body, div, h1, h2, h3, h4, h5, h6, p, ul, ol, li, dl, dt, dd, img, form, fieldset, input, textarea, blockquote, label {	margin:0; padding:0; border:0; }
body { display:block; border:none; text-align:left; line-height:1.6em; font-family:serif; font-size:11pt; hyphens:auto; width:100%; height:auto; }
.fullpage {	max-width:100%; }
.main { margin:0 1% 0 1%; }
footer { margin-top: 4em; }
div.copyright { display:inline; }
p, .p  { text-align:left; }
p.no-indent, .p.no-indent { text-indent:0em; }
p.next, p + p , .p  + .p, .p.next  { margin:0em; text-indent:2em; }
sup.note { color:#7c2529; }
sup { position:relative; top:-.4em; font-size:.8em; vertical-align:initial; }
sub { position:relative; bottom:-.4em; font-size:.8em; vertical-align:initial; }
u { border-bottom:2px solid #aaa; text-decoration:none; }
.fn-wrap { margin-left:-0.2em; }
.bullet { list-style-type:disc; }
.roman-lower { list-style-type:lower-roman;}
.alpha-lower { list-style-type:lower-alpha; }
.pipe {	color:#bbb;	font-weight:normal; }
.pipe.dark { color:#666; }
.italic, i { font-style:italic; }
.bold, b { font-weight:bold; }
.doilink { hyphens:none; -moz-hyphens:none; -ms-hyphens:none; -webkit-hyphens:none; word-break:keep-all; }
.index-link { color:#253776; text-decoration: underline; display:inline; }
.backlinks { display:inline; font-size:.9em; }
.highlight { background-color:#e1bb4c; }
.highlight1 { background-color:#d3d3d3; }
.highlight2 { background-color:#b9b9b9; }
.highlight3 { background-color:#b9b9b9; }
a[name] { display:initial; position:initial; }
a { color:#7c2529; text-decoration:none; cursor:pointer; }
a:hover { border-bottom:.25em solid #e1bb4b; }
a:active { border:0; }
a.shortnote:hover {	border-bottom:0; }
.pagenumber { visibility:collapse; }
.pagenumber-invisible, .word-invisible { visibility:collapse; }
.pagenumbers { font-size:0.95em; }
.notenum, .table-fn { color:#9e2330; font-weight:bold; position:relative; top:-.5em; font-size:.8em; letter-spacing:.05em; margin-right:-.2em; }
.notenum + .notenum:before { content:","; } 
h1 .notenum { background-color:#fff; }
pre .notenum {
	font-family: Roboto, Verdana, "Arial unicode ms", sans serif;
    font-size: 0.8em;
    top: -.2em;
    padding: 0 0.1em;	
}
.space { display:inline-block; width:.33em; }
.small-caps, .sc { text-transform:uppercase; font-size:.8em; letter-spacing:.05em; }
.phonetic, .math, .greek { font-family:"Arial Unicode MS", "Times New Roman"; }
.samedash { letter-spacing:-.15em; font-stretch:expanded; }
.grammar-label { display:block; text-align:right; float:right; text-indent:0; }
blockquote, q { font-size:.95em; padding:1em 0 1em 4em; }
blockquote p.next, q p.next { text-indent:0; padding-top:.5em; }
blockquote p, q p { display:inline-block; }
blockquote.next, q.next { padding-top:0em; }
blockquote + blockquote, q + q { padding-top:0; }
li p + p { text-indent:0; }
blockquote p + p, q p + p { text-indent:0; padding-top:0.5em; }
blockquote .list p, q .list p { display:block; }
blockquote .verse, q .verse { padding-left:0; }
q::before { content:""; }
q::after { content:""; }
.verse { padding-bottom:.5em; padding-left:4em; }
.verse-line { display:block; text-indent:0; position:relative; text-align:left; }
.linenumber { left:-2em; position:relative; }
.terms { overflow:auto; border:2px solid black; padding:5px; font-size:10pt; }
.def-term { display:inline-block; min-width:5em; padding-right:1em; }
.def-def { display:inline-block; }
pre { font-family:Lucida Console,Courier New,Courier; font-size:0.8em; line-height:1.2em; overflow-x:auto; background-color:#eee; padding:10px; tab-size:4; }
pre.dialogue { font-family: Lucida Console,Courier New,Courier; font-size: 0.8em; line-height: 1.2em; overflow-x:auto; background-color: #fff; padding: 10px; padding-top:.7em; margin-top:0; tab-size:4; }
pre .inline-fn, .inline-paragraph {
    font-family: Roboto, Verdana, "Arial unicode ms", sans serif;
    overflow-x:visible;
}
code { color:#253776; white-space:pre-wrap; font-size:.9em; overflow-x:auto; }
p > code { font-size:1em; }
code u { text-decoration:underline; border-bottom:none; }
span.attrib, span.source-label { text-align:left; float:none; display:inline; padding-left:0.1em; }
p.attrib { display:block; text-align:right; float:none; text-indent:0; }
.person-block, .publisher  { line-height:2em; }
.publisher { page-break-after:always; margin-top: 4em;}
h1 { font-family: sans-serif; padding:0 1% 0 4em; text-align:left; line-height:1.25em; hyphens:none; }
h2, h, h4, h5 { font-family: sans-serif; }
h1.title, h1.subtitle, h2.subtitle, h1.review, h1.small { max-width:100%; font-size:1.4em; font-weight:bold; line-height:1.4em; transition:none; padding-right:2em; padding-bottom:2em; background-color:white; color:#253776; display:block; }
h1.title .chapter-label { text-transform: uppercase; letter-spacing: .1em; font-size:0.7em; color:#253776; display:block; font-weight:normal;}
h1.title .chapter-number { font-size:0.95em; color:#253776; display:block; font-weight:normal;}
h1.title .chapter-title { font-size:1.1em; font-weight:bold; display:block; }
h1.title .chapter-subtitle { color:#253776; font-size:1em; display:block; font-weight:normal; }
.back-section h2.title { padding-top:1.6em; }
h1 .subtitle { font-size:1.2em; font-weight:normal; }
h2,h1.sectl, .main-title { font-weight:bold; color:#253776;	line-height:1.5em; padding:0;	margin:0; padding-top:1.6em; padding-bottom:.4em; font-size:1.2em; }
