(i>85){j.webkit=j.version}if(i>=538){j.version="8.0"}else{if(i>=537){j.version="7.0"}else{if(i>=536){j.version="6.0"}else{if(i>=534){j.version="5.1"}else{if(i>=533){j.version="5.0"}else{if(i>=526){j.version="4.0"}else{if(i>=525){j.version="3.1"}else{if(i>500){j.version="3.0"}else{if(i>400){j.version="2.0"}else{if(i>85){j.version="1.0"}}}}}}}}}}j.webkit=(navigator.appVersion.match(/WebKit\/(\d+)\./))[1];j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);j.noContextMenu=j.isMobile},Firefox:function(j){if((j.version==="0.0"||h.match(/Firefox/)==null)&&navigator.product==="Gecko"){var m=h.match(/[\/ ]rv:(\d+\.\d.*?)[\) ]/);if(m){j.version=m[1]}else{var i=(navigator.buildID||navigator.productSub||"0").substr(0,8);if(i>="20111220"){j.version="9.0"}else{if(i>="20111120"){j.version="8.0"}else{if(i>="20110927"){j.version="7.0"}else{if(i>="20110816"){j.version="6.0"}else{if(i>="20110621"){j.version="5.0"}else{if(i>="20110320"){j.version="4.0"}else{if(i>="20100121"){j.version="3.6"}else{if(i>="20090630"){j.version="3.5"}else{if(i>="20080617"){j.version="3.0"}else{if(i>="20061024"){j.version="2.0"}}}}}}}}}}}}j.isMobile=(navigator.appVersion.match(/Android/i)!=null||h.match(/ Fennec\//)!=null||h.match(/Mobile/)!=null)},Opera:function(i){i.version=opera.version()},MSIE:function(j){j.isIE9=!!(document.documentMode&&(window.performance||window.msPerformance));MathJax.HTML.setScriptBug=!j.isIE9||document.documentMode<9;MathJax.Hub.msieHTMLCollectionBug=(document.documentMode<9);if(document.documentMode<10&&!r.params.NoMathPlayer){try{new ActiveXObject("MathPlayer.Factory.1");j.hasMathPlayer=true}catch(m){}try{if(j.hasMathPlayer){var i=document.createElement("object");i.id="mathplayer";i.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";f.appendChild(i);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");j.mpNamespace=true;if(document.readyState&&(document.readyState==="loading"||document.readyState==="interactive")){document.write('');j.mpImported=true}}else{document.namespaces.add("mjx_IE_fix","http://www.w3.org/1999/xlink")}}catch(m){}}}});c.Browser.Select(MathJax.Message.browsers);if(g.AuthorConfig&&typeof g.AuthorConfig.AuthorInit==="function"){g.AuthorConfig.AuthorInit()}c.queue=g.Callback.Queue();c.queue.Push(["Post",r.signal,"Begin"],["Config",r],["Cookie",r],["Styles",r],["Message",r],function(){var i=g.Callback.Queue(r.Jax(),r.Extensions());return i.Push({})},["Menu",r],r.onLoad(),function(){MathJax.isReady=true},["Typeset",r],["Hash",r],["MenuZoom",r],["Post",r.signal,"End"])})("MathJax")}}; diff --git a/config/AM_HTMLorMML-full.js b/config/AM_HTMLorMML-full.js index cf1fd12ed0..916aa72878 100644 --- a/config/AM_HTMLorMML-full.js +++ b/config/AM_HTMLorMML-full.js @@ -37,7 +37,7 @@ MathJax.Ajax.Preloading( MathJax.Hub.Config({"v1.0-compatible":false}); MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.5.0",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g"}var j=[],h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken||this.isChars){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},toMathMLattributes:function(){var h=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var g=(this.attrNames||a.copyAttributeNames),f=a.skipAttributes,k=a.copyAttributes;var d=[];if(this.type==="math"&&(!this.attr||!this.attr.xmlns)){d.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var j in h){if(!f[j]&&!k[j]&&h.hasOwnProperty(j)){if(this[j]!=null&&this[j]!==h[j]){if(this.Get(j,null,1)!==this[j]){d.push(j+'="'+this.toMathMLattribute(this[j])+'"')}}}}}for(var e=0,c=g.length;e126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var o=this.type,j=this.toMathMLattributes();var h=[],n=c+(f?" "+(l?" ":""):"")+" ";for(var g=0,e=this.data.length;g")}}if(h.length===0||(h.length===1&&h[0]==="")){if(!f){return"<"+o+j+" />"}h.push(n+"")}if(f){if(l){h.unshift(c+" ");h.push(c+" ")}h.unshift(c+" ");var k=d.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});h.push(c+' '+k+"");h.push(c+" ")}return c+"<"+o+j+">\n"+h.join("\n")+"\n"+c+""}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(ac){var g;var X=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(i){if(i.parent){i.parent.removeChild(i)}if(this.lastChild){this.lastChild.nextSibling=i}if(!this.firstChild){this.firstChild=i}this.childNodes.push(i);i.parent=this;this.lastChild=i;return i},removeChild:function(af){for(var ae=0,ad=this.childNodes.length;ae=ad-1){this.lastChild=ag}this.childNodes[af]=ag;ag.nextSibling=ae.nextSibling;ae.nextSibling=ae.parent=null;return ae},hasChildNodes:function(i){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var i=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ad=i.apply(this,arguments)||this;ad.childNodes=ad.data;ad.nodeName=ad.type;return ad},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}var ae=arguments;if(ag.isa(X)){ae=ag.childNodes;ag.data=ag.childNodes=[];ag.firstChild=ag.lastChild=null}for(var af=0,ad=ae.length;af=ad-1){this.lastChild=ag}this.SetData(af,ag);ag.nextSibling=ae.nextSibling;ae.nextSibling=ae.parent=null;return ae},hasChildNodes:function(ad){return(this.childNodes.length>0)},setAttribute:function(ad,ae){this[ad]=ae}})};var Q={};var e={getElementById:true,createElementNS:function(ad,i){var ae=g[i]();if(i==="mo"&&ac.config.useMathMLspacing){ae.useMMLspacing=128}return ae},createTextNode:function(i){return g.chars(i).With({nodeValue:i})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var Z;var C="blue";var aa="serif";var p=true;var v=true;var d=".";var f=true;var m=(J.appName.slice(0,9)=="Microsoft");function E(i){if(m){return e.createElement(i)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",i)}}var W="http://www.w3.org/1998/Math/MathML";function P(i){if(m){return e.createElement("m:"+i)}else{return e.createElementNS(W,i)}}function O(i,ae){var ad;if(m){ad=e.createElement("m:"+i)}else{ad=e.createElementNS(W,i)}if(ae){ad.appendChild(ae)}return ad}function u(i,ad){z=z.concat([{input:i,tag:"mo",output:ad,tex:null,ttype:V}]);z.sort(T);for(Z=0;Z",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:h},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:n},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:j},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:j},{input:"^",tag:"msup",output:"^",tex:null,ttype:j},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},l,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ad,i){if(ad.input>i.input){return 1}else{return -1}}var S=[];function o(){var ae=[],ad;for(ad=0;ad>1;if(ae[ad]=S[ad]}s=y;if(ah!