/**
 * Minified by jsDelivr using clean-css v5.3.2.
 * Original file: /gh/dginev/ar5iv-css@0.7.91/css/ar5iv.css
 *
 * Do NOT use SRI with dynamically generated files! More information: https://www.jsdelivr.com/using-sri-with-dynamic-files
 */
:root,
[data-theme=light] {
 --main-width:52rem;
 --main-width-margin:54rem;
 --headings-font-family:"noto-sans",sans-serif;
 --text-font-family:"noto-serif",serif;
 --math-font-family:"STIX Two Math","STIX Two Math Fallback","Cambria Math",math;
 --math-caligraphic-font-family:"STIX Two Math","STIX Two Math Fallback","Cambria Math",math;
 --code-font-family:"noto-mono",monospace;
 --background-color:white;
 --text-color:#292929;
 --border-color:#292929;
 --border-light-color:grey;
 --image-color:black;
 --image-background-color:white;
 --link-text-color:#212121;
 --email-link-color:#026ecb;
 --note-mark-color:#026ecb;
 --note-highlight-color:#ffffd4;
 --info-text-color:#01719d;
 --warning-text-color:#d09e05;
 --error-text-color:#D8000C;
 --fatal-text-color:#D8000C;
 --index-ref-color:#026ecb
}
[data-theme=dark] {
 --background-color:#0d1117;
 --text-color:#c9d1d9;
 --link-text-color:#c9d1d9;
 --border-color:white;
 --border-light-color:#d4d4d4;
 --note-mark-color:#daa002;
 --note-highlight-color:rgb(35, 29, 2);
 --email-link-color:darkcyan;
 --error-text-color:#d52f36;
 --fatal-text-color:#d52f36;
 --index-ref-color:darkcyan;
 --image-color:black;
 --image-background-color:white
}
[data-theme=dark] img,
svg {
 filter:brightness(.8) contrast(1.2);
 background-color:#fff;
 color:#000
}
[data-theme=light] img,
svg {
 filter:none;
 background-color:#fff;
 color:#000
}
body {
 margin:0;
 height:100%;
 width:100%;
 color:var(--text-color);
 background-color:var(--background-color)
}
@media only screen and (max-width:95.99rem) {
 body {
  overflow-x:scroll
 }
}
@media only screen and (min-width:96rem) {
 body {
  overflow-x:hidden
 }
 .ltx_page_content {
  width:100%
 }
}
.ltx_page_main {
 width:100%
}
.ltx_page_content {
 margin:4rem 1rem;
 font-size:1rem;
 font-weight:300;
 clear:both
}
.ltx_page_header {
 border-bottom:.1em solid;
 margin-bottom:.5em
}
.ltx_page_footer {
 clear:both;
 text-align:right;
 width:auto;
 margin:auto;
 border-top:.1em solid;
 max-width:var(--main-width)
}
.ltx_page_logo {
 font-family:var(--text-font-family);
 font-size:1rem;
 text-align:right;
 padding:.5rem
}
.ltx_page_logo>a {
 border-bottom:.063rem dotted var(--link-text-color);
 color:var(--link-text-color);
 text-decoration:none;
 overflow-wrap:break-word
}
.ltx_page_content:after,
.ltx_page_footer:after,
.ltx_page_header:after {
 content:".";
 display:block;
 height:0;
 clear:both;
 visibility:hidden
}
.ltx_page_footer:before {
 content:".";
 display:block;
 height:0;
 clear:both;
 visibility:hidden
}
.ltx_document {
 margin:auto;
 max-width:var(--main-width);
 margin-top:2rem;
 text-rendering:optimizeLegibility
}
.ltx_abstract .ltx_p,
.ltx_acknowledgements,
.ltx_para {
 font-family:var(--text-font-family);
 text-align:justify;
 text-justify:inter-word;
 hyphens:auto;
 line-height:1.5rem;
 margin-bottom:1.5rem
}
.ltx_figure+.ltx_para,
.ltx_flex_figure+.ltx_para {
 clear:both
}
.ltx_p {
 line-height:1.5rem;
 text-indent:0;
 white-space:normal;
 margin-top:0
}
.ltx_text {
 font-family:var(--text-font-family);
 word-wrap:break-word
}
.ltx_tag .ltx_text {
 font-family:inherit
}
.ltx_indent>.ltx_p:first-child,
section.ltx_indent_first>.ltx_title+.ltx_para>.ltx_p,
section.ltx_pruned_first>.ltx_title+.ltx_para>.ltx_p {
 text-indent:2em!important
}
.ltx_noindent>.ltx_p:first-child {
 text-indent:0!important
}
.ltx_pagination.ltx_role_newpage {
 margin-top:2rem;
 display:block
}
math,
mjx-container {
 font-family:var(--math-font-family);
 word-wrap:break-word;
 white-space:nowrap
}
mtd {
 padding:.1rem
}
.ltx_markedasmath {
 white-space:nowrap
}
.ltx_ref {
 border-bottom:.063rem dotted var(--link-text-color);
 color:var(--link-text-color);
 text-decoration:none;
 overflow-wrap:break-word
}
.ltx_ref>.ltx_graphics {
 border-bottom:none;
 display:inline
}
.ltx_cite {
 font-style:normal
}
.ltx_cite+.ltx_cite {
 padding-left:.2rem
}
.ltx_td .ltx_cite {
 white-space:pre-wrap
}
.ltx_cite .ltx_font_italic {
 font-style:normal
}
.ltx_cite>.ltx_ref {
 white-space:nowrap;
 display:inline-block;
 line-height:1.4rem;
 text-indent:0
}
article>div:not(.ltx_minipage)>img:first-of-type {
 max-width:30rem;
 width:auto;
 height:auto
}
.ltx_title.ltx_title_document {
 font-weight:400;
 font-size:1.7rem!important;
 margin-top:1rem;
 margin-bottom:1.5rem;
 text-align:center
}
.ltx_subtitle {
 font-family:var(--headings-font-family);
 font-style:italic;
 font-size:1.3rem;
 margin-top:1rem;
 margin-bottom:1.5rem;
 text-align:center
}
.ltx_subtitle .ltx_text {
 font-family:inherit
}
.ltx_authors {
 display:flex;
 flex-flow:row wrap;
 width:auto;
 justify-content:center;
 align-items:center;
 object-fit:contain;
 margin-top:.75rem;
 margin-bottom:.75rem;
 text-align:center
}
span.ltx_personname {
 font-family:var(--text-font-family);
 font-size:1rem;
 display:inline-block;
 overflow-wrap:break-word;
 min-width:14rem
}
span.ltx_personname span:first {