h3, .section-title { font-weight:normal; font-style:normal; color:#253776; margin:0; line-height:1.5em; padding-top:1.2em; padding-bottom:.6em; font-size:1.1em; }
h4,.subsection-title, .block-title { font-weight:normal; font-style:italic; color:#253776; line-height:1.5em; margin:0; padding-top:1em; padding-bottom:.33em; font-size:1.05em; }
.block-title { display:block; }
h6, .subsubsection-title { font-weight:normal; font-style:normal; color:#253776; line-height:1.5em; margin:0; padding-top:0.5em; padding-bottom:.33em; font-size:1em; }	
h5, .contribgroup_heading { margin-top:.75em; font-style:normal; color:#555; font-size:1.1em; font-weight:bold; }
h5.label { display:inline-block; color:#253776; padding-right:.5em; vertical-align:top; margin-top:0; font-size:.9em; }
.boxed-text { font-family:sans-serif; font-size:.85em; border:.15em solid #666; border-radius:.25em; padding:.1em 1em; margin:1em 0; background-color:#eee;  }
.boxed-text .box-title { font-size:1em; font-weight:bold; color:#000; }
.box-main { padding:0 1em 0 .5em; }
.boxed-text .box-section-title { font-size:inherit; font-weight:normal; padding-top:0.5em; padding-bottom:0.25em; color:black; }
.box-title a { color:#ddd; }
.boxed-text.example .box-title {  margin:0; text-indent:.2em; color:#fff; border-bottom:1px solid #117ab4; background-color:#117ab4; }
.boxed-text.example { border:.1em solid #117ab4; padding:0; margin:1.5em 0; background-color:#eee; }
.boxed-text.reflection { border:none; font-family: sans-serif;}
.boxed-text.example .source-label { text-align:left; float:none; }
.boxed-text p { text-align:left; }
.boxed-text p.attrib { text-align:right; }
.boxed-text ol { margin-top:0; }
.panel { page-break-inside:avoid; }
.invisible { visibility:collapse; }
.entry .pagenumber { margin-left:1em;}
.entry .term { padding-right:1em; font-weight:bold; }
div.figure { margin-top:1.5em; margin-bottom:1.5em; }
.fig-group .fig.panel, .thumbholder { display:inline-block; }
p span.thumbholder { display:inline; vertical-align: bottom; }
.main.object .thumbholder, .main.object .fig.panel { display:block; }
.main.object object { width:100%; }
.object svg, .object img { width:100%; height:100%; }
body, div, h1, h2, h3, h4, h5, h6, p, ul, ol, li, dl, dt, dd, img, form, fieldset, input, textarea, blockquote, label {	margin:0; padding:0; border:0; }
.crossref-logo-container img {
    width: 60px;
    padding-left: .5em;
}
.p .crossref-logo-container {
    margin-left:-.5em;
}
img { max-width:100%; }
div.thumbholder { max-width:95%; }
div.thumbholder svg, div.thumbholder img { width:100%; }
.fig.panel, .table-wrap.panel { margin:1em 0; page-break-inside:avoid; overflow:auto; text-align:center; vertical-align:top; }
.cover { max-width:100%; text-align:center; }
.toc-group { padding-top:1.6em; }
.toc-entry { display:block; }
.toc-entry > .toc-entry { margin-left: .7em; }
.toc-label { padding-right:0.5em; font-weight:bold; }
.toc-contributors { color:#58595b; display:block; font-style:italic; padding-left:2em; }
.toc-contrib { display:inline; }
.toc-pagenumber { padding-left:2em; }
.index-letter {	color:#555;	margin-top:1.6em; font-weight:bold; font-size:1.1em; }
ul.index-entry-list { list-style-type:none; margin-top:0em; margin-bottom:0; padding-left:2em; text-indent:-2em; }
ul.index-entry-list ul.index-entry-list { list-style-type:none; text-indent:-2em; margin-bottom:0; }
ul.index-entry-list ul.index-entry-list ul.index-entry-list { list-style-type:none; text-indent:-2em;  margin-bottom:0; }
li.index-entry { font-size:0.9rem; }
.index-term {
/*    padding-right:0.3em;*/
display:inline;
}
.index-entry .main-entry {
	color:#253776;
    font-weight:normal;
	display:inline;
}
.sub-entry {
	padding-left:.3em;
	display:inline;
}
.index-term+.pagenumbers {
    padding-left:.3em;
}
.index-see-also { pdding-right:0.3em; }
.index-see-also .label { font-style:italic; }
.caption { font-size:.95em; margin-top:1em; text-align:left; line-height:1.6em; }
.list.contributors .list-item {
    padding-top:.8em;
}
.list.contributors .list-item.list-item-content:first-child p {
    font-weight:bold;
}
.list-item-content .caption { margin-top:.33em; }
p.caption {	margin-top:.75em; line-height:1.4em; font-size:11pt; }
.caption p { display:inline; }
.heading-label, .note-label, .caption-label { font-weight:bold; font-style:normal; padding-right:.5em; color:#253776; font-size:.95em; }
.back-section .reference { font-size:1em; }
.ref-list { padding-top:0; }
aside.references { color:#333; font-size:.9em; line-height:1.3em; border-style:none; text-align:left; vertical-align:middle;  margin-left: 2em; margin-top:.4em; text-indent: -2em; display:block !important}
.references.uncited::before {
    content:"*";
}
.refline { margin-top:.1em; margin-bottom:.5em; text-indent:0em; margin-left:0em; position:relative; display:inline; }
.refauth { font-weight:bold; color:#555; }
.refrole { position:relative; left:0em; float:none; }
.refseries { color:#253776; }
.refsource { font-style:italic; }
.refyear { color:#253776; font-weight:bold; }
.keywords, .abstract { padding:0 2em 0 2em; font-size:.95em; }
.keywords { display:inline-block; }
.keywords summary { display:inline; padding-right:1em; }
.keywords ul { display:inline; padding-left:0; margin:0; text-indent:0; }
.keywords li { display:inline-block; margin-right:.5em; }
.keywords li:last-child::after { content:""; }
.abstract .block-title, .keywords .block-title { font-weight:bold; font-size:inherit; font-style:normal; }

