:root{--learn-display:Garamond, var(--font-eb-garamond), serif;--learn-body:Crimson, var(--font-crimson), Palatino, serif;--learn-ui:"Source Sans 3", var(--font-source-sans), "Source Sans Pro", sans-serif;--algo-bg:#fff;--algo-fg:#000;--algo-heading:#111;--algo-muted:#666;--algo-sidebar:#f8f8f8;--algo-border:#eaecef;--algo-code-bg:#f8f8f8;--algo-code-border:#ddd;--algo-link:#0645ad;--algo-link-hover:#06e;--algo-sidebar-w:250px;--algo-menu-h:54px;--ad-box:#fff}html.dark{--algo-bg:#111;--algo-fg:#e8e8e8;--algo-heading:#f2f2f2;--algo-muted:#9a9a9a;--algo-sidebar:#1a1a1a;--algo-border:#333;--algo-code-bg:#1c1c1c;--algo-code-border:#444;--algo-link:#8ab4f8;--algo-link-hover:#bcd4ff;--ad-box:#1c1c1c}html{--nextra-navbar-height:0px;--nextra-content-width:100%}div:has(>.nextra-sidebar){width:100%;max-width:none!important;margin-inline:0!important}html,body{background:var(--algo-bg);color:var(--algo-fg);font-family:var(--learn-body);-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}.nextra-navbar{display:none}.site-chrome{z-index:30;width:max-content;height:var(--algo-menu-h);padding-block:14px;padding-inline:max(14px, env(safe-area-inset-left)) 14px;pointer-events:none;background:0 0;align-items:center;display:flex;position:fixed;inset-block-start:0;inset-inline:0 auto}.site-chrome-cluster{pointer-events:auto;align-items:center;gap:10px;display:flex}.site-chrome-btn{width:24px;height:24px;color:var(--algo-fg);opacity:.4;cursor:pointer;background:0 0;border:0;justify-content:center;align-items:center;margin:0;padding:0;display:inline-flex}.site-chrome-btn:hover,.site-chrome-btn:focus-visible{opacity:1}.site-chrome-btn:focus-visible{outline:1px solid var(--algo-fg);outline-offset:2px}.site-chrome-menu{display:inline-flex}.site-search{width:24px;height:24px;position:relative}.site-search-icon{z-index:1;width:24px;height:24px;color:var(--algo-fg);opacity:.4;pointer-events:none;place-items:center;display:grid;position:absolute;inset:0}.site-search:focus-within{width:min(16rem,100vw - 5rem)}.site-search:focus-within .site-search-icon{opacity:0}.site-search .nextra-search,.site-search .site-search-field{width:100%;height:100%;position:relative}.site-search .nextra-search input{color:#0000;caret-color:#0000;width:24px;height:24px;font-family:var(--learn-ui);background:0 0;border:0;padding:0;font-size:16px}.site-search .nextra-search input::placeholder{color:#0000}.site-search .nextra-search kbd{display:none}.site-search:focus-within .nextra-search input{width:100%;height:28px;color:var(--algo-fg);caret-color:var(--algo-fg);background:var(--algo-sidebar);border:1px solid var(--algo-code-border);padding:4px 8px}.site-search:focus-within .nextra-search input::placeholder{color:var(--algo-muted)}.nextra-sidebar,.nextra-mobile-nav{font-family:var(--learn-ui);color:var(--algo-fg);background:var(--algo-sidebar)!important}.nextra-sidebar{z-index:20;position:sticky;inset-inline-start:0;width:var(--algo-sidebar-w)!important;min-width:var(--algo-sidebar-w)!important;max-width:var(--algo-sidebar-w)!important;border:0!important;height:100dvh!important;top:0!important}.nextra-sidebar:before,.nextra-mobile-nav:before{content:"Algoritmia";font-family:var(--learn-display);text-align:center;color:var(--algo-muted);margin:20px 12px 8px;font-size:1.2em;font-weight:400;display:block}.nextra-sidebar .nextra-scrollbar,.nextra-mobile-nav .nextra-scrollbar{padding:4px 8px 24px!important;-webkit-mask-image:none!important;mask-image:none!important}.nextra-sidebar ul,.nextra-mobile-nav