 font-size:1.5rem
}
span.ltx_personname br.ltx_break {
 margin-top:.25rem
}
span.ltx_personname>br.ltx_break+span {
 display:inline-block;
 padding-top:.75em
}
span.ltx_personname>.ltx_break+.ltx_break {
 display:none
}
.ltx_personname math mtext[mathsize] {
 font-size:inherit!important
}
.ltx_para>.ltx_break:first-child:last-child {
 display:none
}
.ltx_creator {
 flex:1 1 0px;
 max-width:100%;
 padding:.5rem;
 overflow-wrap:break-word
}
.ltx_creator br.ltx_break {
 flex-basis:100%;
 height:0
}
.ltx_author_after,
.ltx_author_before {
 display:none
}
.ltx_dates {
 margin-top:0;
 margin-bottom:1rem;
 text-align:center;
 font-family:var(--text-font-family)
}
.ltx_role_author+.ltx_role_author {
 margin-left:2rem
}
.ltx_affiliation_country,
.ltx_affiliation_department,
.ltx_affiliation_institution {
 margin-left:.25rem;
 margin-right:.25rem;
 white-space:nowrap
}
span.ltx_role_affiliation:not(.ltx_note)+span.ltx_role_affiliation:not(.ltx_note),
span.ltx_role_orcid+span.ltx_role_affiliation:not(.ltx_note) {
 margin-top:.5rem;
 display:block
}
div.ltx_keywords:empty:before {
 content:"Keywords: ";
 font-weight:700
}
.ltx_classification,
.ltx_keywords {
 margin-bottom:1.5rem;
 font-size:1rem;
 font-family:var(--text-font-family);
 font-weight:400
}
.ltx_title.ltx_title_classification,
.ltx_title.ltx_title_keywords {
 display:inline;
 font-size:1rem;
 font-weight:700;
 font-style:normal
}
.ltx_title>br.ltx_break {
 display:none
}
.ltx_date {
 font-family:var(--text-font-family);
 text-align:center;
 font-size:120%;
 margin:.5em 0 .5em 0
}
.ltx_note {
 position:relative;
 text-align:justify;
 text-justify:inter-word;
 hyphens:auto;
 word-spacing:-0.05rem;
 font-style:normal;
 font-size:.85em
}
.ltx_note+.ltx_note {
 padding-left:.2rem
}
.ltx_note_outer {
 font-size:.85rem
}
.ltx_note>.ltx_note_mark {
 position:relative;
 top:-.2em;
 max-height:2rem;
 font-size:.85em;
 color:var(--note-mark-color)
}
.ltx_note_content {
 display:block;
 opacity:100;
 padding-top:.5rem;
 padding-bottom:.5rem;
 margin:.6rem;
 font-family:var(--text-font-family);
 line-height:1.5rem;
 overflow-wrap:break-word
}
.ltx_author_notes {
 display:block;
 opacity:100;
 min-width:20rem;
 margin-top:.5rem;
 margin-bottom:2rem;
 font-family:var(--text-font-family);
 font-size:.9rem;
 padding:.2rem
}
@media only screen and (max-width:46rem) {
 .ltx_note_outer {
  width:20rem
 }
}
@media only screen and (min-width:46.01rem) and (max-width:51.99rem) {
 .ltx_note_outer {
  width:46rem
 }
}
@media only screen and (min-width:52rem) and (max-width:95.99rem) {
 .ltx_note_outer {
  width:50rem
 }
}
@media only screen and (min-width:96rem) and (max-width:108.99rem) {
 .ltx_note_outer {
  width:20rem;
  margin-right:-24rem
 }
}
@media only screen and (min-width:109rem) {
 .ltx_note_outer {
  width:27rem;
  margin-right:-31rem
 }
}
@media only screen and (max-width:95.99rem) {
 .ltx_note_outer {
  display:none;
  opacity:0
 }
 .ltx_note_content {
  overflow-wrap:break-word;
  width:90%
 }
 .ltx_note:not(.ltx_note_frontmatter):not(.ltx_role_affiliationmark):not(.ltx_role_footnotemark):active>.ltx_note_outer,
 .ltx_note:not(.ltx_note_frontmatter):not(.ltx_role_affiliationmark):not(.ltx_role_footnotemark):hover>.ltx_note_outer {
  display:block;
  opacity:100;
  z-index:100;
  position:absolute;
  top:0;
  margin:auto;
  padding:2rem;
  background-color:var(--background-color);
  border-width:.1rem 0;
  border-bottom:double;
  border-top:double
 }
 .ltx_note.ltx_note_frontmatter {
  display:block;
  opacity:100;
  opacity:inherit;
  text-align:left
 }
 .ltx_note.ltx_note_frontmatter>.ltx_note_mark {
  display:none;
  opacity:0
 }
 .ltx_note.ltx_note_frontmatter .ltx_note_outer {
  display:block;
  opacity:100;
  opacity:inherit
 }
 .ltx_note.ltx_note_frontmatter .ltx_note_content {
  border:none;
  margin-left:0
 }
 .ltx_note.ltx_note_frontmatter .ltx_note_content>.ltx_note_mark {
  display:inline
 }
 .ltx_authors>.ltx_note .ltx_note_mark {
  display:none;
  opacity:0
 }
}
@media only screen and (min-width:96rem) {
 .ltx_note_outer {
  display:block;
  opacity:100;
  position:relative;
  clear:both;
  float:right;
  padding-bottom:2rem;
  padding-right:3rem
 }
 .ltx_note_content {
  border-style:double none none none;
  border-width:.1rem 0
 }
 .ltx_note_content>.ltx_note_mark {
  display:block;
  opacity:100;
  margin-top:-1.8rem
 }
 .ltx_author_notes>.ltx_note>.ltx_note_mark:hover+.ltx_note_outer .ltx_note_content,
 .ltx_author_notes>span>.ltx_note>.ltx_note_mark:hover+.ltx_note_outer .ltx_note_content,
 .ltx_note>.ltx_note_mark:active+.ltx_note_outer .ltx_note_content,
 .ltx_note>.ltx_note_mark:hover+.ltx_note_outer .ltx_note_content,
 .ltx_title.ltx_title_document>.ltx_role_affiliation>.ltx_note_mark:active+.ltx_note_outer .ltx_note_content,
 .ltx_title.ltx_title_document>.ltx_role_affiliation>.ltx_note_mark:hover+.ltx_note_outer .ltx_note_content {
  background-color:var(--note-highlight-color);
  z-index:100
 }
 .ltx_title.ltx_title_document .ltx_note_outer {
  display:block;
  opacity:100
 }
 .ltx_title.ltx_title_document .ltx_note_type {
  display:none;