=""){y=z[ag].ttype;return z[ag]}y=c;ad=1;am=aj.slice(0,1);var ak=true;while("0"<=am&&am<="9"&&ad<=aj.length){am=aj.slice(ad,ad+1);ad++}if(am==d){am=aj.slice(ad,ad+1);if("0"<=am&&am<="9"){ak=false;ad++;while("0"<=am&&am<="9"&&ad<=aj.length){am=aj.slice(ad,ad+1);ad++}}}if((ak&&ad>1)||ad>2){am=aj.slice(0,ad-1);al="mn"}else{ad=2;am=aj.slice(0,1);al=(("A">am||am>"Z")&&("a">am||am>"z")?"mo":"mi")}if(am=="-"&&s==j){y=j;return{input:am,tag:al,output:am,ttype:A,func:true}}return{input:am,tag:al,output:am,ttype:c}}function R(ad){var i;if(!ad.hasChildNodes()){return}if(ad.firstChild.hasChildNodes()&&(ad.nodeName=="mrow"||ad.nodeName=="M:MROW")){i=ad.firstChild.firstChild.nodeValue;if(i=="("||i=="["||i=="{"){ad.removeChild(ad.firstChild)}}if(ad.lastChild.hasChildNodes()&&(ad.nodeName=="mrow"||ad.nodeName=="M:MROW")){i=ad.lastChild.firstChild.nodeValue;if(i==")"||i=="]"||i=="}"){ad.removeChild(ad.lastChild)}}}var F,s,y;function G(aj){var af,ae,am,ah,al,ai=e.createDocumentFragment();aj=q(aj,0);af=k(aj);if(af==null||af.ttype==h&&F>0){return[null,aj]}if(af.ttype==V){aj=af.output+q(aj,af.input.length);af=k(aj)}switch(af.ttype){case L:case c:aj=q(aj,af.input.length);return[O(af.tag,e.createTextNode(af.output)),aj];case b:F++;aj=q(aj,af.input.length);am=r(aj,true);F--;if(typeof af.invisible=="boolean"&&af.invisible){ae=O("mrow",am[0])}else{ae=O("mo",e.createTextNode(af.output));ae=O("mrow",ae);ae.appendChild(am[0])}return[ae,am[1]];case Y:if(af!=l){aj=q(aj,af.input.length)}if(aj.charAt(0)=="{"){ah=aj.indexOf("}")}else{if(aj.charAt(0)=="("){ah=aj.indexOf(")")}else{if(aj.charAt(0)=="["){ah=aj.indexOf("]")}else{if(af==l){ah=aj.slice(1).indexOf('"')+1}else{ah=0}}}}if(ah==-1){ah=aj.length}al=aj.slice(1,ah);if(al.charAt(0)==" "){ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae)}ai.appendChild(O(af.tag,e.createTextNode(al)));if(al.charAt(al.length-1)==" "){ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae)}aj=q(aj,ah+1);return[O("mrow",ai),aj];case K:case A:aj=q(aj,af.input.length);am=G(aj);if(am[0]==null){return[O(af.tag,e.createTextNode(af.output)),aj]}if(typeof af.func=="boolean"&&af.func){al=aj.charAt(0);if(al=="^"||al=="_"||al=="/"||al=="|"||al==","||(af.input.length==1&&af.input.match(/\w/)&&al!="(")){return[O(af.tag,e.createTextNode(af.output)),aj]}else{ae=O("mrow",O(af.tag,e.createTextNode(af.output)));ae.appendChild(am[0]);return[ae,am[1]]}}R(am[0]);if(af.input=="sqrt"){return[O(af.tag,am[0]),am[1]]}else{if(typeof af.rewriteleftright!="undefined"){ae=O("mrow",O("mo",e.createTextNode(af.rewriteleftright[0])));ae.appendChild(am[0]);ae.appendChild(O("mo",e.createTextNode(af.rewriteleftright[1])));return[ae,am[1]]}else{if(af.input=="cancel"){ae=O(af.tag,am[0]);ae.setAttribute("notation","updiagonalstrike");return[ae,am[1]]}else{if(typeof af.acc=="boolean"&&af.acc){ae=O(af.tag,am[0]);ae.appendChild(O("mo",e.createTextNode(af.output)));return[ae,am[1]]}else{if(!m&&typeof af.codes!="undefined"){for(ah=0;ah64&&al.charCodeAt(ag)<91){ak=ak+af.codes[al.charCodeAt(ag)-65]}else{if(al.charCodeAt(ag)>96&&al.charCodeAt(ag)<123){ak=ak+af.codes[al.charCodeAt(ag)-71]}else{ak=ak+al.charAt(ag)}}}if(am[0].nodeName=="mi"){am[0]=O("mo").appendChild(e.createTextNode(ak))}else{am[0].replaceChild(O("mo").appendChild(e.createTextNode(ak)),am[0].childNodes[ah])}}}}ae=O(af.tag,am[0]);ae.setAttribute(af.atname,af.atval);return[ae,am[1]]}}}}case U:aj=q(aj,af.input.length);am=G(aj);if(am[0]==null){return[O("mo",e.createTextNode(af.input)),aj]}R(am[0]);var ad=G(am[1]);if(ad[0]==null){return[O("mo",e.createTextNode(af.input)),aj]}R(ad[0]);if(af.input=="color"){if(aj.charAt(0)=="{"){ah=aj.indexOf("}")}else{if(aj.charAt(0)=="("){ah=aj.indexOf(")")}else{if(aj.charAt(0)=="["){ah=aj.indexOf("]")}}}al=aj.slice(1,ah);ae=O(af.tag,ad[0]);ae.setAttribute("mathcolor",al);return[ae,ad[1]]}if(af.input=="root"||af.input=="stackrel"){ai.appendChild(ad[0])}ai.appendChild(am[0]);if(af.input=="frac"){ai.appendChild(ad[0])}return[O(af.tag,ai),ad[1]];case j:aj=q(aj,af.input.length);return[O("mo",e.createTextNode(af.output)),aj];case a:aj=q(aj,af.input.length);ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae);ai.appendChild(O(af.tag,e.createTextNode(af.output)));ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae);return[O("mrow",ai),aj];case n:F++;aj=q(aj,af.input.length);am=r(aj,false);F--;al="";if(am[0].lastChild!=null){al=am[0].lastChild.firstChild.nodeValue}if(al=="|"){ae=O("mo",e.createTextNode(af.output));ae=O("mrow",ae);ae.appendChild(am[0]);return[ae,am[1]]}else{ae=O("mo",e.createTextNode("\u2223"));ae=O("mrow",ae);return[ae,aj]}default:aj=q(aj,af.input.length);return[O(af.tag,e.createTextNode(af.output)),aj]}}function t(ai){var ag,aj,ah,af,i,ae;ai=q(ai,0);aj=k(ai);i=G(ai);af=i[0];ai=i[1];ag=k(ai);if(ag.ttype==j&&ag.input!="/"){ai=q(ai,ag.input.length);i=G(ai);if(i[0]==null){i[0]=O("mo",e.createTextNode("\u25A1"))}else{R(i[0])}ai=i[1];ae=(aj.ttype==L||aj.ttype==K);if(ag.input=="_"){ah=k(ai);if(ah.input=="^"){ai=q(ai,ah.input.length);var ad=G(ai);R(ad[0]);ai=ad[1];af=O((ae?"munderover":"msubsup"),af);af.appendChild(i[0]);af.appendChild(ad[0]);af=O("mrow",af)}else{af=O((ae?"munder":"msub"),af);af.appendChild(i[0])}}else{if(ag.input=="^"&&ae){af=O("mover",af);af.appendChild(i[0])}else{af=O(ag.tag,af);af.appendChild(i[0])}}if(typeof aj.func!="undefined"&&aj.func){ah=k(ai);if(ah.ttype!=j&&ah.ttype!=h){i=t(ai);af=O("mrow",af);af.appendChild(i[0]);ai=i[1]}}}return[af,ai]}function r(al,ak){var ap,am,ah,at,ai=e.createDocumentFragment();do{al=q(al,0);ah=t(al);am=ah[0];al=ah[1];ap=k(al);if(ap.ttype==j&&ap.input=="/"){al=q(al,ap.input.length);ah=t(al);if(ah[0]==null){ah[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ah[0])}al=ah[1];R(am);am=O(ap.tag,am);am.appendChild(ah[0]);ai.appendChild(am);ap=k(al)}else{if(am!=undefined){ai.appendChild(am)}}}while((ap.ttype!=h&&(ap.ttype!=n||ak)||F==0)&&ap!=null&&ap.output!="");if(ap.ttype==h||ap.ttype==n){var au=ai.childNodes.length;if(au>0&&ai.childNodes[au-1].nodeName=="mrow"){var aw=ai.childNodes[au-1].lastChild.firstChild.nodeValue;if(aw==")"||aw=="]"){var ae=ai.childNodes[au-1].firstChild.firstChild.nodeValue;if(ae=="("&&aw==")"&&ap.output!="}"||ae=="["&&aw=="]"){var af=[];var aq=true;var an=ai.childNodes.length;for(at=0;aq&&at1){aq=af[at].length==af[at-2].length}}aq=aq&&(af.length>1||af[0].length>0);if(aq){var ag,ad,aj,ao,av=e.createDocumentFragment();for(at=0;at2){ai.removeChild(ai.firstChild);ai.removeChild(ai.firstChild)}av.appendChild(O("mtr",ag))}am=O("mtable",av);if(typeof ap.invisible=="boolean"&&ap.invisible){am.setAttribute("columnalign","left")}ai.replaceChild(am,ai.firstChild)}}}}al=q(al,ap.input.length);if(typeof ap.invisible!="boolean"||!ap.invisible){am=O("mo",e.createTextNode(ap.output));ai.appendChild(am)}}return[ai,al]}function M(ae,ad){var af,i;F=0;ae=ae.replace(/ /g,"");ae=ae.replace(/>/g,">");ae=ae.replace(/</g,"<");ae=ae.replace(/(Sin|Cos|Tan|Arcsin|Arccos|Arctan|Sinh|Cosh|Tanh|Cot|Sec|Csc|Log|Ln|Abs)/g,function(ag){return ag.toLowerCase()});af=r(ae.replace(/^\s+/g,""),false)[0];i=O("mstyle",af);if(C!=""){i.setAttribute("mathcolor",C)}if(aa!=""){i.setAttribute("fontfamily",aa)}if(p){i.setAttribute("displaystyle","true")}i=O("math",i);if(v){i.setAttribute("title",ae.replace(/\s+/g," "))}return i}v=false;aa="";C="";(function(){for(var ae=0,ad=z.length;ae span":{"text-align":o+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);f.math(f.