ul{font-size:.9em;list-style:none;gap:0!important;margin:0 0 0 10px!important;padding:0!important}.nextra-sidebar ul ul,.nextra-mobile-nav ul ul{margin-inline-start:4px!important;padding-block-start:0!important;padding-inline-start:0!important}.nextra-sidebar ul ul:before,.nextra-mobile-nav ul ul:before{display:none!important}.nextra-sidebar li,.nextra-mobile-nav li{margin:6px!important}.nextra-sidebar a,.nextra-sidebar button,.nextra-mobile-nav a,.nextra-mobile-nav button{max-width:100%;line-height:1.35;width:auto!important;color:var(--algo-fg)!important;font-weight:400!important;font-size:inherit!important;box-shadow:none!important;background:0 0!important;border:0!important;border-radius:0!important;justify-content:flex-start!important;align-items:flex-start!important;padding:0!important;display:block!important}.nextra-sidebar a:hover,.nextra-mobile-nav a:hover{color:var(--algo-link-hover)!important;background:0 0!important}.nextra-sidebar li.active>a,.nextra-sidebar a[aria-current],.nextra-mobile-nav li.active>a,.nextra-mobile-nav a[aria-current]{color:var(--algo-link)!important;background:0 0!important;font-weight:400!important}.nextra-sidebar svg,.nextra-mobile-nav svg,.nextra-sidebar-footer{display:none!important}.nextra-sidebar>div>div>ul,.nextra-mobile-nav>ul{counter-reset:part-counter}.nextra-sidebar>div>div>ul>li:has(ul){counter-increment:part-counter;margin-block-start:16px!important}.nextra-mobile-nav>ul>li:has(ul){counter-increment:part-counter;margin-block-start:16px!important}.nextra-sidebar>div>div>ul>li:has(ul)>a{color:var(--algo-muted)!important;font-size:18px!important}.nextra-mobile-nav>ul>li:has(ul)>a{color:var(--algo-muted)!important;font-size:18px!important}.nextra-sidebar>div>div>ul>li:has(ul)>a:before{content:counter(part-counter, upper-roman) ". ";color:var(--algo-heading);font-weight:700}.nextra-mobile-nav>ul>li:has(ul)>a:before{content:counter(part-counter, upper-roman) ". ";color:var(--algo-heading);font-weight:700}.nextra-sidebar ul ul,.nextra-mobile-nav ul ul{counter-reset:chapter-counter}:is(.nextra-sidebar ul ul>li:has(>a),.nextra-mobile-nav ul ul>li:has(>a)){counter-increment:chapter-counter}.nextra-sidebar ul ul>li:has(>a)>a:before{content:counter(chapter-counter) ". ";font-weight:700}.nextra-mobile-nav ul ul>li:has(>a)>a:before{content:counter(chapter-counter) ". ";font-weight:700}:is(.nextra-sidebar li:not(:has(a)):not(:has(button)),.nextra-mobile-nav li:not(:has(a)):not(:has(button))){color:var(--algo-muted);margin-block-start:14px!important;padding:0!important;font-size:15px!important;font-weight:400!important}@media (max-width:1199px){.nextra-sidebar{display:none!important}.nextra-mobile-nav{padding-block-start:var(--algo-menu-h);display:flex!important}article{padding-block-start:calc(var(--algo-menu-h) + 8px)!important}}@media (min-width:768px) and (max-width:1199px){.nextra-mobile-nav.x\:md\:hidden,.nextra-mobile-nav{display:flex!important}}@media (min-width:1200px){.site-chrome{padding-inline-start:14px;inset-inline-start:var(--algo-sidebar-w)}.site-chrome-menu{display:none}.nextra-sidebar{display:flex!important}article{padding-block-start:calc(var(--algo-menu-h) + 4px)!important}}article{min-height:100dvh;font-family:var(--learn-body);color:var(--algo-fg);background:var(--algo-bg);flex-direction:column;display:flex;padding-inline:18px!important}article main{width:100%;min-width:0;max-width:850px;font-family:var(--learn-body);text-align:justify;-webkit-hyphens:auto;hyphens:auto;flex:1 0 