rb, rt { padding-right:.5em; }
rt { font-size:.8em; color:#c6371b; }
rt { position:relative; bottom:-.25em; }
rb, ruby.sign-modifier rb { color:black; padding-right:0; text-align:left; }
rt, ruby.sign-modifier rt { color:black; padding-right:0; text-align:right; border-bottom:1px solid black; }
.sig-block { text-align:right; margin-top:1em; }

table { line-height:1.6em; vertical-align:top; margin-top:.5em; margin-bottom:1em; border:none; border-collapse:collapse; border-top:solid #253776 2px; border-bottom:solid #253776 2px; font-size:.9em; }
tr {
	padding:0;
	margin:0;
	vertical-align:bottom;
}
th {
	line-height:1.65em;
	color:#253776;
	padding:.5em 0;
	padding-right:1em;
}
.vertical-align-top {
 vertical-align:top;
}
.vertical-align-bottom {
 vertical-align:bottom;
}
.vertical-align-middle {
 vertical-align:middle;
}
.horizontal-align-left{
 text-align:left;
}
.horizontal-align-center{
 text-align:center;
}
.horizontal-align-right{
 text-align:right;
}
tbody th {
 color:#666;
}
.booktext th {
	border-bottom:1px solid #253776;
}
.booktext tr {
	border-bottom:1px solid #ccc;
}
thead > tr {
	vertical-align:text-top;
}
tbody tr {
 vertical-align:text-top;
}
tr.total {
 font-weight:bold;
}
td {
	vertical-align:top;
	padding-right:1em;
}
td .p + .p {
	text-indent:0em;
}
td.hdr {
	border-bottom:solid 1px;
}
	