  opacity:0
 }
 .ltx_author_notes>.ltx_note .ltx_note_outer,
 .ltx_author_notes>span>.ltx_note .ltx_note_outer,
 .ltx_role_affiliation>.ltx_note_outer,
 .ltx_td .ltx_note_outer,
 .ltx_th .ltx_note_outer,
 figcaption .ltx_note_outer,
 td .ltx_note_outer,
 th .ltx_note_outer {
  display:none;
  opacity:0
 }
 figcaption .ltx_note_content,
 td .ltx_note_content,
 th .ltx_note_content {
  font-weight:400;
  overflow-wrap:break-word;
  width:90%
 }
 .ltx_td .ltx_note:active>.ltx_note_outer,
 .ltx_td .ltx_note:hover>.ltx_note_outer,
 .ltx_th .ltx_note:active>.ltx_note_outer,
 .ltx_th .ltx_note:hover>.ltx_note_outer,
 figcaption .ltx_note:active>.ltx_note_outer,
 figcaption .ltx_note:hover>.ltx_note_outer,
 td .ltx_note:active>.ltx_note_outer,
 td .ltx_note:hover>.ltx_note_outer,
 th .ltx_note:active>.ltx_note_outer,
 th .ltx_note:hover>.ltx_note_outer {
  display:block;
  opacity:100;
  z-index:100;
  position:absolute;
  top:0;
  margin:auto;
  padding:2rem;
  background-color:var(--background-color);
  border-width:.1rem 0;
  border-bottom:double;
  border-top:double
 }
 .ltx_author_notes>.ltx_note>.ltx_note_mark:hover+.ltx_note_outer,
 .ltx_author_notes>span>.ltx_note>.ltx_note_mark:hover+.ltx_note_outer,
 .ltx_personname .ltx_role_footnote>.ltx_note_mark:active+.ltx_note_outer,
 .ltx_personname .ltx_role_footnote>.ltx_note_mark:hover+.ltx_note_outer,
 .ltx_role_affiliation>.ltx_note_mark:active+.ltx_note_outer,
 .ltx_role_affiliation>.ltx_note_mark:hover+.ltx_note_outer {
  display:block;
  opacity:100;
  z-index:100;
  position:absolute;
  left:0
 }
 .ltx_personname .ltx_role_footnote .ltx_note_outer {
  display:none;
  opacity:0
 }
 .ltx_note.ltx_role_footnotetext .ltx_note_outer {
  position:absolute;
  left:var(--main-width-margin)
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(2) .ltx_note_outer {
  top:8rem
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(3) .ltx_note_outer {
  top:16rem
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(4) .ltx_note_outer {
  top:24rem
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(5) .ltx_note_outer {
  top:32rem
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(6) .ltx_note_outer {
  top:40rem
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(7) .ltx_note_outer {
  top:48rem
 }
 .ltx_note.ltx_role_footnotetext:nth-of-type(8) .ltx_note_outer {
  top:56rem
 }
 .ltx_abstract>.ltx_note>.ltx_note_mark,
 .ltx_author_notes>.ltx_note>.ltx_note_outer .ltx_note_mark,
 .ltx_author_notes>span>.ltx_note>.ltx_note_outer .ltx_note_mark,
 .ltx_document>.ltx_note:not(.ltx_role_footnotetext)>.ltx_note_outer>.ltx_note_content>.ltx_note_mark,
 .ltx_document>.ltx_note>.ltx_note_mark,
 .ltx_note.ltx_note_frontmatter>.ltx_note_mark,
 .ltx_note.ltx_note_frontmatter>.ltx_note_outer>.ltx_note_content>.ltx_note_mark,
 .ltx_title_document>.ltx_note>.ltx_note_mark {
  display:none;
  opacity:0
 }
 .ltx_note.ltx_note_frontmatter .ltx_note_content {
  border:none;
  margin-bottom:0;
  padding-bottom:0;
  margin-top:0;
  padding-top:0
 }
 .ltx_note.ltx_note_frontmatter>.ltx_note_outer {
  margin-bottom:0;
  padding-bottom:0
 }
}
.ltx_note.ltx_role_footnotetext .ltx_note_type {
 display:none;
 opacity:0
}
.ltx_note.ltx_role_margin .ltx_note_type {
 display:none;
 opacity:0
}
.ltx_note.ltx_role_affiliationmark>.ltx_note_mark,
.ltx_note.ltx_role_footnotemark>.ltx_note_mark {
 color:var(--text-color)
}
.ltx_note.ltx_role_affiliationmark>.ltx_note_outer,
.ltx_note.ltx_role_footnotemark>.ltx_note_outer {
 display:none!important;
 opacity:0!important
}
.ltx_note.ltx_marginpar_left {
 display:none
}
.ltx_title {
 font-size:100%;
 font-weight:400;
 font-family:var(--headings-font-family);
 text-wrap:balance;
 max-inline-size:52rem
}
.ltx_abstract {
 margin-top:4rem;
 margin-bottom:2rem
}
.ltx_TOC>h6,
.ltx_title_abstract,
.ltx_title_contents {
 margin-top:0;
 margin-bottom:1.5rem;
 padding-top:0;
 color:var(--link-text-color);
 text-decoration:none;
 font-size:1.4rem;
 font-weight:700;
 font-family:var(--headings-font-family);
 line-height:1.15rem;
 box-sizing:border-box;
 list-style:none
}
.ltx_abstract p:first-of-type {
 text-indent:0
}
.ltx_role_dedicatory {
 font-size:100%;
 font-style:italic;
 text-align:center;
 margin:1em
}
.ltx_role_email {
 display:block
}
.ltx_role_email>a {
 color:var(--email-link-color);
 text-decoration:none
}
.ltx_TOC {
 margin-top:2rem;
 margin-bottom:2rem
}
ul.ltx_toclist {
 padding-left:2.5rem
}
ul.ltx_toclist>.ltx_tocentry:first-of-type {
 margin-top:.3rem
}
.ltx_TOC>ul.ltx_toclist {
 padding-left:0
}
.ltx_TOC>.ltx_toclist>.ltx_tocentry {
 list-style-type:none;
 margin-bottom:1.3rem
}
.ltx_tocentry {
 list-style-type:none;
 margin-bottom:.5rem
}
.ltx_TOC>.ltx_toclist>.ltx_tocentry>a.ltx_ref {
 display:inline-block;
 border-bottom:none;
 font-weight:700;
 margin-bottom:.5em
}
.ltx_tocentry_chapter>.ltx_ref>.ltx_ref_title>.ltx_tag,
.ltx_tocentry_part>.ltx_ref>.ltx_ref_title>.ltx_tag,
.ltx_tocentry_section>.ltx_ref>.ltx_ref_title>.ltx_tag {
 margin-right:1rem;
 display:inline-block;
 min-width:1.5rem
}
.ltx_toclist_part>.ltx_tocentry_chapter>.ltx_ref>.ltx_ref_title>.ltx_tag {