auto;margin-inline:auto;padding:6px;font-size:18px;line-height:1.5}article h1,article h2,article h3,article h4,article h5,article h6,article.nextra-body-typesetting-article h1,article.nextra-body-typesetting-article h2,article.nextra-body-typesetting-article h3{font-family:var(--learn-display);color:var(--algo-heading);text-align:start;letter-spacing:0;font-weight:400;line-height:1.25}article main h1,article main h2{text-align:start;border-block-end:1px solid var(--algo-border);padding-block-end:5px;font-size:1.75em}article main>h1:first-child{text-align:center;text-wrap:balance;border-block-end:0;margin-block:0 20px;padding-block-end:0;font-size:2.5em}article main h3{border-block-end:1px solid var(--algo-border);padding-block-end:5px;font-size:1.5em}article main p{margin-block:.5em}.katex-math.is-display,.katex-math .katex-display{margin-block:.75em;display:block;overflow:auto hidden}.learn-note{border:1px solid var(--algo-code-border);border-inline-start:3px solid var(--algo-muted);background:var(--algo-sidebar);color:var(--algo-fg);font-family:var(--learn-body);text-align:start;align-items:flex-start;gap:.65rem;margin-block:1.15em;padding:.7rem .95rem;display:flex}.learn-note.is-warning{border-inline-start-color:#8a6d1b}.learn-note.is-info{border-inline-start-color:var(--algo-link)}.learn-note-mark{color:var(--algo-muted);flex:none;margin-block-start:.28rem;line-height:0}.learn-note.is-warning .learn-note-mark{color:#8a6d1b}.learn-note.is-info .learn-note-mark{color:var(--algo-link)}.learn-note-body{flex:1;min-width:0}.learn-note-body>:first-child{margin-block-start:0}.learn-note-body>:last-child{margin-block-end:0}.learn-note-title{font-family:var(--learn-ui);color:var(--algo-heading);margin:0 0 .2rem;font-size:.92rem;font-weight:600}html.dark .learn-note.is-warning{border-inline-start-color:#c4a35a}html.dark .learn-note.is-warning .learn-note-mark{color:#c4a35a}.nextra-callout{margin-block:1.15em;color:var(--algo-fg)!important;background:var(--algo-sidebar)!important;border:1px solid var(--algo-code-border)!important;border-inline-start:3px solid var(--algo-muted)!important;border-radius:0!important}article main table{border-collapse:collapse;font-variant-numeric:tabular-nums;margin-block:1em}article main th,article main td{text-align:center;vertical-align:middle;padding:.3rem .65rem}.grid{display:grid}.grid-cols-2{grid-template-columns:repeat(2,minmax(0,1fr))}.gap-y-6{row-gap:1.5rem}.justify-evenly{justify-content:space-evenly}.place-items-center{place-items:center}.max-w-lg{max-width:32rem;margin-inline:auto}@media (min-width:40rem){.sm\:grid-cols-3{grid-template-columns:repeat(3,minmax(0,1fr))}.sm\:gap-y-12{row-gap:2.5rem}}.bg-red-200{background:#fecaca}.bg-blue-200{background:#bfdbfe}html.dark .bg-red-200,html.dark .dark\:bg-red-800,html.dark .dark\:bg-red-900{color:#fff7f2;background:#7f1d1d}html.dark .bg-blue-200,html.dark .dark\:bg-blue-800,html.dark .dark\:bg-blue-900,html.dark .dark\:bg-purple-900{color:#eef4ff;background:#1e3a8a}article main .grid table{margin-block:0}article main .grid td,article main .cell-grid td{border:1px solid var(--algo-code-border);width:1.7rem;height:1.7rem;font-family:var(--learn-ui);font-variant-numeric:tabular-nums;padding:0}.queens-board{font-family:var(--learn-ui);margin-inline:auto}.queens-board td{width:1.9rem;height:1.9rem;padding:0;line-height:1}.queens-board tr:first-child td,.queens-board td:first-child{color:var(--algo-muted);background:0 0;border:0;font-size:.78rem}.queens-board tr:not(:first-child) td:not(:first-child){border:1px