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement("object");m.id="mathplayer";m.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(m);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;ut){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r0;u--){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.5.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var I=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aK=I.width.match(/%$/);var ax=b.createStack(r);var aH=this.HTMLgetScale(),aA=this.HTMLgetMu(r),aB=-1;var ap=[],at=[],aj=[],av=[],au=[],ae,ad,ao=-1,ac,an,X,aF,Q,aC,aP=[],aU;var G=b.FONTDATA.lineH*aH*I.useHeight,N=b.FONTDATA.lineD*aH*I.useHeight;for(ae=0,ac=this.data.length;aeao){ao=ad}au[ad]=b.createStack(b.createBox(ax));aj[ad]=-b.BIGDIMEN}av[ae][ad]=b.createBox(au[ad]);aP.push(aF.data[ad-X].toHTML(av[ae][ad]))}}b.MeasureSpans(aP);for(ae=0,ac=this.data.length;aeap[ae]){ap[ae]=aT*aM.h/aU}if(aT*aM.d/aU>at[ae]){at[ae]=aT*aM.d/aU}}}else{if(aC.HTMLcanStretch("Horizontal")){aT=b.length2em(aT,aA,aM.w);if(aT>aj[ad]){aj[ad]=aT}}}}}if(av[ae][ad].bbox.h>ap[ae]){ap[ae]=av[ae][ad].bbox.h}if(av[ae][ad].bbox.d>at[ae]){at[ae]=av[ae][ad].bbox.d}if(av[ae][ad].bbox.w>aj[ad]){aj[ad]=av[ae][ad].bbox.w}}}var aE=MathJax.Hub.SplitList;var az=aE(I.columnspacing),aR=aE(I.rowspacing),e=aE(I.columnalign),B=aE(I.rowalign),d=aE(I.columnlines),w=aE(I.rowlines),aN=aE(I.columnwidth),U=[];for(ae=0,ac=az.length;aeav.length){aa=av.length}}ai=0;aV=-(aU+aI)+ap[0];for(ae=0,ac=aa-1;ae0.98){R=0.98/af;af=0.98}}else{if(I.width==="auto"){if(af>0.98){R=K/(z+K);ab=z+K}else{ab=z/(1-af)}}else{ab=b.length2em(I.width,aA);for(ae=0,ac=Math.min(ao+1,az.length);ae0.01){if(ag&&ab>z){ab=(ab-z)/ag;for(ae=0,ac=ar.length;aeap[ae]){av[ae][ad].bbox.H=av[ae][ad].bbox.h;av[ae][ad].bbox.h=ap[ae]}if(av[ae][ad].bbox.d>at[ae]){av[ae][ad].bbox.D=av[ae][ad].bbox.d;av[ae][ad].bbox.d=at[ae]}aC.symmetric=aL}}aS=Q.rowalign||this.data[ae].rowalign||B[ae];o=({top:ap[ae]-av[ae][ad].bbox.h,bottom:av[ae][ad].bbox.d-at[ae],center:((ap[ae]-at[ae])-(av[ae][ad].bbox.h-av[ae][ad].bbox.d))/2,baseline:0,axis:0})[aS]||0;aS=(Q.columnalign||U[ae][ad]||e[ad]);b.alignBox(av[ae][ad],aS,S+o)}if(ae *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2])}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[f]});if(e.texClass===a.TEXCLASS.OP){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(e instanceof Array){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g span":{"text-align":o+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);f.math(f.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement("object");m.id="mathplayer";m.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(m);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;ut){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r0;u--){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.5.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var I=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aK=I.width.match(/%$/);var ax=b.createStack(r);var aH=this.HTMLgetScale(),aA=this.HTMLgetMu(r),aB=-1;var ap=[],at=[],aj=[],av=[],au=[],ae,ad,ao=-1,ac,an,X,aF,Q,aC,aP=[],aU;var G=b.FONTDATA.lineH*aH*I.useHeight,N=b.FONTDATA.lineD*aH*I.useHeight;for(ae=0,ac=this.data.length;aeao){ao=ad}au[ad]=b.createStack(b.createBox(ax));aj[ad]=-b.BIGDIMEN}av[ae][ad]=b.createBox(au[ad]);aP.push(aF.data[ad-X].toHTML(av[ae][ad]))}}b.MeasureSpans(aP);for(ae=0,ac=this.data.length;aeap[ae]){ap[ae]=aT*aM.h/aU}if(aT*aM.d/aU>at[ae]){at[ae]=aT*aM.d/aU}}}else{if(aC.HTMLcanStretch("Horizontal")){aT=b.length2em(aT,aA,aM.w);if(aT>aj[ad]){aj[ad]=aT}}}}}if(av[ae][ad].bbox.h>ap[ae]){ap[ae]=av[ae][ad].bbox.h}if(av[ae][ad].bbox.d>at[ae]){at[ae]=av[ae][ad].bbox.d}if(av[ae][ad].bbox.w>aj[ad]){aj[ad]=av[ae][ad].bbox.w}}}var aE=MathJax.Hub.SplitList;var az=aE(I.columnspacing),aR=aE(I.rowspacing),e=aE(I.columnalign),B=aE(I.rowalign),d=aE(I.columnlines),w=aE(I.rowlines),aN=aE(I.columnwidth),U=[];for(ae=0,ac=az.length;aeav.length){aa=av.length}}ai=0;aV=-(aU+aI)+ap[0];for(ae=0,ac=aa-1;ae0.98){R=0.98/af;af=0.98}}else{if(I.width==="auto"){if(af>0.98){R=K/(z+K);ab=z+K}else{ab=z/(1-af)}}else{ab=b.length2em(I.width,aA);for(ae=0,ac=Math.min(ao+1,az.length);ae0.01){if(ag&&ab>z){ab=(ab-z)/ag;for(ae=0,ac=ar.length;aeap[ae]){av[ae][ad].bbox.H=av[ae][ad].bbox.h;av[ae][ad].bbox.h=ap[ae]}if(av[ae][ad].bbox.d>at[ae]){av[ae][ad].bbox.D=av[ae][ad].bbox.d;av[ae][ad].bbox.d=at[ae]}aC.symmetric=aL}}aS=Q.rowalign||this.data[ae].rowalign||B[ae];o=({top:ap[ae]-av[ae][ad].bbox.h,bottom:av[ae][ad].bbox.d-at[ae],center:((ap[ae]-at[ae])-(av[ae][ad].bbox.h-av[ae][ad].bbox.d))/2,baseline:0,axis:0})[aS]||0;aS=(Q.columnalign||U[ae][ad]||e[ad]);b.alignBox(av[ae][ad],aS,S+o)}if(ae *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g"}var j=[],h=(this.isToken?"":k+(g?"":" "));for(var f=0,c=this.data.length;f")}}}if(this.isToken||this.isChars){return k+"<"+e+d+">"+j.join("")+""}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+""},toMathMLattributes:function(){var h=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var g=(this.attrNames||a.copyAttributeNames),f=a.skipAttributes,k=a.copyAttributes;var d=[];if(this.type==="math"&&(!this.attr||!this.attr.xmlns)){d.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var j in h){if(!f[j]&&!k[j]&&h.hasOwnProperty(j)){if(this[j]!=null&&this[j]!==h[j]){if(this.Get(j,null,1)!==this[j]){d.push(j+'="'+this.toMathMLattribute(this[j])+'"')}}}}}for(var e=0,c=g.length;e126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var o=this.type,j=this.toMathMLattributes();var h=[],n=c+(f?" "+(l?" ":""):"")+" ";for(var g=0,e=this.data.length;g")}}if(h.length===0||(h.length===1&&h[0]==="")){if(!f){return"<"+o+j+" />"}h.push(n+"")}if(f){if(l){h.unshift(c+" ");h.push(c+" ")}h.unshift(c+" ");var k=d.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});h.push(c+' '+k+"");h.push(c+" ")}return c+"<"+o+j+">\n"+h.join("\n")+"\n"+c+""}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f\n"+g.join("\n")+"\n"+h+""}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"\n"+this.data[0].toMathML(d+" ")+"\n"+d+""}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!=="string"){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var g=j.getElementsByTagName("parsererror")[0];if(g){c.Error(["ParsingError","Error parsing MathML: %1",g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(j.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(j.firstChild.nodeName.toLowerCase()==="html"){var f=j.getElementsByTagName("h1")[0];if(f&&f.textContent==="XML parsing error"&&f.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2])}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[f]});if(e.texClass===a.TEXCLASS.OP){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(e instanceof Array){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g span":{"text-align":o+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);f.math(f.