td.hdrb {
	border-top:solid 1px;
	border-bottom:solid 1px;
}
tfoot {
 border-top:solid 1px;
 font-weight:bold;
}
tbody {
 vertical-align:bottom;
 border-top:1px solid #253776;
}
tbody:last-of-type tr:last-child td {
 padding-bottom:0;
}
td:last-child, th:last-child {
 padding-right:.1em;
}

.table-wrap td {
 border-top:1px solid #ddd;
}
.table-wrap tr:first-child td {
	border-top:solid #253776 1px;
}
.table-wrap th {
	border-bottom:solid #253776 1px;
}
table.zerotable, .array table {
	border:0;
	line-height:1.6em;
	vertical-align:top;
	margin:0em;
	padding:0em;
	border:none;
	font-size:1em;
}
table.array {
 border:none;
 font-size:1em;
 line-height:2em;
 margin:0;
}
table.array tbody {
 border:none;
}
.array td {
	padding-right:.5em;
	text-align:left;
	vertical-align:top;
}
.array {
 display:block;
 clear:both;
 width:100%;
}
section > table.array {
 margin:1em 0;
}
table.zerotable td {
	padding:0em;
	margin:0em;
}
table.lines {
	border:solid 1px black;
}
table.lines td {
	border:solid 1px black;
	padding-left:1em;
	padding-right:1em;
	margin:0em;
}
table.example, table.subexample {
	margin-top:.6em;
	margin-bottom:.6em;
	border-top:none;
	border-bottom:none;
	font-size:1em;
}
table.subexample {
 margin-top:0;
 font-size:1em;
}
table.nextexample {
	margin-top:-.4em;
	margin-bottom:.6em;
	border-top:none;
	border-bottom:none;
}
.example td {
	vertical-align:top;
}
table.example td:first-child  {
 min-width:3.5em;
}
table.subexample td:first-child {
 min-width:2em;
}
table.enum {
	margin-top:.6em;
	margin-bottom:.6em;
	border-top:none;
	border-bottom:none;
}
.enum td {
	vertical-align:top;
	padding-right:.5em;
}
table.nextenum {
	margin-top:0em;
	margin-bottom:0em;
	border-top:none;
	border-bottom:none;
}
table.table {
	font-size:10pt;
}
table caption {
	padding-top:.5em;
	text-align:left;
	font-size:12pt;
}
.lin-example tbody {
    border-top:0px;
}
.lin-example {
 display:inline-block;
 padding-right:.1em;
}
.lin-example p {
 display:inline-block;
}
.line1, .line2 {
 display:block;
}
.line2 {
 color:#777;
 line-height:1.6em;
}
table.note-group {
	margin-top:.6em;
	margin-bottom:.6em;
	border-top:solid 0px;
	border-bottom:solid 0px;
	width:100%;
}
.rotate-90 {
 -ms-transform:rotate(90deg); /* IE 9 */
 -webkit-transform:rotate(90deg); /* Chrome, Safari, Opera */
 transform:rotate(90deg);   
 display:inline-block;
 vertical-align:middle;
 text-align:center;
}
.rotate-270 {
 -ms-transform:rotate(270deg); /* IE 9 */
 -webkit-transform:rotate(270deg); /* Chrome, Safari, Opera */
 transform:rotate(270deg);   
 display:inline-block;
 vertical-align:middle;
 text-align:center;
}
.note {
	padding-bottom:.5em;
	line-height:1.6em;
}
.todo {
	font-weight:bold;
	background-color:yellow;
}
.empty {
	padding:0;
	height:20px;
}
.addresses {
	vertical-align:top;
	width:100%;
}
.address, person-block {
	vertical-align:top;
	font-size:.9em;
	padding-right:1em;
	padding-bottom:1.5em;
	display:inline-block;
}
.person-block {
    margin-bottom:4em;
}
.name, .affiliation, .addressline {
	display:block;
}
.address .name {
	display:block;
	font-weight:bold;
}
.keyrefs {
	display:block;
	color:gray;
	margin-top:1em;
}
.translation {
	color:#253776;
}
.stars {
	margin-top:1em;
	text-align:center;
}
section.references {
	padding-top:1.6em;
	padding-bottom:.4em;
}
.back-section {
    font-size:.95em;