solid var(--algo-border)}.queens-board tr:not(:first-child):nth-child(2n) td:nth-child(odd):not(:first-child),.queens-board tr:not(:first-child):nth-child(odd) td:nth-child(2n){background:#0000000b;background:lab(0% 0 0/.045)}html.dark .queens-board tr:not(:first-child):nth-child(2n) td:nth-child(odd):not(:first-child),html.dark .queens-board tr:not(:first-child):nth-child(odd) td:nth-child(2n){background:#ffffff0f;background:lab(100% 0 0/.06)}.reconocimientos{color:var(--algo-muted);text-align:start;margin-block-start:3rem;padding-block-start:.25rem;font-size:.95em}.reconocimientos h2{color:var(--algo-heading);font-size:1.35em}.para-entender{border-block-start:1px solid var(--algo-border);max-width:850px;font-family:var(--learn-body);text-align:start;margin:2.5rem auto 0;padding-block-start:1.25rem}.para-entender h2{border:0;margin-block:0 .35rem;padding:0;font-size:1.35em}.para-entender-note{color:var(--algo-muted);margin:0 0 .75rem;font-size:.95em}.para-entender ul{margin:0;padding-inline-start:1.2em}.para-entender li{margin-block:.45em}.ps-demo{font-family:var(--learn-ui);margin-block:1.5rem}.ps-demo-hint{color:var(--algo-muted);margin:0 0 .75rem;font-size:.95em}.ps-demo-body{flex-wrap:wrap;align-items:flex-start;gap:1.5rem 2rem;display:flex}.ps-demo-steps{flex-direction:column;gap:.4rem;min-width:14rem;display:flex}.ps-demo-step{font:inherit;text-align:start;cursor:pointer;border:1px solid var(--algo-code-border);background:var(--algo-code-bg);color:var(--algo-fg);padding:.35rem .6rem}.ps-demo-step:hover,.ps-demo-step:focus-visible{border-color:var(--algo-link)}.ps-demo-step.is-on{background:#e8f0e4;border-color:#3d6b3d}html.dark .ps-demo-step.is-on{background:#1d3320;border-color:#7dba7d}.ps-demo-peek{color:var(--algo-muted);margin:.25rem 0 0;font-size:.95em}.ps-demo-grid{border:1px solid var(--algo-code-border);width:max-content;display:grid}.ps-demo-cell{border-inline-end:1px solid var(--algo-code-border);border-block-end:1px solid var(--algo-code-border);font-variant-numeric:tabular-nums;justify-content:center;align-items:center;width:2.5rem;height:2.5rem;display:flex}.ps-demo-cell.is-add{background:#dbeafe}.ps-demo-cell.is-sub{background:#fecaca}.ps-demo-cell.is-twice.is-add{background:#93c5fd}.ps-demo-cell.is-twice.is-sub{background:#f87171}.ps-demo-cell.is-hover{box-shadow:inset 0 0 0 2px var(--algo-link)}html.dark .ps-demo-cell.is-add{background:#1e3a5f}html.dark .ps-demo-cell.is-sub{background:#5c1f1f}.ps1d,.tp-demo,.fence-demo,.bs-demo{font-family:var(--learn-ui);margin-block:1.5rem}.ps1d-hint,.tp-demo-hint,.tp-demo-note,.tp-demo-meta,.ps1d-formula,.fence-demo-hint,.fence-demo-formula,.bs-demo-hint,.bs-demo-note,.bs-demo-meta{margin:.4rem 0;font-size:.95em}.ps1d-hint,.tp-demo-hint,.fence-demo-hint,.bs-demo-hint{color:var(--algo-muted)}.ps1d-row,.tp-demo-row{flex-wrap:wrap;align-items:center;gap:.35rem;margin-block:.45rem;display:flex}.ps1d-label{width:2.5rem;color:var(--algo-muted);font-size:.85em}.ps1d-cell,.tp-demo-cell{border:1px solid var(--algo-code-border);background:var(--algo-code-bg);font-variant-numeric:tabular-nums;flex-direction:column;justify-content:center;align-items:center;min-width:2.5rem;min-height:2.7rem;padding:.2rem .35rem;display:flex}.ps1d-cell{font:inherit;cursor:pointer;color:inherit}.ps1d-cell small,.tp-demo-cell small{color:var(--algo-muted);font-size:.65em}.ps1d-cell.is-range,.tp-demo-cell.is-in{background:#fef9c3}.ps1d-cell.is-add{background:#dcfce7}.ps1d-cell.is-sub{background:#fee2e2}.tp-demo-cell.is-left,.tp-demo-cell.is-right{box-shadow:inset 