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement("object");m.id="mathplayer";m.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(m);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;ut){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r0;u--){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.5.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var I=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aK=I.width.match(/%$/);var ax=b.createStack(r);var aH=this.HTMLgetScale(),aA=this.HTMLgetMu(r),aB=-1;var ap=[],at=[],aj=[],av=[],au=[],ae,ad,ao=-1,ac,an,X,aF,Q,aC,aP=[],aU;var G=b.FONTDATA.lineH*aH*I.useHeight,N=b.FONTDATA.lineD*aH*I.useHeight;for(ae=0,ac=this.data.length;aeao){ao=ad}au[ad]=b.createStack(b.createBox(ax));aj[ad]=-b.BIGDIMEN}av[ae][ad]=b.createBox(au[ad]);aP.push(aF.data[ad-X].toHTML(av[ae][ad]))}}b.MeasureSpans(aP);for(ae=0,ac=this.data.length;aeap[ae]){ap[ae]=aT*aM.h/aU}if(aT*aM.d/aU>at[ae]){at[ae]=aT*aM.d/aU}}}else{if(aC.HTMLcanStretch("Horizontal")){aT=b.length2em(aT,aA,aM.w);if(aT>aj[ad]){aj[ad]=aT}}}}}if(av[ae][ad].bbox.h>ap[ae]){ap[ae]=av[ae][ad].bbox.h}if(av[ae][ad].bbox.d>at[ae]){at[ae]=av[ae][ad].bbox.d}if(av[ae][ad].bbox.w>aj[ad]){aj[ad]=av[ae][ad].bbox.w}}}var aE=MathJax.Hub.SplitList;var az=aE(I.columnspacing),aR=aE(I.rowspacing),e=aE(I.columnalign),B=aE(I.rowalign),d=aE(I.columnlines),w=aE(I.rowlines),aN=aE(I.columnwidth),U=[];for(ae=0,ac=az.length;aeav.length){aa=av.length}}ai=0;aV=-(aU+aI)+ap[0];for(ae=0,ac=aa-1;ae0.98){R=0.98/af;af=0.98}}else{if(I.width==="auto"){if(af>0.98){R=K/(z+K);ab=z+K}else{ab=z/(1-af)}}else{ab=b.length2em(I.width,aA);for(ae=0,ac=Math.min(ao+1,az.length);ae0.01){if(ag&&ab>z){ab=(ab-z)/ag;for(ae=0,ac=ar.length;aeap[ae]){av[ae][ad].bbox.H=av[ae][ad].bbox.h;av[ae][ad].bbox.h=ap[ae]}if(av[ae][ad].bbox.d>at[ae]){av[ae][ad].bbox.D=av[ae][ad].bbox.d;av[ae][ad].bbox.d=at[ae]}aC.symmetric=aL}}aS=Q.rowalign||this.data[ae].rowalign||B[ae];o=({top:ap[ae]-av[ae][ad].bbox.h,bottom:av[ae][ad].bbox.d-at[ae],center:((ap[ae]-at[ae])-(av[ae][ad].bbox.h-av[ae][ad].bbox.d))/2,baseline:0,axis:0})[aS]||0;aS=(Q.columnalign||U[ae][ad]||e[ad]);b.alignBox(av[ae][ad],aS,S+o)}if(ae *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2])}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[f]});if(e.texClass===a.TEXCLASS.OP){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(e instanceof Array){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g span":{"text-align":o+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);f.math(f.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement("object");m.id="mathplayer";m.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(m);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;ut){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r0;u--){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.5.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var I=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aK=I.width.match(/%$/);var ax=b.createStack(r);var aH=this.HTMLgetScale(),aA=this.HTMLgetMu(r),aB=-1;var ap=[],at=[],aj=[],av=[],au=[],ae,ad,ao=-1,ac,an,X,aF,Q,aC,aP=[],aU;var G=b.FONTDATA.lineH*aH*I.useHeight,N=b.FONTDATA.lineD*aH*I.useHeight;for(ae=0,ac=this.data.length;aeao){ao=ad}au[ad]=b.createStack(b.createBox(ax));aj[ad]=-b.BIGDIMEN}av[ae][ad]=b.createBox(au[ad]);aP.push(aF.data[ad-X].toHTML(av[ae][ad]))}}b.MeasureSpans(aP);for(ae=0,ac=this.data.length;aeap[ae]){ap[ae]=aT*aM.h/aU}if(aT*aM.d/aU>at[ae]){at[ae]=aT*aM.d/aU}}}else{if(aC.HTMLcanStretch("Horizontal")){aT=b.length2em(aT,aA,aM.w);if(aT>aj[ad]){aj[ad]=aT}}}}}if(av[ae][ad].bbox.h>ap[ae]){ap[ae]=av[ae][ad].bbox.h}if(av[ae][ad].bbox.d>at[ae]){at[ae]=av[ae][ad].bbox.d}if(av[ae][ad].bbox.w>aj[ad]){aj[ad]=av[ae][ad].bbox.w}}}var aE=MathJax.Hub.SplitList;var az=aE(I.columnspacing),aR=aE(I.rowspacing),e=aE(I.columnalign),B=aE(I.rowalign),d=aE(I.columnlines),w=aE(I.rowlines),aN=aE(I.columnwidth),U=[];for(ae=0,ac=az.length;aeav.length){aa=av.length}}ai=0;aV=-(aU+aI)+ap[0];for(ae=0,ac=aa-1;ae0.98){R=0.98/af;af=0.98}}else{if(I.width==="auto"){if(af>0.98){R=K/(z+K);ab=z+K}else{ab=z/(1-af)}}else{ab=b.length2em(I.width,aA);for(ae=0,ac=Math.min(ao+1,az.length);ae0.01){if(ag&&ab>z){ab=(ab-z)/ag;for(ae=0,ac=ar.length;aeap[ae]){av[ae][ad].bbox.H=av[ae][ad].bbox.h;av[ae][ad].bbox.h=ap[ae]}if(av[ae][ad].bbox.d>at[ae]){av[ae][ad].bbox.D=av[ae][ad].bbox.d;av[ae][ad].bbox.d=at[ae]}aC.symmetric=aL}}aS=Q.rowalign||this.data[ae].rowalign||B[ae];o=({top:ap[ae]-av[ae][ad].bbox.h,bottom:av[ae][ad].bbox.d-at[ae],center:((ap[ae]-at[ae])-(av[ae][ad].bbox.h-av[ae][ad].bbox.d))/2,baseline:0,axis:0})[aS]||0;aS=(Q.columnalign||U[ae][ad]||e[ad]);b.alignBox(av[ae][ad],aS,S+o)}if(ae *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var r=new Image();r.src=p.button.src}}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var l=this.config.Macros;for(var m in l){if(l.hasOwnProperty(m)){if(typeof(l[m])==="string"){f.macros[m]=["Macro",l[m]]}else{f.macros[m]=["Macro"].concat(l[m])}f.macros[m].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(m,n){this.string=m;this.i=0;this.macroCount=0;var l;if(n){l={};for(var o in n){if(n.hasOwnProperty(o)){l[o]=n[o]}}}this.stack=d.Stack(l,!!n);this.Parse();this.Push(b.stop())},Parse:function(){var m,l;while(this.i=55296&&l<56320){m+=this.string.charAt(this.i++)}if(f.special[m]){this[f.special[m]](m)}else{if(f.letter.test(m)){this.Variable(m)}else{if(f.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(l){return l},ControlSequence:function(o){var l=this.GetCS(),n=this.csFindMacro(l);if(n){if(!(n instanceof Array)){n=[n]}var m=n[0];if(!(m instanceof Function)){m=this[m]}m.apply(this,[o+l].concat(n.slice(1)))}else{if(f.mathchar0mi[l]){this.csMathchar0mi(l,f.mathchar0mi[l])}else{if(f.mathchar0mo[l]){this.csMathchar0mo(l,f.mathchar0mo[l])}else{if(f.mathchar7[l]){this.csMathchar7(l,f.mathchar7[l])}else{if(f.delimiter["\\"+l]!=null){this.csDelimiter(l,f.delimiter["\\"+l])}else{this.csUndefined(o+l)}}}}}},csFindMacro:function(l){return f.macros[l]},csMathchar0mi:function(l,n){var m={mathvariant:h.VARIANT.ITALIC};if(n instanceof Array){m=n[1];n=n[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+n)).With(m)))},csMathchar0mo:function(l,n){var m={stretchy:false};if(n instanceof Array){m=n[1];m.stretchy=false;n=n[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+n)).With(m)))},csMathchar7:function(l,n){var m={mathvariant:h.VARIANT.NORMAL};if(n instanceof Array){m=n[1];n=n[0]}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+n)).With(m)))},csDelimiter:function(l,n){var m={};if(n instanceof Array){m=n[1];n=n[0]}if(n.length===4){n=h.entity("#x"+n)}else{n=h.chars(n)}this.Push(this.mmlToken(h.mo(n).With({fence:false,stretchy:false}).With(m)))},csUndefined:function(l){d.Error(["UndefinedControlSequence","Undefined control sequence %1",l])},Variable:function(m){var l={};if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(m)).With(l)))},Number:function(o){var l,m=this.string.slice(this.i-1).match(f.number);if(m){l=h.mn(m[0].replace(/[{}]/g,""));this.i+=m[0].length-1}else{l=h.mo(h.chars(o))}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(l))},Open:function(l){this.Push(b.open())},Close:function(l){this.Push(b.close())},Tilde:function(l){this.Push(h.mtext(h.chars(g)))},Space:function(l){},Superscript:function(q){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var p,n,o=this.stack.Top();if(o.type==="prime"){n=o.data[0];p=o.data[1];this.stack.Pop()}else{n=this.stack.Prev();if(!n){n=h.mi("")}}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}var m=n.movesupsub,l=n.sup;if((n.type==="msubsup"&&n.data[n.sup])||(n.type==="munderover"&&n.data[n.over]&&!n.