 min-width:.5rem
}
.ltx_tocentry_chapter .ltx_tocentry_section>.ltx_ref>.ltx_ref_title,
.ltx_tocentry_part .ltx_tocentry_chapter>.ltx_ref,
.ltx_tocentry_subsection>.ltx_ref>.ltx_ref_title {
 font-family:var(--text-font-family)
}
.ltx_tocentry_chapter .ltx_tocentry_section>.ltx_ref,
.ltx_tocentry_part .ltx_tocentry_chapter>.ltx_ref,
.ltx_tocentry_subsection>.ltx_ref,
.ltx_tocentry_subsubsection>.ltx_ref {
 border-bottom:none
}
.ltx_tocentry_chapter .ltx_tocentry_section>.ltx_ref>.ltx_ref_title>.ltx_tag_ref,
.ltx_tocentry_part .ltx_tocentry_chapter>.ltx_ref>.ltx_ref_title>.ltx_tag_ref,
.ltx_tocentry_subsection>.ltx_ref>.ltx_ref_title>.ltx_tag_ref,
.ltx_tocentry_subsubsection>.ltx_ref>.ltx_ref_title>.ltx_tag_ref {
 border-bottom:.063rem dotted var(--link-text-color);
 width:min-content;
 display:inline-block;
 line-height:1.1rem;
 margin-right:.3rem
}
.ltx_tag_appendix,
.ltx_tag_chapter,
.ltx_tag_part,
.ltx_tag_section,
.ltx_tag_subsection,
.ltx_tag_subsubsection {
 display:inline-block;
 padding-right:1rem;
 min-width:1.33em
}
.ltx_tag_figure,
.ltx_tag_table {
 display:inline-block;
 padding-right:.2rem;
 min-width:1.33em
}
.ltx_title_chapter,
.ltx_title_part {
 font-size:1.6rem;
 font-weight:700;
 margin-bottom:1.5rem
}
.ltx_title_acknowledgements,
.ltx_title_appendix,
.ltx_title_bibliography,
.ltx_title_index,
.ltx_title_section,
span.ltx_font_bold>.ltx_break:last-child {
 font-size:1.4rem;
 font-weight:700;
 margin-bottom:1.5rem
}
span.ltx_font_bold>.ltx_break:last-child {
 margin-top:2rem
}
.ltx_title_subsection {
 font-size:1.2rem;
 font-weight:700;
 margin-bottom:1rem
}
.ltx_title_subsubsection {
 font-size:1rem;
 font-weight:700;
 margin-bottom:1rem
}
.ltx_title_paragraph {
 font-size:1rem;
 font-weight:700;
 margin-right:1rem;
 margin-bottom:.5rem
}
.ltx_title_subparagraph {
 font-size:1rem;
 font-weight:700;
 display:inline;
 margin:0 1rem 0 2rem
}
.ltx_section .ltx_subparagraph>.ltx_para:first-of-type>.ltx_p {
 text-indent:2rem
}
.ltx_runin {
 display:inline
}
.ltx_runin:after {
 content:" "
}
.ltx_runin+.ltx_para,
.ltx_runin+.ltx_para p:first-child,
.ltx_runin+p:first-child {
 display:inline
}
.ltx_outdent {
 margin-left:-2em
}
.ltx_chapter,
.ltx_part {
 margin-bottom:5rem
}
.ltx_bibliography,
.ltx_section {
 margin-bottom:2.5rem
}
.ltx_subsection {
 margin-bottom:2rem
}
.ltx_subsubsection {
 margin-bottom:.5rem
}
.ltx_section .ltx_para:first-of-type .ltx_p:first-of-type {
 text-indent:0
}
.ltx_proof,
.ltx_theorem {
 margin:2rem 0 1rem 0
}
.ltx_item>.ltx_theorem {
 margin-left:1em
}
.ltx_theorem>.ltx_para {
 margin-bottom:.5rem
}
.ltx_title_proof,
.ltx_title_theorem {
 font-family:var(--headings-font-family);
 font-size:1rem;
 font-weight:700;
 display:inline;
 padding-right:.25em
}
.ltx_bibliography dt {
 margin-right:.5em;
 float:left
}
.ltx_bibliography dd {
 margin-left:clamp(1em,4.5%,3em)
}
.ltx_bibitem {
 display:table;
 table-layout:fixed;
 list-style-type:none;
 width:100%;
 padding-bottom:.75em;
 font-family:var(--text-font-family)
}
.ltx_bibitem .ltx_tag {
 display:table-cell;
 position:relative;
 left:-2.5rem;
 top:.24rem;
 line-height:1.5rem;
 text-align:left;
 vertical-align:text-top;
 word-break:normal;
 overflow-wrap:break-word
}
@media only screen and (max-width:52rem) {
 .ltx_bibitem .ltx_tag {
  display:block;
  padding-bottom:.33em;
  width:36%
 }
}
@media only screen and (min-width:52.01rem) {
 .ltx_bibitem .ltx_tag {
  width:14%
 }
}
.ltx_bibitem .ltx_bibblock {
 display:inline-block;
 text-align:left;
 padding-left:.5em;
 max-width:40em;
 line-height:1.5rem;
 vertical-align:text-top
}
.ltx_bib_title {
 font-style:italic
}
.ltx_bib_article .bib-title {
 font-style:normal!important
}
.ltx_bib_journal {
 font-style:italic
}
.ltx_bib_volume {
 font-weight:700
}
.ltx_tag_bibitem:active~*,
.ltx_tag_bibitem:hover~*,
.ltx_tag_bibitem~:active,
.ltx_tag_bibitem~:hover {
 background-color:var(--note-highlight-color);
 z-index:100
}
.ltx_indexlist {
 columns:2;
 -webkit-columns:2;
 -moz-columns:2;
 list-style-type:none;
 padding-left:0
}
.ltx_indexentry>.ltx_indexlist {
 columns:1;
 -webkit-columns:1;
 -moz-columns:1;
 margin:.2rem 1rem 0
}
.ltx_indexentry {
 font-family:var(--text-font-family);
 font-size:.85rem;
 padding-bottom:.15rem
}
.ltx_indexrefs .ltx_ref {
 color:var(--index-ref-color);
 white-space:nowrap
}
section.ltx_conversion_report>.ltx_para {
 background:#f5f5f5;
 width:var(--main-width);
 padding:.1rem 1rem .1rem 1rem;
 border-radius:.8rem;
 line-height:1rem;
 font-family:var(--code-font-family);
 font-size:.8rem;
 word-break:break-word
}
section.ltx_conversion_report>.ltx_para>.ltx_p {
 text-align:left;
 line-height:1rem
}
:not(.ltx_quote)>blockquote.ltx_quote:not(.ltx_epigraph) {
 border-left:.188rem solid var(--border-color);
 font-size:1em;
 font-style:italic;
 line-height:1.5em;
 margin:1.1em 0;
 padding:.5em 2em;
 position:relative;
 z-index:0
}
:not(.ltx_quote)>blockquote.ltx_quote:not(.ltx_epigraph):before {
 content:"";
 position:absolute;
 top:50%;
 left:-.25rem;
 height:2rem;
 background-color:var(--background-color);
 width:.25rem;
 margin-top:-1rem
}
