.paper-main {
    padding: 36px 0 110px;
}

.paper-main .ltx_page_main {
    margin: 0 auto;
    font-size: 0.9375rem;
    line-height: 1.62;
    aspect-ratio: auto;
    min-height: calc(var(--page-width) * 11 / 8.5);
}

.paper-main .ltx_title_document {
    font-family: var(--serif);
    font-size: clamp(1.25rem, 3.2vw, 1.625rem);
    font-weight: 400;
    line-height: 1.25;
    text-align: center;
    margin: 0 0 1.4em;
}

.paper-main .ltx_abstract {
    margin: 0 auto 2.5em;
    font-style: italic;
    color: var(--paper-muted);
    font-size: 0.9375rem;
    line-height: 1.62;
}

.paper-main .ltx_title_section {
    font-family: var(--serif);
    font-size: 1.25rem;
    font-weight: 400;
    margin: 2.2em 0 1em;
}

.paper-main .ltx_title_subsection {
    font-family: var(--serif);
    font-size: 1.0625rem;
    font-weight: 400;
    margin: 1.8em 0 0.8em;
}

.paper-main .ltx_title_subsubsection {
    font-family: var(--serif);
    font-size: 0.9375rem;
    font-weight: 400;
    font-style: italic;
    margin: 1.5em 0 0.7em;
}

.paper-main .ltx_title_paragraph,
.paper-main .ltx_title_subparagraph {
    font-family: var(--serif);
    font-size: 0.9375rem;
    font-weight: 400;
    font-style: italic;
    display: inline;
    margin: 0 0.55em 0 0;
}

.paper-main .ltx_title_part {
    font-family: var(--serif);
    font-size: clamp(1.25rem, 3.2vw, 1.5rem);
    font-weight: 400;
    text-align: center;
    margin: 2.8em 0 1.4em;
}

.paper-main .ltx_title_appendix,
.paper-main .ltx_title_bibliography {
    font-family: var(--serif);
    font-size: 1.25rem;
    font-weight: 400;
    margin: 2.2em 0 1em;
}

.paper-main .ltx_titlepage {
    text-align: center;
    margin: 0 0 2.8em;
}

.paper-main .ltx_titlepage .ltx_p {
    margin: 0 0 0.7em;
}

.paper-main .ltx_titlepage .ltx_text {
    font-size: inherit !important;
    font-weight: 400 !important;
}

.paper-main .ltx_titlepage .ltx_p:first-child {
    color: var(--paper-muted);
    font-size: 0.9375rem;
}

.paper-main .ltx_titlepage .ltx_p:last-child {
    font-family: var(--serif);
    font-size: clamp(1.25rem, 3.2vw, 1.625rem);
    font-weight: 400;
    line-height: 1.25;
}

.paper-main .ltx_section,
.paper-main .ltx_part,
.paper-main .ltx_appendix,
.paper-main .ltx_subsection,
.paper-main .ltx_subsubsection {
    scroll-margin-top: 1.2em;
}

.paper-main .ltx_p,
.paper-main .ltx_para > .ltx_p:first-child,
.paper-main .ltx_indent > .ltx_p:first-child,
.paper-main .ltx_title_abstract + .ltx_p {
    text-indent: 0 !important;
}

.paper-main img {
    max-width: 100%;
    height: auto;
}

.paper-main #S5.F1 {
    margin: 1.6em auto;
}

.paper-main #S5.F1 img {
    width: min(100%, 420px);
    height: auto;
}

.paper-main .ltx_ref {
    white-space: nowrap;
}

.paper-main .ltx_equationgroup,
.paper-main table.ltx_equationgroup {
    display: block;
    width: 100%;
    max-width: 100%;
    overflow: visible;
}

.paper-main .ltx_equationgroup tbody,
.paper-main .ltx_equationgroup tr {
    display: block;
    width: 100%;
}

.paper-main .ltx_equationgroup td.ltx_eqn_cell,
.paper-main .ltx_equationgroup td.ltx_td {
    display: block;
    width: 100% !important;
    max-width: 100%;
    text-align: left !important;
    overflow: visible;
}

.paper-main .ltx_eqn_center_padleft,
.paper-main .ltx_eqn_center_padright {
    display: none;
}

.paper-main a {
    color: inherit;
    text-decoration: underline;
    text-underline-offset: 2px;
}

.paper-main .ltx_math_display {
    margin: 0.6em 0;
    text-align: center;
    max-width: 100%;
    overflow: visible;
}

.paper-main .prop-eq {
    font-size: 0.9em;
}

.paper-main .ltx_equation .ltx_math_display {
    margin: 0;
}

.paper-main mjx-container {
    font-size: 95%;
    max-width: 100%;
    overflow: visible !important;
}

.paper-main .ltx_equation,
.paper-main .ltx_equationgroup,
.paper-main .ltx_math_display,
.paper-main .ltx_eqn_table,
.paper-main .ltx_eqn_cell {
    max-width: 100%;
    overflow: visible !important;
}

.paper-main .ltx_eqn_table {
    width: 100%;
    table-layout: fixed;
}

.paper-main .ltx_eqn_center_padleft,
.paper-main .ltx_eqn_center_padright {
    width: 1%;
    min-width: 0;
}

.paper-main .ltx_eqn_cell.ltx_align_center {
    overflow: visible;
    max-width: 100%;
}

.paper-main .ltx_eqn_eqno {
    width: 2.2em;
}

/* Algorithm */
.paper-main .algorithm,
.paper-main .ltx_float_algorithm {
    margin: 1.6em 0 2em;
    padding: 0.7em 0.85em 0.9em;
    border: 1px solid var(--ink);
    background: #f8f7f2;
    font-family: var(--serif);
    font-size: 0.84375rem;
    line-height: 1.45;
    overflow: visible;
}