    line-height:1.6em;
}
.transparent {
	opacity:0;
	display:none;
	transition:all .5s;
}
.titlesubtitle {
	opacity:1;
}
.titlesubtitle .subtitle, .title .subtitle {
    font-weight:normal;
}
.author, div.author { font-weight:normal; line-height:1.4em; color:#253776; font-size:.85em; padding-top:.75em; padding-bottom:.5em; }
.contrib { word-break:keep-all; }
.affiliation { color:#58595b; }
.affiliation p { display:inline; }
h1.translator {
	line-height:1.4em;
	color:	#00a9b7;
	background-color:#ddd;
	font-size:1.3em;
	padding-top:.5em;
	padding-bottom:.5em;
	margin-top:	0em;
}
h1.translation {
	line-height:1.2em;
	color:	#666;
	background-color:#ddd;
	font-size:12pt;
	padding-top:.5em;
	padding-bottom:.5em;
	margin-top:	0em;
}
.titleauthor {
	font-weight:normal;
	font-style:italic;
	font-size:.9em;
}
.contribgroup {
 margin-top:.5em;
 vertical-align:top;
 font-weight:normal;
 padding-bottom:.35em;
 line-height:1.85em;
}
p.entry {
	text-align:left;
	margin-left:4em;
	text-indent:-4em;
	line-height:2em;
	font-size:.9em;
}
p.subentry {
	text-align:left;
	margin-left:6em;
	text-indent:-4em;
	line-height:1.75em;
	font-size:.85em;
}
.booktext {
 padding-top:.35em;
}
a.crossref-main {
	color:#444;
	font-weight:bold;
}
.crossref-main-missing {
	font-weight:bold;
	color:#a0a0a0;
	cursor:help;
}
a.crossref-sub {
	color:#444;
	font-weight:normal;
}
a.crossref {
	color:#c6371b;
	font-weight:bold;
}
img.crossref {
	border:0;
}
a.arabic {
	color:#339966;
	font-weight:bold;
}
a.toc {
	color:#555;
}		
div.coverimage {
 float:right;
 height:300px;
 width:225px;
 margin-right:-3.5em;
}
.imageContainer {
 float:right;
 height:300px;
 margin:auto;
 margin-left:2em;
 margin-top:1.5em;
 overflow:hidden;
 padding:0;
 position:relative;
 top:0;
 width:225px;
}
.crossref {
	border:0px;
	padding-right:.05em;
	padding-left:.05em;
}
.meta { 
	font-size:10pt;
	color:#a65f66;
	text-align:left;
	margin:0;
	padding:0 6.5%;	
}
.metarule { 
	color:gray;
}
div.metadata-area, div.metadata-area p, div.metadata-area div  {
 display:inline-block;
}
.list-title { font-weight:bold; line-height:1.6em; margin-top:1em; text-align:left; }
.list {	margin-top:.6em; margin-bottom:.6em; border-top:none; border-bottom:none; width:100%; clear:both; }
.list .list {
 margin-top:0em;
}
.list.example {
 font-size:.95em;
}
.list.example pre {
	margin-top:0em;
}
.list-item {
 display:flex;
}
.list-item-label {
 min-width:3em;
 display:flex;
 flex:none;
}
.list-item-content {
 -webkit-flex:1;
    flex:1;
}
.list .list-item-content {
	margin-left:1em;
}
.list-item-content .list-item-label {
 min-width:2em;
}
.disp-quote-item, .disp-formula-item {
    display:flex;
    margin-top:0.6em;
}
.disp-quote-label, .disp-formula-label {
    min-width:3em;
    display:flex;
    flex: none;
    padding-right:1em;
}
.disp-quote-title {
    display:flex;
    min-width:6em;
    font-weight:bold;
    overflow:auto;
}
.disp-quote-content, .disp-formula-content {
    -webkit-flex: 1;
          flex: 1;
}
.list-item-content .list-item-label {
 min-width:2em;
}
.list-item-content p  + p, .list-item-content .p  + .p { text-indent:0em; }
ul, ol { margin-top:0.33em; padding-left:2em; margin-bottom:.66em; }
ul ul {	padding:0; margin:0em; padding-left:1.2em; }
ul ul ul { padding:0; margin-top:0em; padding-left:2em; text-indent:-2em; }