:not(.ltx_quote)>blockquote.ltx_quote:not(.ltx_epigraph):after {
 content:"“";
 position:absolute;
 top:50%;
 left:-.6rem;
 color:var(--border-color);
 font-style:normal;
 font-size:1.5rem;
 line-height:2rem;
 text-align:center;
 width:1rem;
 margin-top:-.7rem
}
.ltx_quote>.ltx_p:last-child {
 margin-bottom:0
}
.ltx_quote>.ltx_break:last-child {
 display:none
}
.ltx_quote .ltx_break+.ltx_break+.ltx_break {
 display:none
}
.ltx_quote>.ltx_break:first-child,
.ltx_quote>.ltx_break:first-child+.ltx_break,
.ltx_quote>.ltx_break:first-child+.ltx_break+.ltx_break {
 display:none
}
blockquote.ltx_epigraph {
 width:calc(.5*var(--main-width))!important;
 margin-left:calc(.45*var(--main-width))!important
}
.ltx_abstract>.ltx_title_abstract+blockquote.ltx_quote:last-child,
.ltx_authors+.ltx_para:has(+ .ltx_section)>blockquote.ltx_quote:only-child,
.ltx_titlepage:not(:has(.ltx_abstract))>blockquote.ltx_quote:last-child {
 max-width:90%;
 margin:auto;
 border-left:initial;
 font-size:initial;
 font-style:initial;
 line-height:initial;
 padding:initial;
 position:initial;
 z-index:initial
}
.ltx_block,
.ltx_logical-block,
.ltx_p,
.ltx_para,
.ltx_quote {
 display:block
}
.ltx_inline-quote,
.ltx_quote.ltx_innerquote,
.ltx_quote.ltx_outerquote {
 display:inline
}
.ltx_align_left {
 text-align:left
}
.ltx_align_right {
 text-align:right
}
.ltx_align_center {
 text-align:center
}
.ltx_align_justify {
 text-align:justify;
 text-justify:inter-word;
 hyphens:auto
}
.ltx_align_top {
 vertical-align:top
}
.ltx_align_bottom {
 vertical-align:bottom
}
.ltx_align_middle {
 vertical-align:middle
}
.ltx_align_baseline {
 vertical-align:baseline
}
.ltx_align_floatleft {
 float:left
}
.ltx_align_floatright {
 float:right
}
.ltx_td.ltx_align_center,
.ltx_td.ltx_align_left,
.ltx_td.ltx_align_right,
.ltx_th.ltx_align_center,
.ltx_th.ltx_align_left,
.ltx_th.ltx_align_right {
 white-space:nowrap
}
.ltx_td.ltx_align_center.ltx_wrap,
.ltx_td.ltx_align_justify,
.ltx_td.ltx_align_left.ltx_wrap,
.ltx_td.ltx_align_right.ltx_wrap,
.ltx_th.ltx_align_center.ltx_wrap,
.ltx_th.ltx_align_justify,
.ltx_th.ltx_align_left.ltx_wrap,
.ltx_th.ltx_align_right.ltx_wrap {
 white-space:normal
}
.ltx_graphics {
 display:block
}
@media only screen and (max-width:52rem) {
 .ltx_graphics {
  max-width:95%
 }
}
@media only screen and (min-width:52.01rem) {
 .ltx_graphics {
  max-width:var(--main-width)
 }
}
.ltx_caption .ltx_graphics {
 display:inline-block
}
:not(mtext):not(.ltx_flex_cell)>:not(mtext):not(.ltx_flex_cell)>.ltx_img_landscape {
 max-width:100%;
 max-height:calc(var(--main-width)/1.66);
 width:auto;
 height:auto
}
:not(mtext):not(.ltx_flex_cell)>:not(mtext):not(.ltx_flex_cell)>.ltx_img_portrait {
 max-height:var(--main-width);
 max-width:calc(var(--main-width)/1.33);
 width:auto
}
:not(mtext):not(.ltx_flex_cell)>:not(mtext):not(.ltx_flex_cell)>.ltx_img_square {
 max-height:calc(var(--main-width)/1.33);
 width:auto
}
@media only screen and (max-width:52rem) {
 :not(mtext):not(.ltx_flex_cell)>:not(mtext):not(.ltx_flex_cell)>.ltx_img_portrait {
  height:auto
 }
 :not(mtext):not(.ltx_flex_cell)>:not(mtext):not(.ltx_flex_cell)>.ltx_img_square {
  height:auto
 }
}
:not(.ltx_eqn_cell)>math mtext img.ltx_img_landscape,
:not(.ltx_eqn_cell)>math mtext img.ltx_img_portrait,
:not(.ltx_eqn_cell)>math mtext img.ltx_img_square,
:not(.ltx_eqn_cell)>math mtext object.ltx_img_landscape,
:not(.ltx_eqn_cell)>math mtext object.ltx_img_portrait,
:not(.ltx_eqn_cell)>math mtext object.ltx_img_square,
:not(.ltx_flex_cell):not(.ltx_figure):not(.ltx_transformed_inner):not(.ltx_td):not(.ltx_th)>.ltx_p:not(.ltx_align_center) img.ltx_img_landscape,
:not(.ltx_flex_cell):not(.ltx_figure):not(.ltx_transformed_inner):not(.ltx_td):not(.ltx_th)>.ltx_p:not(.ltx_align_center) img.ltx_img_portrait,
:not(.ltx_flex_cell):not(.ltx_figure):not(.ltx_transformed_inner):not(.ltx_td):not(.ltx_th)>.ltx_p:not(.ltx_align_center) img.ltx_img_square,
:not(.ltx_flex_cell):not(.ltx_figure):not(.ltx_transformed_inner):not(.ltx_td):not(.ltx_th)>.ltx_p:not(.ltx_align_center) object.ltx_img_landscape,
:not(.ltx_flex_cell):not(.ltx_figure):not(.ltx_transformed_inner):not(.ltx_td):not(.ltx_th)>.ltx_p:not(.ltx_align_center) object.ltx_img_portrait,
:not(.ltx_flex_cell):not(.ltx_figure):not(.ltx_transformed_inner):not(.ltx_td):not(.ltx_th)>.ltx_p:not(.ltx_align_center) object.ltx_img_square {
 width:1rem;
 min-width:1rem!important;
 min-height:1rem!important
}
.ltx_markedasmath.ltx_graphics,
.ltx_markedasmath>.ltx_graphics,
mtext>.ltx_graphics {
 display:inline;
 max-width:calc(.9*var(--main-width))!important
}
.ltx_flex_cell .ltx_img_landscape,
.ltx_flex_cell .ltx_img_portrait,
.ltx_flex_cell .ltx_img_square {
 width:100%;
 height:auto;
 max-height:var(--main-width)
}
.ltx_note_content .ltx_graphics {
 max-width:10rem;
 max-height:3rem
}
.ltx_flex_figure {
 display:flex;
 flex-flow:row wrap;
 width:auto;
 justify-content:center;
 align-items:flex-end;
 object-fit:contain;
 margin-bottom:1rem
}
.ltx_flex_figure>.ltx_flex_cell>.ltx_figure,
.ltx_flex_figure>.ltx_flex_cell>.ltx_float,
.ltx_flex_figure>.ltx_flex_cell>.ltx_graphics,