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(n.type!=="msubsup"){if(m){if(n.type!=="munderover"||n.data[n.over]){if(n.movablelimits&&n.isa(h.mi)){n=this.mi2mo(n)}n=h.munderover(n,null,null).With({movesupsub:true})}l=n.over}else{n=h.msubsup(n,null,null);l=n.sup}}this.Push(b.subsup(n).With({position:l,primes:p,movesupsub:m}))},Subscript:function(q){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var p,n,o=this.stack.Top();if(o.type==="prime"){n=o.data[0];p=o.data[1];this.stack.Pop()}else{n=this.stack.Prev();if(!n){n=h.mi("")}}if(n.isEmbellishedWrapper){n=n.data[0].data[0]}var m=n.movesupsub,l=n.sub;if((n.type==="msubsup"&&n.data[n.sub])||(n.type==="munderover"&&n.data[n.under]&&!n.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(n.type!=="msubsup"){if(m){if(n.type!=="munderover"||n.data[n.under]){if(n.movablelimits&&n.isa(h.mi)){n=this.mi2mo(n)}n=h.munderover(n,null,null).With({movesupsub:true})}l=n.under}else{n=h.msubsup(n,null,null);l=n.sub}}this.Push(b.subsup(n).With({position:l,primes:p,movesupsub:m}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}return m},Comment:function(l){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,u,q,t,n,l,v,s){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(t||"1em")}});if(v){p.isCases=true}if(s){p.isNumbered=true;p.arraydef.side=s}if(o||u){p.open=o;p.close=u}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(pd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}}this.Push(m)},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}else{if(l){q.arraydef.displaystyle=false}}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline -1"}else{if(l==="c"){m.arraydef.align="center"}else{if(l){m.arraydef.align=l}}}}return m},convertDelimiter:function(l){if(l){l=f.delimiter[l]}if(l==null){return null}if(l instanceof Array){l=l[0]}if(l.length===4){l=String.fromCharCode(parseInt(l,16))}return l},trimSpaces:function(l){if(typeof(l)!="string"){return l}return l.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var l=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(l){this.i+=l[1].length;return l[1]}else{this.i++;return" "}},GetArgument:function(m,n){switch(this.GetNext()){case"":if(!n){d.Error(["MissingArgFor","Missing argument for %1",m])}return null;case"}":if(!n){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var l=++this.i,o=1;while(this.i1){n=[h.mrow.apply(h,n)]}}return n},InternalText:function(m,l){m=m.replace(/^\s+/,g).replace(/\s+$/,g);return h.mtext(h.chars(m)).With(l)},SubstituteArgs:function(m,l){var p="";var o="";var q;var n=0;while(nm.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}o=this.AddArgs(this.AddArgs(o,p),m[q-1]);p=""}}else{p+=q}}}return this.AddArgs(o,p)},AddArgs:function(m,l){if(l.match(/^[a-z]/i)&&m.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){m+=" "}if(m.length+l.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return m+l}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:k,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(l){var m,n=false,p=MathJax.HTML.getScript(l);var r=(l.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var q={math:p,display:r,script:l};var s=this.prefilterHooks.Execute(q);if(s){return s}p=q.math;try{m=d.Parse(p).mml()}catch(o){if(!o.texError){throw o}m=this.formatError(o,p,r,l);n=true}if(m.isa(h.mtable)&&m.displaystyle==="inherit"){m.displaystyle=r}if(m.inferred){m=h.apply(MathJax.ElementJax,m.data)}else{m=h(m)}if(r){m.root.display="block"}if(n){m.texError=true}q.math=m;return this.postfilterHooks.Execute(q)||q.math},prefilterMath:function(m,n,l){return m},postfilterMath:function(m,n,l){this.combineRelations(m.root);return m},formatError:function(o,n,p,l){var m=o.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",m,n,p,l]);return h.Error(m)},Error:function(l){if(l instanceof Array){l=j.apply(j,l)}throw c.Insert(Error(l),{texError:true})},Macro:function(l,m,n){f.macros[l]=["Macro"].concat([].slice.call(arguments,1));f.macros[l].isUser=true},fenced:function(n,m,o){var l=h.mrow().With({open:n,close:o,texClass:h.TEXCLASS.INNER});l.Append(h.mo(n).With({fence:true,stretchy:true,texClass:h.TEXCLASS.OPEN}));if(m.type==="mrow"){l.Append.apply(l,m.data)}else{l.Append(m)}l.Append(h.mo(o).With({fence:true,stretchy:true,texClass:h.TEXCLASS.CLOSE}));return l},fixedFence:function(n,m,o){var l=h.mrow().With({open:n,close:o,texClass:h.TEXCLASS.ORD});if(n){l.Append(this.mathPalette(n,"l"))}if(m.type==="mrow"){l.Append.apply(l,m.data)}else{l.Append(m)}if(o){l.Append(this.mathPalette(o,"r"))}return l},mathPalette:function(o,m){if(o==="{"||o==="}"){o="\\"+o}var n="{\\bigg"+m+" "+o+"}",l="{\\big"+m+" "+o+"}";return d.Parse("\\mathchoice"+n+l+l+l).mml()},combineRelations:function(p){var q,l,o,n;for(q=0,l=p.data.length;q0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i.With({subsupOK:true}))},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]){return i}g.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",h])},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h).With({id:a.formatID(i.tagID)})}},getTag:function(){var l=this.global,j=l.tag;l.tagged=true;if(l.label){if(a.useLabelIds){j.id=a.formatID(l.label)}f.eqlabels[l.label]={tag:l.tagID,id:j.id}}if(document.getElementById(j.id)||f.IDs[j.id]||f.eqIDs[j.id]){var k=0,h;do{k++;h=j.id+"_"+k}while(document.getElementById(h)||f.IDs[h]||f.eqIDs[h]);j.id=h;if(l.label){f.eqlabels[l.label].id=h}}f.eqIDs[j.id]=1;this.clearTag();return j},clearTag:function(){var h=this.global;delete h.tag;delete h.tagID;delete h.label},fixInitialMO:function(k){for(var j=0,h=k.length;j=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.5.