ul ul.bullet li {
 list-style-type:disc;
 padding-left:0;
 margin-left:0em;
 text-indent:0;
}
ul ul li.toc {
	margin-left:0;
}
nav ol li {
	list-style:none;
}
ul.nomarker, ul.contribgroup_members {
 list-style-type:none;
 padding-left:0;
 margin-left:0em;
 text-indent:0em;
}
ul.nomarker li {
 list-style-type:none;
 padding-left:0;
 margin-left:0em;
 text-indent:0;
}
ul.nomarker li p + p { text-indent:0em; }
.inlineparagraph {
	color:black;
	font-style:normal;
	font-weight:normal;
	display:inline-block;
}
.inlineparagraph + .inlineparagraph {
 text-indent:2em;
}
.inlinequote {
	display:inline-block;
	margin:1% 7.5%;
}
.page p {
	text-align:left;
}
th p {
 text-align:inherit;
}
p.first	{
	margin-top:.5em;
	text-indent:0;
}
.page p + p {
 text-indent:0;
 padding-top:.5em;
}
td p + p {
	text-indent:0;
}
p.first[lang=ja], p.next[lang=ja] {
 text-indent:1em;
}
td p {
 text-align:inherit;
}
.table-wrap-foot {
 font-size:.8em;
 line-height:1.5em;
}
span.table-p {
 position:relative;
}
.array .lin-example:first-child span.grammaticality-marker {
 margin-left:-1.6em;
 text-align:right;
 min-width:1.5em;
}
p.quotenext {
	margin-top:.25em;
}
p.address, p.address-line, p.copyright {
 text-indent:0;
}
.pagenumber:first-child {
 display:none;
}
.speech {
    padding-left:5em;
    text-indent:-5em;
    padding-top:.6em;
    padding-bottom:.6em;
}
.speech p + p {
    text-indent:0em;
}
.reference .note p, .note p + p, .note p.first, .ref-note-label {
    font-size:.95em;
    margin-top:0em;
    padding-left:4.8em;
    padding-right:0em;
    text-indent:0em;
    font-weight:normal;
}

@media screen and (max-width:400px) { 
	h1 { padding-right:0; padding-left:0; }
	img, .thumbholder { overflow:auto; } 
	table { max-width:100%; overflow:auto; font-size:1.0em; } 
	body { font-size:10pt; line-height:1.5em; } 
	.back-section { line-height:1.3em; } 
	.keywords, .abstract { padding:0 1em 0 1em; font-size:.9em; }
	}
	
/* MathML */
@namespace "http://www.w3.org/1998/Math/MathML";

/* mml:math */
math {
    display: inline;
    text-indent: 0;
}
math[display="block"] {
    display: block;
    text-align: center;
}

/* fraction */
mfrac {
    display: inline-table;
    vertical-align: middle;
    border-collapse: collapse;
}
mfrac > * {
    display: table-row;
}
mfrac:not([linethickness="0"]) > *:first-child {
    border-bottom: solid thin;
}