.ltx_flex_figure>.ltx_flex_cell>.ltx_graphics.ltx_centering,
.ltx_flex_figure>.ltx_flex_cell>.ltx_minipage {
 margin:.1rem 1px .1rem;
 width:100%;
 max-height:100%
}
.ltx_flex_figure>.ltx_flex_cell>.ltx_inline-block,
.ltx_flex_figure>.ltx_flex_cell>.ltx_minipage {
 width:100%!important
}
@media only screen and (max-width:46rem) {
 .ltx_flex_figure>.ltx_flex_cell.ltx_flex_size_1 {
  min-width:20rem
 }
}
@media only screen and (min-width:46.01rem) {
 .ltx_flex_figure>.ltx_flex_cell.ltx_flex_size_1 {
  min-width:25rem
 }
}
.ltx_flex_figure>.ltx_flex_cell.ltx_flex_size_2 img.ltx_graphics {
 min-width:20rem
}
.ltx_flex_figure>.ltx_flex_cell.ltx_flex_size_3 img.ltx_graphics {
 min-width:15rem
}
.ltx_flex_figure>.ltx_flex_cell.ltx_flex_size_4 img.ltx_graphics {
 min-width:10rem
}
.ltx_flex_figure>.ltx_flex_cell img.ltx_graphics {
 min-width:7rem
}
.ltx_flex_cell.ltx_flex_size_1,
.ltx_flex_cell.ltx_flex_size_1 .ltx_tabular,
.ltx_lstlisting.ltx_flex_size_1,
.ltx_minipage.ltx_flex_size_1 .ltx_float .ltx_caption,
.ltx_table.ltx_flex_size_1 .ltx_caption {
 max-width:var(--main-width)
}
.ltx_flex_figure.ltx_flex_table .ltx_flex_size_2 {
 max-width:calc(.5*var(--main-width))
}
.ltx_flex_cell.ltx_flex_size_2,
.ltx_flex_size_2 .ltx_tabular,
.ltx_flex_size_2.ltx_tabular,
.ltx_lstlisting.ltx_flex_size_2,
.ltx_minipage.ltx_flex_size_2 .ltx_float .ltx_caption,
.ltx_table.ltx_flex_size_2 .ltx_caption {
 max-width:calc(.5*var(--main-width))
}
.ltx_flex_figure.ltx_flex_table .ltx_flex_size_3 {
 max-width:calc(.33*var(--main-width))
}
.ltx_flex_cell.ltx_flex_size_3,
.ltx_flex_size_3 .ltx_tabular,
.ltx_flex_size_3.ltx_tabular,
.ltx_lstlisting.ltx_flex_size_3,
.ltx_minipage.ltx_flex_size_3 .ltx_float .ltx_caption,
.ltx_table.ltx_flex_size_3 .ltx_caption {
 max-width:calc(.33*var(--main-width))
}
.ltx_flex_figure.ltx_flex_table .ltx_flex_size_4,
.ltx_flex_figure.ltx_flex_table .ltx_flex_size_many {
 max-width:calc(.25*var(--main-width))
}
.ltx_flex_cell.ltx_flex_size_4,
.ltx_flex_size_4 .ltx_tabular,
.ltx_flex_size_4.ltx_tabular,
.ltx_lstlisting.ltx_flex_size_4,
.ltx_minipage.ltx_flex_size_4 .ltx_float .ltx_caption,
.ltx_table.ltx_flex_size_4 .ltx_caption {
 max-width:calc(.25*var(--main-width))
}
.ltx_flex_figure.ltx_flex_table .ltx_flex_size_many {
 max-width:calc(.28*var(--main-width))
}
.ltx_flex_cell.ltx_flex_size_many,
.ltx_flex_size_many .ltx_tabular,
.ltx_flex_size_many.ltx_tabular,
.ltx_lstlisting.ltx_flex_size_many,
.ltx_minipage.ltx_flex_size_many .ltx_float .ltx_caption,
.ltx_table.ltx_flex_size_many .ltx_caption {
 max-width:calc(.25*var(--main-width))
}
.ltx_flex_figure .ltx_flex_cell {
 flex:1 1 0px;
 margin:.1rem 1px .1rem
}
.ltx_flex_figure .ltx_flex_break {
 flex-basis:100%;
 height:0
}
.ltx_flex_cell>.ltx_figure {
 margin:0
}
.ltx_flex_figure .ltx_tabular .ltx_td,
.ltx_flex_figure .ltx_tabular .ltx_th {
 padding:.1rem .2rem
}
.ltx_figure img {
 color:var(--image-color);
 background-color:var(--image-background-color);
 -webkit-transition:all .2s ease;
 -moz-transition:all .2s ease;
 -ms-transition:all .2s ease;
 -o-transition:all .2s ease;
 transition:all .2s ease
}
.ltx_figure img:active,
.ltx_p>img.ltx_graphics:active,
.ltx_text>img.ltx_graphics:active {
 -webkit-transform:scale(1.8);
 -moz-transform:scale(1.8);
 -ms-transform:scale(1.8);
 -o-transform:scale(1.8);
 transform:scale(1.8);
 overflow:visible;
 background-color:#fff
}
.ltx_p>img.ltx_graphics {
 display:inline
}
.ltx_para>svg:only-child {
 margin:auto;
 display:block;
 max-width:var(--main-width)
}
svg {
 color:var(--image-color);
 background-color:var(--image-background-color);
 z-index:-1
}
foreignObject .ltx_text {
 word-wrap:initial;
 white-space:nowrap
}
.ltx_para>.ltx_tabular {
 margin-bottom:1rem
}
.ltx_tabular .ltx_tabular {
 width:100%
}
.ltx_tabular.ltx_tabbing {
 display:table
}
.ltx_inline-logical-block,
.ltx_inline-logical-block .ltx_para {
 display:inline
}
.ltx_inline-block,
.ltx_inline-block .ltx_para {
 display:inline-block
}
.ltx_nodisplay {
 display:none
}
.ltx_inline-block>.ltx_p {
 width:auto!important
}
.ltx_title_document>.ltx_inline-block,
.ltx_title_document>.ltx_parbox {
 width:auto!important
}
:not(.ltx_flex_cell)>.ltx_figure,
:not(.ltx_flex_cell)>.ltx_table {
 display:flex;
 flex-direction:column;
 align-items:center;
 text-align:center;
 margin:4rem auto 4rem
}
.ltx_caption {
 font-family:var(--text-font-family)
}
.ltx_figure .ltx_caption,
.ltx_table .ltx_caption {
 text-align:justify;
 line-height:1.5rem;
 margin-top:1.5rem;
 margin-bottom:1.5rem
}
.ltx_flex_figure .ltx_figure .ltx_caption {
 text-align:center
}
.ltx_figure .ltx_parbox,
.ltx_table {
 text-align:justify
}
.ltx_parbox {
 text-indent:0;
 display:inline-block
}
.ltx_minipage {
 align-self:normal;
 display:inline-block
}
.ltx_minipage.ltx_align_center {
 align-self:center
}
.ltx_minipage .ltx_float,
.ltx_minipage .ltx_float .ltx_caption {
 display:inline-block
}
.ltx_minipage.ltx_align_middle {
 margin:auto;
 width:auto!important
}
.ltx_minipage>.ltx_graphics {
 max-width:100%
}
.ltx_flex_size_2 .ltx_tabular.ltx_minipage {
 margin:1rem
}
.ltx_flex_size_3 .ltx_tabular.ltx_minipage {
 margin:.66rem