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var I=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aK=I.width.match(/%$/);var ax=b.createStack(r);var aH=this.HTMLgetScale(),aA=this.HTMLgetMu(r),aB=-1;var ap=[],at=[],aj=[],av=[],au=[],ae,ad,ao=-1,ac,an,X,aF,Q,aC,aP=[],aU;var G=b.FONTDATA.lineH*aH*I.useHeight,N=b.FONTDATA.lineD*aH*I.useHeight;for(ae=0,ac=this.data.length;aeao){ao=ad}au[ad]=b.createStack(b.createBox(ax));aj[ad]=-b.BIGDIMEN}av[ae][ad]=b.createBox(au[ad]);aP.push(aF.data[ad-X].toHTML(av[ae][ad]))}}b.MeasureSpans(aP);for(ae=0,ac=this.data.length;aeap[ae]){ap[ae]=aT*aM.h/aU}if(aT*aM.d/aU>at[ae]){at[ae]=aT*aM.d/aU}}}else{if(aC.HTMLcanStretch("Horizontal")){aT=b.length2em(aT,aA,aM.w);if(aT>aj[ad]){aj[ad]=aT}}}}}if(av[ae][ad].bbox.h>ap[ae]){ap[ae]=av[ae][ad].bbox.h}if(av[ae][ad].bbox.d>at[ae]){at[ae]=av[ae][ad].bbox.d}if(av[ae][ad].bbox.w>aj[ad]){aj[ad]=av[ae][ad].bbox.w}}}var aE=MathJax.Hub.SplitList;var az=aE(I.columnspacing),aR=aE(I.rowspacing),e=aE(I.columnalign),B=aE(I.rowalign),d=aE(I.columnlines),w=aE(I.rowlines),aN=aE(I.columnwidth),U=[];for(ae=0,ac=az.length;aeav.length){aa=av.length}}ai=0;aV=-(aU+aI)+ap[0];for(ae=0,ac=aa-1;ae0.98){R=0.98/af;af=0.98}}else{if(I.width==="auto"){if(af>0.98){R=K/(z+K);ab=z+K}else{ab=z/(1-af)}}else{ab=b.length2em(I.width,aA);for(ae=0,ac=Math.min(ao+1,az.length);ae0.01){if(ag&&ab>z){ab=(ab-z)/ag;for(ae=0,ac=ar.length;aeap[ae]){av[ae][ad].bbox.H=av[ae][ad].bbox.h;av[ae][ad].bbox.h=ap[ae]}if(av[ae][ad].bbox.d>at[ae]){av[ae][ad].bbox.D=av[ae][ad].bbox.d;av[ae][ad].bbox.d=at[ae]}aC.symmetric=aL}}aS=Q.rowalign||this.data[ae].rowalign||B[ae];o=({top:ap[ae]-av[ae][ad].bbox.h,bottom:av[ae][ad].bbox.d-at[ae],center:((ap[ae]-at[ae])-(av[ae][ad].bbox.h-av[ae][ad].bbox.d))/2,baseline:0,axis:0})[aS]||0;aS=(Q.columnalign||U[ae][ad]||e[ad]);b.alignBox(av[ae][ad],aS,S+o)}if(ae *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var r=new Image();r.src=p.button.src}}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.5.0",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2])}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[f]});if(e.texClass===a.TEXCLASS.OP){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(e instanceof Array){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g=ad-1){this.lastChild=ag}this.childNodes[af]=ag;ag.nextSibling=ae.nextSibling;ae.nextSibling=ae.parent=null;return ae},hasChildNodes:function(i){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var i=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ad=i.apply(this,arguments)||this;ad.childNodes=ad.data;ad.nodeName=ad.type;return ad},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}var ae=arguments;if(ag.isa(X)){ae=ag.childNodes;ag.data=ag.childNodes=[];ag.firstChild=ag.lastChild=null}for(var af=0,ad=ae.length;af=ad-1){this.lastChild=ag}this.SetData(af,ag);ag.nextSibling=ae.nextSibling;ae.nextSibling=ae.parent=null;return ae},hasChildNodes:function(ad){return(this.childNodes.length>0)},setAttribute:function(ad,ae){this[ad]=ae}})};var Q={};var e={getElementById:true,createElementNS:function(ad,i){var ae=g[i]();if(i==="mo"&&ac.config.useMathMLspacing){ae.useMMLspacing=128}return ae},createTextNode:function(i){return g.chars(i).With({nodeValue:i})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var Z;var C="blue";var aa="serif";var p=true;var v=true;var d=".";var f=true;var m=(J.appName.slice(0,9)=="Microsoft");function E(i){if(m){return e.createElement(i)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",i)}}var W="http://www.w3.org/1998/Math/MathML";function P(i){if(m){return e.createElement("m:"+i)}else{return e.createElementNS(W,i)}}function O(i,ae){var ad;if(m){ad=e.createElement("m:"+i)}else{ad=e.createElementNS(W,i)}if(ae){ad.appendChild(ae)}return ad}function u(i,ad){z=z.concat([{input:i,tag:"mo",output:ad,tex:null,ttype:V}]);z.sort(T);for(Z=0;Z",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:h},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:n},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:j},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:j},{input:"^",tag:"msup",output:"^",tex:null,ttype:j},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},l,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ad,i){if(ad.input>i.input){return 1}else{return -1}}var S=[];function o(){var ae=[],ad;for(ad=0;ad>1;if(ae[ad]=S[ad]}s=y;if(ah!=""){y=z[ag].ttype;return z[ag]}y=c;ad=1;am=aj.slice(0,1);var ak=true;while("0"<=am&&am<="9"&&ad<=aj.length){am=aj.slice(ad,ad+1);ad++}if(am==d){am=aj.slice(ad,ad+1);if("0"<=am&&am<="9"){ak=false;ad++;while("0"<=am&&am<="9"&&ad<=aj.length){am=aj.slice(ad,ad+1);ad++}}}if((ak&&ad>1)||ad>2){am=aj.slice(0,ad-1);al="mn"}else{ad=2;am=aj.slice(0,1);al=(("A">am||am>"Z")&&("a">am||am>"z")?"mo":"mi")}if(am=="-"&&s==j){y=j;return{input:am,tag:al,output:am,ttype:A,func:true}}return{input:am,tag:al,output:am,ttype:c}}function R(ad){var i;if(!ad.hasChildNodes()){return}if(ad.firstChild.hasChildNodes()&&(ad.nodeName=="mrow"||ad.nodeName=="M:MROW")){i=ad.firstChild.firstChild.nodeValue;if(i=="("||i=="["||i=="{"){ad.removeChild(ad.firstChild)}}if(ad.lastChild.hasChildNodes()&&(ad.nodeName=="mrow"||ad.nodeName=="M:MROW")){i=ad.lastChild.firstChild.nodeValue;if(i==")"||i=="]"||i=="}"){ad.removeChild(ad.lastChild)}}}var F,s,y;function G(aj){var af,ae,am,ah,al,ai=e.createDocumentFragment();aj=q(aj,0);af=k(aj);if(af==null||af.ttype==h&&F>0){return[null,aj]}if(af.ttype==V){aj=af.output+q(aj,af.input.length);af=k(aj)}switch(af.ttype){case L:case c:aj=q(aj,af.input.length);return[O(af.tag,e.createTextNode(af.output)),aj];case b:F++;aj=q(aj,af.input.length);am=r(aj,true);F--;if(typeof af.invisible=="boolean"&&af.invisible){ae=O("mrow",am[0])}else{ae=O("mo",e.createTextNode(af.output));ae=O("mrow",ae);ae.appendChild(am[0])}return[ae,am[1]];case Y:if(af!=l){aj=q(aj,af.input.length)}if(aj.charAt(0)=="{"){ah=aj.indexOf("}")}else{if(aj.charAt(0)=="("){ah=aj.indexOf(")")}else{if(aj.charAt(0)=="["){ah=aj.indexOf("]")}else{if(af==l){ah=aj.slice(1).indexOf('"')+1}else{ah=0}}}}if(ah==-1){ah=aj.length}al=aj.slice(1,ah);if(al.charAt(0)==" "){ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae)}ai.appendChild(O(af.tag,e.createTextNode(al)));if(al.charAt(al.length-1)==" "){ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae)}aj=q(aj,ah+1);return[O("mrow",ai),aj];case K:case A:aj=q(aj,af.input.length);am=G(aj);if(am[0]==null){return[O(af.tag,e.createTextNode(af.output)),aj]}if(typeof af.func=="boolean"&&af.func){al=aj.charAt(0);if(al=="^"||al=="_"||al=="/"||al=="|"||al==","||(af.input.length==1&&af.input.match(/\w/)&&al!="(")){return[O(af.tag,e.createTextNode(af.output)),aj]}else{ae=O("mrow",O(af.tag,e.createTextNode(af.output)));ae.appendChild(am[0]);return[ae,am[1]]}}R(am[0]);if(af.input=="sqrt"){return[O(af.tag,am[0]),am[1]]}else{if(typeof af.rewriteleftright!="undefined"){ae=O("mrow",O("mo",e.createTextNode(af.rewriteleftright[0])));ae.appendChild(am[0]);ae.appendChild(O("mo",e.createTextNode(af.rewriteleftright[1])));return[ae,am[1]]}else{if(af.input=="cancel"){ae=O(af.tag,am[0]);ae.setAttribute("notation","updiagonalstrike");return[ae,am[1]]}else{if(typeof af.acc=="boolean"&&af.acc){ae=O(af.tag,am[0]);ae.appendChild(O("mo",e.createTextNode(af.output)));return[ae,am[1]]}else{if(!m&&typeof af.codes!