.paper-main .algorithm-caption,
.paper-main .ltx_float_algorithm .ltx_caption {
    display: block;
    margin: 0 0 0.7em;
    padding-bottom: 0.45em;
    border-bottom: 1px solid var(--ink);
    font-size: 0.84375rem;
}

.paper-main .algorithm-tag {
    font-weight: 700;
    margin-right: 0.4em;
}

.paper-main .algorithm-lines {
    list-style: none;
    margin: 0;
    padding: 0;
}

.paper-main .algorithm-lines li {
    display: grid;
    grid-template-columns: 1.8em 1fr;
    column-gap: 0.55em;
    margin: 0.18em 0;
    align-items: baseline;
}

.paper-main .algorithm-lines li::before {
    content: attr(data-n) ":";
    font-family: var(--mono);
    font-size: 0.6875rem;
    color: var(--paper-muted);
}

.paper-main .algorithm-lines .indent-1 { padding-left: 1.1em; }
.paper-main .algorithm-lines .indent-2 { padding-left: 2.2em; }
.paper-main .algorithm-lines .indent-3 { padding-left: 3.3em; }
.paper-main .algorithm-lines li > span {
    min-width: 0;
}

.paper-main .algo-kw {
    font-weight: 700;
}

.paper-main .algo-comment {
    display: inline;
    color: var(--paper-muted);
    font-style: italic;
}

.paper-main .algo-comment::before {
    content: " ▷ ";
    font-style: normal;
}

.paper-main .ltx_listing {
    margin: 0;
    overflow-x: auto;
}

.paper-main .ltx_listingline {
    white-space: normal;
    min-height: 1.35em;
}

.paper-main .ltx_listingline > span[style*="float:right"] {
    float: none !important;
    display: block;
    color: var(--paper-muted);
    font-style: italic;
    margin: 0.15em 0 0.35em 2.4em;
}

.paper-main .ltx_bibliography {
    margin-top: 3em;
    padding-top: 2em;
    border-top: 1px solid var(--paper-muted);
}

.paper-main .ltx_biblist {
    list-style: none;
    margin: 0;
    padding: 0;
}

.paper-main .ltx_bibitem {
    margin: 0 0 1.15em;
    padding: 0;
}

.paper-main .ltx_bibitem .ltx_tag {
    display: block;
    font-weight: 400;
    margin: 0 0 0.15em;
    width: auto;
}

.paper-main .ltx_bibblock {
    display: block;
}

.paper-main .ltx_bibliography a {
    text-decoration: underline;
    text-underline-offset: 2px;
}

.paper-main .ltx_bibliography .ltx_ref {
    white-space: normal;
}

.paper-main .ltx_TOC {
    margin: 0 0 3em;
    padding: 0 0 2.2em;
    border-bottom: 1px solid var(--paper-muted);
}

.paper-main .ltx_title_contents {
    font-family: var(--serif);
    font-size: 1.25rem;
    font-weight: 400;
    margin: 0 0 1.1em;
}

.paper-main .ltx_toclist {
    list-style: none;
    margin: 0;
    padding: 0;
}

.paper-main .ltx_toclist .ltx_toclist {
    margin: 0.15em 0 0.45em 1.35em;
}

.paper-main .ltx_tocentry {
    margin: 0.22em 0;
}

.paper-main .ltx_tocentry_part > a {
    display: inline-block;
    margin-top: 0.85em;
}

.paper-main .ltx_TOC a {
    text-decoration: none;
}

.paper-main .ltx_TOC a:hover {
    text-decoration: underline;
    text-underline-offset: 2px;
}

.paper-main .ltx_TOC .ltx_ref {
    white-space: normal;
}

.paper-main .ltx_tag_ref {
    margin-right: 0.35em;
}

.paper-main .ltx_figure,
.paper-main .ltx_table {
    width: 100%;
    max-width: 100%;
    margin: 1.6em auto;
    align-items: stretch;
}

.paper-main .ltx_flex_figure,
.paper-main .ltx_flex_cell,
.paper-main .ltx_flex_size_1,
.paper-main .ltx_flex_size_1 .ltx_graphics {
    max-width: 100%;
}

.paper-main .ltx_tabular {
    display: table;
    width: 100%;
    max-width: 100%;
    font-size: 0.84375rem;
    border-collapse: collapse;
}

.paper-main .ltx_td,
.paper-main .ltx_th {
    white-space: normal !important;
    padding: 0.25em 0.45em;
}

.paper-main .ltx_caption {
    max-width: 100%;
    font-size: 0.84375rem;
    line-height: 1.45;
}

@media (max-width: 600px) {
    .paper-main .ltx_page_main {
        margin-inline: -6px;
    }
}

@media (max-width: 600px) and (hover: none) and (pointer: coarse) {
    .paper-main .ltx_page_main {
        font-size: 0.75rem;
    }

    .paper-main .ltx_title_document,
    .paper-main .ltx_titlepage .ltx_p:last-child,
    .paper-main .ltx_title_part {
        font-size: 1.125rem;
    }

    .paper-main .ltx_title_section,
    .paper-main .ltx_title_appendix,
    .paper-main .ltx_title_bibliography,
    .paper-main .ltx_title_contents {
        font-size: 0.9375rem;
    }

    .paper-main .ltx_title_subsection {
        font-size: 0.8125rem;
    }

    .paper-main .ltx_abstract,
    .paper-main .ltx_titlepage .ltx_p:first-child {
        font-size: 0.75rem;
    }
}