}
.ltx_flex_size_4 .ltx_tabular.ltx_minipage {
 margin:.5rem
}
.ltx_listing {
 display:block;
 max-width:var(--main-width);
 margin-bottom:1rem
}
.ltx_listing>.ltx_framed_rectangle {
 border-style:none
}
.ltx_listing .ltx_listingline {
 text-align:justify;
 white-space:nowrap;
 min-height:1rem;
 display:block;
 font-size:.7rem
}
.ltx_listing .ltx_listingline .ltx_text {
 font-size:.7rem!important
}
.ltx_listing .ltx_tag_listingline {
 padding-right:.3rem;
 border-right:solid;
 border-width:thin;
 margin-right:.3rem;
 text-align:right;
 width:1rem;
 display:inline-block
}
.ltx_lst_space {
 white-space:pre
}
.ltx_listing_data {
 display:none
}
.ltx_lstlisting.ltx_text {
 white-space:break-spaces
}
.ltx_lstlisting.ltx_align_center {
 text-align:left
}
.ltx_float {
 margin:3.5rem auto 3.5rem
}
.ltx_minipage>.ltx_float {
 margin:.2rem auto .2rem
}
.ltx_float .ltx_caption {
 text-align:justify;
 text-justify:inter-word;
 hyphens:auto;
 border-top:solid var(--border-color);
 border-bottom:solid var(--border-color);
 border-width:.1rem;
 margin-top:.2rem;
 margin-bottom:.2rem;
 padding-top:.2rem;
 padding-bottom:.2rem
}
.ltx_rule {
 color:var(--border-color);
 vertical-align:middle;
 background-color:var(--border-color)!important
}
.ltx_transformed_outer {
 width:auto!important;
 height:auto!important
}
.ltx_figure.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_figure>.ltx_inline-block>.ltx_transformed_inner,
.ltx_figure>.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_inline-block.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_para>.ltx_inline-block:only-child.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_table.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_table>.ltx_inline-block>.ltx_transformed_inner,
.ltx_table>.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_tr:only-child>.ltx_td:only-child>.ltx_inline-block>.ltx_transformed_inner,
.ltx_tr:only-child>.ltx_td:only-child>.ltx_p:only-child>.ltx_inline-block>.ltx_transformed_inner,
.ltx_tr:only-child>.ltx_td:only-child>.ltx_p:only-child>.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_tr:only-child>.ltx_td:only-child>.ltx_transformed_outer>.ltx_transformed_inner {
 transform:none!important;
 width:initial!important
}
span.ltx_transformed_inner {
 display:inline-block
}
.ltx_transformed_inner>.ltx_p {
 margin:0;
 padding:0
}
.ltx_eqn_cell>.ltx_transformed_outer>.ltx_transformed_inner,
.ltx_flex_cell>.ltx_transformed_outer>.ltx_transformed_inner {
 transform:none!important
}
.ltx_phantom {
 visibility:hidden
}
.ltx_font_serif {
 font-family:var(--text-font-family)
}
.ltx_font_sansserif {
 font-family:var(--headings-font-family)
}
.ltx_font_typewriter {
 font-family:var(--code-font-family)
}
.ltx_font_bold {
 font-weight:700
}
.ltx_font_medium {
 font-weight:400
}
.ltx_font_italic {
 font-style:italic
}
.ltx_font_upright {
 font-style:normal;
 font-variant:normal
}
.ltx_font_slanted {
 font-style:oblique
}
.ltx_font_smallcaps {
 font-variant:small-caps;
 font-style:normal
}
.ltx_font_mathcaligraphic {
 font-family:var(--math-caligraphic-font-family)
}
.ltx_mathvariant_italic {
 font-style:italic
}
.ltx_mathvariant_bold {
 font-weight:700
}
.ltx_mathvariant_bold-italic {
 font-style:italic;
 font-weight:700
}
.ltx_mathvariant_sans-serif {
 font-family:sans-serif
}
.ltx_mathvariant-bold-sans-serif {
 font-family:sans-serif;
 font-weight:700
}
.ltx_mathvariant-sans-serif-italic {
 font-family:sans-serif;
 font-style:italic
}
.ltx_mathvariant-bold-sans-serif-italic {
 font-family:sans-serif;
 font-style:italic;
 font-weight:700
}
.ltx_mathvariant_monospace {
 font-family:monospace
}
.ltx_mathvariant_double-struck {
 font-weight:700
}
.ltx_mathvariant_script {
 font-family:var(--math-caligraphic-font-family),cursive
}
.ltx_mathvariant_bold-script {
 font-family:var(--math-caligraphic-font-family),cursive;
 font-weight:700
}
.ltx_mathvariant_bold-fraktur {
 font-weight:700
}
.ltx_eqn_div {
 display:block;
 width:95%;
 text-align:center
}
.ltx_eqn_table {
 display:table;
 width:100%;
 border-collapse:collapse;
 margin:.65rem auto .65rem
}
.ltx_eqn_row {
 display:table-row
}
.ltx_eqn_cell {
 display:table-cell;
 width:auto;
 padding-top:.3rem;
 padding-bottom:.3rem;
 padding-right:.2rem;
 padding-left:.2rem
}
.ltx_eqn_cell.ltx_eqn_eqno {
 width:3em;
 white-space:nowrap
}
.ltx_tag.ltx_tag_equation,
.ltx_tag.ltx_tag_equationgroup {
 font-size:.9em
}
table.ltx_eqn_align tr.ltx_equation td.ltx_align_center+td.ltx_align_center,
table.ltx_eqn_align tr.ltx_equation td.ltx_align_center+td.ltx_align_right,
table.ltx_eqn_align tr.ltx_equation td.ltx_align_left+td.ltx_align_center,
table.ltx_eqn_align tr.ltx_equation td.ltx_align_left+td.ltx_align_right {
 padding-left:3em
}
table.ltx_eqn_eqnarray tr.ltx_eqn_lefteqn+tr td.ltx_align_right {
 min-width:2em
}
.ltx_eqn_eqno.ltx_align_right .ltx_tag {
 float:right
}
.ltx_eqn_center_padleft,
.ltx_eqn_center_padright {
 width:50%;
 min-width:2em
}
.ltx_eqn_left_padleft,
.ltx_eqn_right_padright {
 min-width:2em
}
.ltx_eqn_left_padright,
.ltx_eqn_right_padleft {
 width:100%
}
.ltx_description,
.ltx_enumerate,