="undefined"){for(ah=0;ah64&&al.charCodeAt(ag)<91){ak=ak+af.codes[al.charCodeAt(ag)-65]}else{if(al.charCodeAt(ag)>96&&al.charCodeAt(ag)<123){ak=ak+af.codes[al.charCodeAt(ag)-71]}else{ak=ak+al.charAt(ag)}}}if(am[0].nodeName=="mi"){am[0]=O("mo").appendChild(e.createTextNode(ak))}else{am[0].replaceChild(O("mo").appendChild(e.createTextNode(ak)),am[0].childNodes[ah])}}}}ae=O(af.tag,am[0]);ae.setAttribute(af.atname,af.atval);return[ae,am[1]]}}}}case U:aj=q(aj,af.input.length);am=G(aj);if(am[0]==null){return[O("mo",e.createTextNode(af.input)),aj]}R(am[0]);var ad=G(am[1]);if(ad[0]==null){return[O("mo",e.createTextNode(af.input)),aj]}R(ad[0]);if(af.input=="color"){if(aj.charAt(0)=="{"){ah=aj.indexOf("}")}else{if(aj.charAt(0)=="("){ah=aj.indexOf(")")}else{if(aj.charAt(0)=="["){ah=aj.indexOf("]")}}}al=aj.slice(1,ah);ae=O(af.tag,ad[0]);ae.setAttribute("mathcolor",al);return[ae,ad[1]]}if(af.input=="root"||af.input=="stackrel"){ai.appendChild(ad[0])}ai.appendChild(am[0]);if(af.input=="frac"){ai.appendChild(ad[0])}return[O(af.tag,ai),ad[1]];case j:aj=q(aj,af.input.length);return[O("mo",e.createTextNode(af.output)),aj];case a:aj=q(aj,af.input.length);ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae);ai.appendChild(O(af.tag,e.createTextNode(af.output)));ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae);return[O("mrow",ai),aj];case n:F++;aj=q(aj,af.input.length);am=r(aj,false);F--;al="";if(am[0].lastChild!=null){al=am[0].lastChild.firstChild.nodeValue}if(al=="|"){ae=O("mo",e.createTextNode(af.output));ae=O("mrow",ae);ae.appendChild(am[0]);return[ae,am[1]]}else{ae=O("mo",e.createTextNode("\u2223"));ae=O("mrow",ae);return[ae,aj]}default:aj=q(aj,af.input.length);return[O(af.tag,e.createTextNode(af.output)),aj]}}function t(ai){var ag,aj,ah,af,i,ae;ai=q(ai,0);aj=k(ai);i=G(ai);af=i[0];ai=i[1];ag=k(ai);if(ag.ttype==j&&ag.input!="/"){ai=q(ai,ag.input.length);i=G(ai);if(i[0]==null){i[0]=O("mo",e.createTextNode("\u25A1"))}else{R(i[0])}ai=i[1];ae=(aj.ttype==L||aj.ttype==K);if(ag.input=="_"){ah=k(ai);if(ah.input=="^"){ai=q(ai,ah.input.length);var ad=G(ai);R(ad[0]);ai=ad[1];af=O((ae?"munderover":"msubsup"),af);af.appendChild(i[0]);af.appendChild(ad[0]);af=O("mrow",af)}else{af=O((ae?"munder":"msub"),af);af.appendChild(i[0])}}else{if(ag.input=="^"&&ae){af=O("mover",af);af.appendChild(i[0])}else{af=O(ag.tag,af);af.appendChild(i[0])}}if(typeof aj.func!="undefined"&&aj.func){ah=k(ai);if(ah.ttype!=j&&ah.ttype!=h){i=t(ai);af=O("mrow",af);af.appendChild(i[0]);ai=i[1]}}}return[af,ai]}function r(al,ak){var ap,am,ah,at,ai=e.createDocumentFragment();do{al=q(al,0);ah=t(al);am=ah[0];al=ah[1];ap=k(al);if(ap.ttype==j&&ap.input=="/"){al=q(al,ap.input.length);ah=t(al);if(ah[0]==null){ah[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ah[0])}al=ah[1];R(am);am=O(ap.tag,am);am.appendChild(ah[0]);ai.appendChild(am);ap=k(al)}else{if(am!=undefined){ai.appendChild(am)}}}while((ap.ttype!=h&&(ap.ttype!=n||ak)||F==0)&&ap!=null&&ap.output!="");if(ap.ttype==h||ap.ttype==n){var au=ai.childNodes.length;if(au>0&&ai.childNodes[au-1].nodeName=="mrow"){var aw=ai.childNodes[au-1].lastChild.firstChild.nodeValue;if(aw==")"||aw=="]"){var ae=ai.childNodes[au-1].firstChild.firstChild.nodeValue;if(ae=="("&&aw==")"&&ap.output!="}"||ae=="["&&aw=="]"){var af=[];var aq=true;var an=ai.childNodes.length;for(at=0;aq&&at1){aq=af[at].length==af[at-2].length}}aq=aq&&(af.length>1||af[0].length>0);if(aq){var ag,ad,aj,ao,av=e.createDocumentFragment();for(at=0;at2){ai.removeChild(ai.firstChild);ai.removeChild(ai.firstChild)}av.appendChild(O("mtr",ag))}am=O("mtable",av);if(typeof ap.invisible=="boolean"&&ap.invisible){am.setAttribute("columnalign","left")}ai.replaceChild(am,ai.firstChild)}}}}al=q(al,ap.input.length);if(typeof ap.invisible!="boolean"||!ap.invisible){am=O("mo",e.createTextNode(ap.output));ai.appendChild(am)}}return[ai,al]}function M(ae,ad){var af,i;F=0;ae=ae.replace(/ /g,"");ae=ae.replace(/>/g,">");ae=ae.replace(/</g,"<");ae=ae.replace(/(Sin|Cos|Tan|Arcsin|Arccos|Arctan|Sinh|Cosh|Tanh|Cot|Sec|Csc|Log|Ln|Abs)/g,function(ag){return ag.toLowerCase()});af=r(ae.replace(/^\s+/g,""),false)[0];i=O("mstyle",af);if(C!=""){i.setAttribute("mathcolor",C)}if(aa!=""){i.setAttribute("fontfamily",aa)}if(p){i.setAttribute("displaystyle","true")}i=O("math",i);if(v){i.setAttribute("title",ae.replace(/\s+/g," "))}return i}v=false;aa="";C="";(function(){for(var ae=0,ad=z.length;ae span":{"text-align":o+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);f.math(f.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement("object");m.id="mathplayer";m.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(m);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;ut){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r0;u--){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.5.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var I=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aK=I.width.match(/%$/);var ax=b.createStack(r);var aH=this.HTMLgetScale(),aA=this.HTMLgetMu(r),aB=-1;var ap=[],at=[],aj=[],av=[],au=[],ae,ad,ao=-1,ac,an,X,aF,Q,aC,aP=[],aU;var G=b.FONTDATA.lineH*aH*I.useHeight,N=b.FONTDATA.lineD*aH*I.useHeight;for(ae=0,ac=this.data.length;aeao){ao=ad}au[ad]=b.createStack(b.createBox(ax));aj[ad]=-b.BIGDIMEN}av[ae][ad]=b.createBox(au[ad]);aP.push(aF.data[ad-X].toHTML(av[ae][ad]))}}b.MeasureSpans(aP);for(ae=0,ac=this.data.length;aeap[ae]){ap[ae]=aT*aM.h/aU}if(aT*aM.d/aU>at[ae]){at[ae]=aT*aM.d/aU}}}else{if(aC.HTMLcanStretch("Horizontal")){aT=b.length2em(aT,aA,aM.w);if(aT>aj[ad]){aj[ad]=aT}}}}}if(av[ae][ad].bbox.h>ap[ae]){ap[ae]=av[ae][ad].bbox.h}if(av[ae][ad].bbox.d>at[ae]){at[ae]=av[ae][ad].bbox.d}if(av[ae][ad].bbox.w>aj[ad]){aj[ad]=av[ae][ad].bbox.w}}}var aE=MathJax.Hub.SplitList;var az=aE(I.columnspacing),aR=aE(I.rowspacing),e=aE(I.columnalign),B=aE(I.rowalign),d=aE(I.columnlines),w=aE(I.rowlines),aN=aE(I.columnwidth),U=[];for(ae=0,ac=az.length;aeav.length){aa=av.length}}ai=0;aV=-(aU+aI)+ap[0];for(ae=0,ac=aa-1;ae0.98){R=0.98/af;af=0.98}}else{if(I.width==="auto"){if(af>0.98){R=K/(z+K);ab=z+K}else{ab=z/(1-af)}}else{ab=b.length2em(I.width,aA);for(ae=0,ac=Math.min(ao+1,az.length);ae0.01){if(ag&&ab>z){ab=(ab-z)/ag;for(ae=0,ac=ar.length;aeap[ae]){av[ae][ad].bbox.H=av[ae][ad].bbox.h;av[ae][ad].bbox.h=ap[ae]}if(av[ae][ad].bbox.d>at[ae]){av[ae][ad].bbox.D=av[ae][ad].bbox.d;av[ae][ad].bbox.d=at[ae]}aC.symmetric=aL}}aS=Q.rowalign||this.data[ae].rowalign||B[ae];o=({top:ap[ae]-av[ae][ad].bbox.h,bottom:av[ae][ad].bbox.d-at[ae],center:((ap[ae]-at[ae])-(av[ae][ad].bbox.h-av[ae][ad].bbox.d))/2,baseline:0,axis:0})[aS]||0;aS=(Q.columnalign||U[ae][ad]||e[ad]);b.alignBox(av[ae][ad],aS,S+o)}if(ae *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.5.0",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); -MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;rk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]); +(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;qk){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em0&&(n+p)*this.em0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(uC.