0 0 0 2px var(--algo-link)}.tp-demo-cell.is-both{background:#dbeafe}.tp-demo-actions{gap:.5rem;margin-block-start:.6rem;display:flex}.tp-demo-actions button{font:inherit;cursor:pointer;border:1px solid var(--algo-code-border);background:var(--algo-bg);padding:.3rem .7rem}.tp-demo-actions button:disabled{opacity:.4;cursor:not-allowed}.viz-plate{--viz-paper:#f3eee4;--viz-line:#cfc6b6;--viz-wood:#e4d4b6;--viz-wood-ink:#6a5d48;--viz-fj:#0645ad;--viz-be:#2f6b4f;--viz-both:#8a4b12;--viz-mid:#9a3412;border:1px solid var(--viz-line);background:radial-gradient(120% 80% at 0% 0%, #ffffff8c, transparent 46%), var(--viz-paper);color:var(--algo-fg);padding:1rem 1.05rem 1.1rem}html.dark .viz-plate{--viz-paper:#1b1915;--viz-line:#3a352c;--viz-wood:#2a241c;--viz-wood-ink:#cbb89a;--viz-fj:#8ab4f8;--viz-be:#8fca9f;--viz-both:#e0b07a;--viz-mid:#f0b090}.viz-dots{--viz-dot:url(/texture.svg);background-color:var(--algo-bg);background-image:var(--viz-dot);background-repeat:repeat;position:relative}html.dark .viz-dots{--viz-dot:url(/texture-dark.svg)}.viz-dots-frame span{background-image:var(--viz-dot);pointer-events:none;background-repeat:repeat;position:absolute}.viz-dots-frame .is-t,.viz-dots-frame .is-b{height:2px;inset-inline:0}.viz-dots-frame .is-t{top:0}.viz-dots-frame .is-b{bottom:0}.viz-dots-frame .is-l,.viz-dots-frame .is-r{width:2px;inset-block:0}.viz-dots-frame .is-l{inset-inline-start:0}.viz-dots-frame .is-r{inset-inline-end:0}.viz-kicker{font-family:var(--learn-display);color:var(--algo-muted);margin:0 0 .35rem;font-size:.92em;font-style:italic}.viz-term.is-fj{color:var(--viz-fj)}.viz-term.is-be{color:var(--viz-be)}.viz-term.is-both{color:var(--viz-both)}.fence-demo-who{flex-wrap:wrap;gap:.55rem;margin-block:.55rem .75rem;display:flex}.fence-demo-who button{font:inherit;cursor:pointer;color:inherit;background:0 0;border:1px solid #0000;align-items:center;gap:.4rem;padding:.28rem .65rem;display:inline-flex}.fence-demo-who button i{border-radius:99px;width:.7rem;height:.7rem}.fence-demo-who .is-fj i{background:var(--viz-fj)}.fence-demo-who .is-be i{background:var(--viz-be)}.fence-demo-who button.is-on{border-color:currentColor}.fence-stage{margin-block:.35rem .7rem}.fence-bands{height:.7rem;margin-block-end:.45rem;position:relative}.fence-stroke{border-radius:99px;height:.32rem;position:absolute;top:0}.fence-stroke.is-fj{background:var(--viz-fj)}.fence-stroke.is-be{background:var(--viz-be);top:.38rem}.fence-demo-row{border-block-end:3px solid #8a7760;align-items:flex-end;gap:3px;padding:0 1px;display:flex}html.dark .fence-demo-row{border-block-end-color:#5c4e3c}.fence-demo-cell{background:linear-gradient(90deg, #00000012, transparent 18%, transparent 82%, #00000014), var(--viz-wood);min-width:0;height:4.6rem;color:var(--viz-wood-ink);font:inherit;font-variant-numeric:tabular-nums;cursor:pointer;border:0;border-radius:2px 2px 0 0;flex:1 1 0;justify-content:center;align-items:flex-end;margin:0;padding:0 0 .28rem;font-size:.68rem;display:flex}.fence-demo-cell:active{scale:.96}.fence-demo-cell.is-fj{background:linear-gradient(180deg, color-mix(in srgb, var(--viz-fj) 78%, white), color-mix(in srgb, var(--viz-fj) 55%, var(--viz-wood))), var(--viz-wood);color:#fff}.fence-demo-cell.is-be{background:linear-gradient(180deg, color-mix(in srgb, var(--viz-be) 78%, white), color-mix(in srgb, var(--viz-be) 55%, var(--viz-wood))), var(--viz-wood);color:#fff}.fence-demo-cell.is-both{background:repeating-linear-gradient(-32deg, color-mix(in