.ltx_itemize {
 display:block
}
.ltx_item>.ltx_para>.ltx_description,
.ltx_item>.ltx_para>.ltx_enumerate,
.ltx_item>.ltx_para>.ltx_itemize {
 margin-top:.5rem;
 margin-left:.5rem
}
.ltx_description .ltx_item,
.ltx_enumerate .ltx_item,
.ltx_itemize .ltx_item {
 display:list-item
}
li.ltx_item>.ltx_tag {
 display:inline;
 margin-left:-2.5rem;
 padding-right:.5rem;
 text-align:right
}
.ltx_item .ltx_tag+.ltx_para,
.ltx_item .ltx_tag+.ltx_para .ltx_p {
 display:inline
}
.ltx_item .ltx_para {
 margin-bottom:0;
 display:inline
}
.ltx_item+.ltx_item {
 margin-top:1em
}
dd.ltx_item+dt.ltx_item {
 margin-top:0
}
dl.ltx_description {
 list-style-type:none
}
dl.ltx_description dt {
 margin-right:.5em;
 float:left;
 font-weight:700;
 font-size:95%
}
dl.ltx_description dd.ltx_item {
 margin-left:3em;
 text-indent:0
}
dl.ltx_description dl.ltx_description dd {
 margin-left:3em;
 margin-bottom:.75em
}
.ltx_table .ltx_description,
.ltx_table .ltx_enumerate,
.ltx_table .ltx_itemize {
 text-align:justify;
 text-justify:inter-word;
 hyphens:auto;
 font-family:var(--text-font-family);
 line-height:1.5rem
}
.ltx_tabular {
 display:inline-table;
 border-collapse:collapse
}
.ltx_tabular.ltx_centering {
 display:table;
 margin-left:auto;
 margin-right:auto
}
.ltx_graphics.ltx_centering,
.ltx_picture.ltx_centering {
 margin-left:auto;
 margin-right:auto;
 text-align:center
}
.ltx_picture.ltx_centering {
 vertical-align:middle
}
.ltx_tbody,
.ltx_tfoot,
.ltx_thead {
 display:table-row-group
}
.ltx_tr {
 display:table-row
}
.ltx_td,
.ltx_th {
 display:table-cell
}
.ltx_framed {
 border:.063rem solid var(--border-color)
}
span.ltx_framed {
 display:inline-block;
 text-indent:0
}
.ltx_tabular .ltx_td,
.ltx_tabular .ltx_th {
 padding:.1em .5em;
 max-width:var(--main-width);
 word-wrap:break-word;
 white-space:normal
}
.ltx_tabular .ltx_td.ltx_nopad_l,
.ltx_tabular .ltx_th.ltx_nopad_l {
 padding-left:0
}
.ltx_tabular .ltx_td.ltx_nopad_r,
.ltx_tabular .ltx_th.ltx_nopad_r {
 padding-right:0
}
.ltx_tabular .ltx_tr td:first-child::after,
.ltx_tabular .ltx_tr th:first-child::after {
 content:"";
 display:inline-block;
 vertical-align:top;
 min-height:1em
}
.ltx_tabular .ltx_th.ltx_th_column {
 white-space:nowrap
}
.ltx_border_t {
 border-top:.063rem solid var(--border-color)
}
.ltx_border_r {
 border-right:.063rem solid var(--border-color)
}
.ltx_border_b {
 border-bottom:.063rem solid var(--border-color)
}
.ltx_border_l {
 border-left:.063rem solid var(--border-color)
}
.ltx_border_tt {
 border-top:.188rem double var(--border-color)
}
.ltx_border_rr {
 border-right:.188rem double var(--border-color)
}
.ltx_border_bb {
 border-bottom:.188rem double var(--border-color)
}
.ltx_border_ll {
 border-left:.188rem double var(--border-color)
}
.ltx_border_T {
 border-top:.063rem solid var(--border-light-color)
}
.ltx_border_R {
 border-right:.063rem solid var(--border-light-color)
}
.ltx_border_B {
 border-bottom:.063rem solid var(--border-light-color)
}
.ltx_border_L {
 border-left:.063rem solid var(--border-light-color)
}
.ltx_framed_bottom:not(:empty),
.ltx_framed_left:not(:empty),
.ltx_framed_rectangle:not(:empty),
.ltx_framed_right:not(:empty),
.ltx_framed_top:not(:empty),
.ltx_framed_topbottom:not(:empty),
.ltx_framed_underline:not(:empty) {
 display:inline-block
}
.ltx_framed_rectangle {
 border-style:solid;
 border-width:.063rem;
 padding-left:.3rem;
 padding-right:.3rem
}
.ltx_framed_top {
 border-top-style:solid;
 border-top-width:.063rem
}
.ltx_framed_left {
 border-left-style:solid;
 border-left-width:.063rem
}
.ltx_framed_right {
 border-right-style:solid;
 border-right-width:.063rem
}
.ltx_framed_bottom,
.ltx_framed_underline {
 border-bottom-style:solid;
 border-bottom-width:.063rem
}
.ltx_framed_topbottom {
 border-top-style:solid;
 border-top-width:.063rem;
 border-bottom-style:solid;
 border-bottom-width:.063rem
}
.ltx_framed_leftright {
 border-left-style:solid;
 border-left-width:.063rem;
 border-right-style:solid;
 border-right-width:.063rem
}
.ltx_verbatim {
 text-align:left;
 font-size:90%
}
.ltx_tag_note {
 display:none
}
.ltx_ERROR,
.ltx_FATAL,
.ltx_INFO,
.ltx_WARNING {
 text-align:left;
 display:inline
}
.ltx_INFO {
 color:var(--info-text-color)
}
.ltx_WARNING {
 color:var(--warning-text-color)
}
.ltx_ERROR {
 font-weight:400;
 color:var(--error-text-color)
}
.ltx_FATAL {
 font-weight:400;
 color:var(--fatal-text-color)
}
.ltx_rdf {
 display:none
}
.ltx_missing,
.ltx_nounicode {
 color:var(--error-text-color)
}
.ltx_nodisplay {
 display:none
}
.ltx_missing_label {
 color:var(--warning-text-color)
}
merror.ltx_ERROR {
 font-size:.75rem;
 background-color:var(--background-color)
}
mjx-merror {
 background-color:var(--background-color)!important
}
.ltx_item:has(> .ltx_para > .ltx_p > math mrow:nth-of-type(7)),
.ltx_p:has(> math mrow:nth-of-type(7)) {
 text-align:left
}
mfrac>* {
 font-size:inherit;
 padding:.1em
}
.ltx_section:has(> .ltx_title_section:only-child):has(+ .ltx_bibliography) {
 display:none
}
.ltx_th .ltx_parbox,
.ltx_tr .ltx_parbox {
 width:initial!important
}
.ltx_para.ltx_minipage.ltx_align_center {
 margin:auto;
 display:block
}