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&tB){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&ou){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;ll.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lwl.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.tw){l.tw=m.tw}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){l.exactW=m.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}this.HTMLaddAttributes(k);return k},HTMLaddAttributes:function(n){if(this.attrNames){var s=this.attrNames,o=g.nocopyAttributes,r=b.config.ignoreMMLattributes;var p=(this.type==="mstyle"?g.math.prototype.defaults:this.defaults);for(var l=0,k=s.length;l0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){this.HTMLgetScale();p=d.length2em(p,this.scale)/(o.scale||1)*this.mscale;if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){if(this.scale){return this.scale*this.mscale}var m=1,k=this.getValues("scriptlevel","fontsize");k.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}n.bbox=null;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(d.config.scale/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}delete n.bbox;var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lp.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic/this.mscale);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;lv.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var n=m.data[m.over],l=m.data[m.under];if(n&&this===n.CoreMO()&&m.Get("accent")){p=d.FONTDATA.REMAPACCENT[p]||p}else{if(l&&this===l.CoreMO()&&m.Get("accentunder")){p=d.FONTDATA.REMAPACCENTUNDER[p]||p}}}p=d.FONTDATA.DELIMITERS[p.charCodeAt(0)];var k=(p&&p.dir===o.substr(0,1));this.forceStretch=(k&&(this.Get("minsize",true)||this.Get("maxsize",true)));return k},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var l=this.HTMLgetScale(),k=d.TeX.axis_height*l;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));if(q!=r.minsize){q=[Math.max(q*d.TeX.delimiterfactor/1000,q-d.TeX.delimitershortfall),q]}p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){var p=this.Get("mathvariant");if(p==="monospace"){o.className+=" MJX-monospace"}else{if(p.match(/sans-serif/)){o.className+=" MJX-sans-serif"}}n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;ld.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,this.scale)*this.mscale,A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(zy){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||oK){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;MK){K=w.bbox.w}}}var E=d.TeX.rule_thickness*this.mscale,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;MK){L.bbox.skew+=(K-w.bbox.w-v)/2}}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m=N;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&I==null&&C==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n[0].scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.annotation.Augment({toHTML:function(k){return this.HTMLcreateSpan(k)}});g.math.Augment({toHTML:function(A,x,n){var q,s,t,m;if(!n||n===d.PHASE.I){var y=d.addElement(A,"nobr",{isMathJax:true});A=this.HTMLcreateSpan(y);var k=this.Get("alttext");if(k&&!A.getAttribute("aria-label")){A.setAttribute("aria-label",k)}if(!A.getAttribute("role")){A.setAttribute("role","math")}q=d.createStack(A);s=d.createBox(q);q.style.fontSize=y.parentNode.style.fontSize;y.parentNode.style.fontSize="";if(this.data[0]!=null){g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;if(String(b.config.displayIndent).match(/^0($|[a-z%])/i)){g.mbase.prototype.displayIndent="0"}t=this.data[0].toHTML(s);t.bbox.exactW=false}}else{A=A.firstChild.firstChild;if(this.href){A=A.firstChild}q=A.firstChild;if(q.style.position!=="relative"){q=q.nextSibling}s=q.firstChild;t=s.firstChild}m=((!n||n===d.PHASE.II)?d.Measured(t,s):t);if(!n||n===d.PHASE.III){d.placeBox(s,0,0);A.style.width=d.Em(Math.max(0,Math.round(m.bbox.w*this.em)+0.25)/d.outerEm);A.style.display="inline-block";var w=1/d.em,C=d.em/d.outerEm;d.em/=C;A.bbox.h*=C;A.bbox.d*=C;A.bbox.w*=C;A.bbox.lw*=C;A.bbox.rw*=C;if(A.bbox.H){A.bbox.H*=C}if(A.bbox.D){A.bbox.D*=C}if(m&&m.bbox.width!=null){A.style.minWidth=(m.bbox.minWidth||A.style.width);A.style.width=m.bbox.width;s.style.width=q.style.width="100%"}var z=this.HTMLhandleColor(A);if(m){d.createRule(A,(m.bbox.h+w)*C,(m.bbox.d+w)*C,0)}if(!this.isMultiline&&this.Get("display")==="block"&&A.bbox.width==null){var l=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(l.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){l.indentalign=l.indentalignfirst}if(l.indentalign===g.INDENTALIGN.AUTO){l.indentalign=this.displayAlign}if(l.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){l.indentshift=l.indentshiftfirst}if(l.indentshift==="auto"){l.indentshift="0"}var B=d.length2em(l.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var u=d.length2em(this.displayIndent,1,d.scale*d.cwidth);B+=(l.indentalign===g.INDENTALIGN.RIGHT?-u:u)}x.style.textAlign=l.indentalign;if(B){B*=d.em/d.outerEm;b.Insert(A.style,({left:{marginLeft:d.Em(B)},right:{marginLeft:d.Em(Math.max(0,A.bbox.w+B)),marginRight:d.Em(-B)},center:{marginLeft:d.Em(B),marginRight:d.Em(-B)}})[l.indentalign]);if(z){var r=parseFloat(z.style.marginLeft||"0")+B,o=parseFloat(z.style.marginRight||"0")-B;z.style.marginLeft=d.Em(r);z.style.marginRight=d.Em(o+(l.indentalign==="right"?Math.min(0,A.bbox.w+B)-A.bbox.w:0));if(d.msieColorBug&&l.indentalign==="right"){if(parseFloat(z.style.marginLeft)>0){var v=MathJax.HTML.addElement(z.parentNode,"span");v.style.marginLeft=d.Em(o+Math.min(0,A.bbox.w+B));z.nextSibling.style.marginRight="0em"}z.nextSibling.style.marginLeft="0em";z.style.marginRight=z.style.marginLeft="0em"}}}}}return A},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(o,m,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(o);var p=d.createBox(k);var r=this.data[0].toHTML(p);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(p,m,q),p)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(p,m),p)}else{d.Measured(r,p)}}var l=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(p,0,l-(p.bbox.h+p.bbox.d)/2+p.bbox.d)}else{var n=this.data[0].toHTML(o,m,q);if(q!=null){n=this.data[0].HTMLstretchV(p,m,q)}else{if(m!=null){n=this.data[0].HTMLstretchH(p,m)}}o.bbox=n.bbox}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:(o<8),msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,msieRuleBug:(o<7),cloneNodeBug:(m&&k.version==="8.0"),msieItalicWidthBug:true,initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:(o<9),msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:!l.versionAtLeast("20.0"),AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},Em:((p.webkit||0)>=538?d.EmRounded:d.Em),rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,FontFaceBug:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:-0.02,AccentBug:true,AdjustSurd:true,FontFaceBug:k.versionAtLeast("32.0"),negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);