/* sub/sup scripts */
msub > *:nth-child(2), msubsup > *:nth-child(2),
mmultiscripts > *:nth-child(2n+2),
mmultiscripts > mprescripts ~ *:nth-child(2n+3) {
    font-size: 0.8em;
    vertical-align: sub;
}
msup > *:nth-child(2), msubsup > *:nth-child(3),
mmultiscripts > *:nth-child(2n+3),
mmultiscripts > mprescripts ~ *:nth-child(2n+2) {
    font-size: 0.8em;
    vertical-align: super;
}
mprescripts:after {
    content: ";";
}

/* under/over scripts */
munder, mover, munderover {
    display: inline-flex;
    flex-direction: column;
}
munder > *:nth-child(2), munderover > *:nth-child(2) {
    font-size: 0.8em;
    order: +1;
}
mover > *:nth-child(2), munderover > *:nth-child(3) {
    font-size: 0.8em;
    order: -1;
}
munder {
    vertical-align: text-top;
}
mover {
    vertical-align: text-bottom;
}
munderover {
    vertical-align: middle;
}

/* roots */
msqrt, mroot {
    display: inline-flex;
    margin-left: .5em;
    vertical-align: middle;
    border-top: solid thin;
}
msqrt:before, mroot:before {
    margin-left: -.5em;
    content: "\221A";
}
mroot > *:nth-child(2) {
    margin-right: .25em;
    margin-left: -.75em;
    font-size: 0.8em;
    order: -1;
}

/* menclose */
menclose {
  display: inline-table;
  border-collapse: separate;
  border-spacing: 0.4ex 0;
}
menclose[notation*="top"], menclose[notation*="actuarial"] {
  border-top: solid thin;
}
menclose[notation*="bottom"], menclose[notation*="madruwb"] {
    border-bottom: solid thin;
}
menclose[notation*="right"], menclose[notation*="actuarial"],
menclose[notation*="madruwb"] {
    border-right: solid thin;
}
menclose[notation*="left"] {
    border-left: solid thin;
}
menclose[notation*="box"], menclose[notation*="roundedbox"],
menclose[notation*="circle"] {
    border: solid thin;
}
menclose[notation*="roundedbox"] {
    border-radius: 15%;
}
menclose[notation*="circle"] {
    border-radius: 50%;
}
menclose[notation*="horizontalstrike"] {
    text-decoration: line-through;
}

/* table */
mtable {
    display: inline-table;
    vertical-align: middle;
}
mtr {
    display: table-row;
}
mtd {
    display: table-cell;
    padding: 0 0.5ex;
}

/* token elements */
mspace {
    margin: .2em;
}
mi {
    font-style: italic;
}
mo {
    margin-right: .2em;
    margin-left: .2em;
}
ms:before, ms:after {
    content:"\0022";
}
ms[lquote]:before {
    content: attr(lquote);
}
ms[rquote]:after {
    content: attr(rquote);
}

/* mathvariants */
[mathvariant="bold"], [mathvariant="bold-italic"],
[mathvariant="bold-sans-serif"], [mathvariant="sans-serif-bold-italic"] {
    font-weight: bold;
    font-style: normal;
}
[mathvariant="monospace"] {
    font-family: monospace;
    font-style: normal;
}
[mathvariant="sans-serif"],
[mathvariant="bold-sans-serif"], [mathvariant="sans-serif-italic"],
[mathvariant="sans-serif-bold-italic"] {
    font-family: sans-serif;
    font-style: normal;
}
[mathvariant="italic"], [mathvariant="bold-italic"],
[mathvariant="sans-serif-italic"], [mathvariant="sans-serif-bold-italic"] {
    font-style: italic;
}
[mathvariant="normal"] {
    font-style: normal;
}

/* mphantom */
mphantom {
    visibility: hidden;
}

/* merror */
merror {
  outline: solid thin red;
}
merror:before {
  content: "Error: ";
}

/* annotations */
annotation, annotation-xml {
    font-family: monospace;
    display: none;
}
math:hover > semantics > *:first-child,
math:hover > semantics > *:first-child {
    display: none;
}
math:hover annotation {
    display: inline;
}