srgb, var(--viz-fj) 70%, black 8%), color-mix(in srgb, var(--viz-fj) 70%, black 8%) 6px, color-mix(in srgb, var(--viz-be) 70%, black 8%) 6px, color-mix(in srgb, var(--viz-be) 70%, black 8%) 12px);color:#fff}.bs-stage{margin-block:.4rem .65rem;padding-block-start:1.05rem;position:relative}.bs-window{border:1.5px solid var(--viz-fj);pointer-events:none;border-block-end:0;height:.85rem;position:absolute;top:0}.bs-demo-row{z-index:1;border-block-end:1px solid var(--viz-line);gap:0;display:flex;position:relative}.bs-demo-cell{min-width:0;color:inherit;font-family:var(--learn-display);font-variant-numeric:tabular-nums;cursor:pointer;opacity:.28;background:0 0;border:0;flex-direction:column;flex:1 1 0;align-items:center;gap:.2rem;margin:0;padding:.35rem 0 .45rem;font-size:1.55rem;line-height:1;display:flex;position:relative}.bs-demo-cell em{font-family:var(--learn-ui);color:var(--algo-muted);font-size:.62rem;font-style:normal}.bs-demo-cell.is-range{opacity:1}.bs-demo-cell.is-mid{color:var(--viz-mid)}.bs-demo-cell.is-found{color:var(--viz-fj)}.bs-pin{border-inline:5px solid #0000;border-top:7px solid var(--viz-mid);width:0;height:0;position:absolute;top:.05rem}.apples-demo{--ad-ink:#3f3428;--ad-apple:#b84532;--ad-apple-fg:#fff7f2;--ad-a:var(--viz-fj,#0645ad);--ad-b:var(--viz-be,#2f6b4f);--ad-ok:var(--viz-be,#2f6b4f);font-family:var(--learn-ui);margin-block:1.5rem}.apples-demo-plate{padding:.85rem 1.05rem .35rem}.apples-demo:has(>.lang-section){grid-template-columns:minmax(0,1fr) auto;align-items:center;display:grid}.apples-demo:has(>.lang-section)>.apples-demo-plate{grid-column:1/-1}.apples-demo:has(>.lang-section)>.lang-section{display:contents}.apples-demo:has(>.lang-section)>.lang-section>.lang-head{grid-area:2/1;margin-block:1rem .65rem}.apples-demo:has(>.lang-section)>.ad-player{grid-area:2/2;margin-block:1rem .65rem}.apples-demo:has(>.lang-section)>.lang-section>.lang-panel{grid-area:3/1/auto/-1}html.dark .apples-demo{--ad-ink:#d7cbb8;--ad-a:#8ab4f8;--ad-b:#8fca9f;--ad-ok:#8fca9f;--lightningcss-light: ;--lightningcss-dark:initial;color-scheme:dark}.apples-demo-iconbtns{flex-shrink:0;gap:.55rem;display:flex}.apples-demo-iconbtn{border:1px solid var(--algo-code-border);background:var(--ad-box);width:2.5rem;height:2.5rem;color:var(--algo-fg);cursor:pointer;border-radius:999px;place-items:center;margin:0;padding:0;display:grid}.apples-demo-iconbtn.is-play{color:var(--algo-link)}.apples-demo-iconbtn:hover{background:var(--ad-box)}.apples-demo-iconbtn:active{scale:.96}.apples-demo-iconbtn:disabled{opacity:.4;cursor:not-allowed;scale:1}.apples-demo-status{clip:rect(0 0 0 0);white-space:nowrap;width:1px;height:1px;position:absolute;overflow:hidden}.apples-demo-stage{width:min(100%,26rem);margin:.1rem auto .35rem;position:relative}.apples-demo-rig{width:100%;height:auto;display:block}.apples-demo-ink{fill:none;stroke:var(--ad-ink);stroke-width:1.75px;stroke-linecap:round;stroke-linejoin:round}.apples-demo-fulcrum,.apples-demo-pivot{fill:var(--ad-ink);stroke:none}.apples-demo-ink text{fill:var(--ad-ink);stroke:none;font-size:10px;font-family:var(--learn-ui);letter-spacing:.06em}.apples-demo-pan-fill{fill:var(--ad-box);stroke:none}.apples-demo-beam{transform-box:view-box;transform-origin:200px 38px}.apples-demo-apples{position:absolute;inset:0}.apples-demo-cell{--s:1.4rem;left:calc(var(--x) * 1%);top:calc(var(--y) * 1%);width:var(--s);height:var(--s);background:var(--ad-apple);color:var(--ad-apple-fg);font-variant-numeric:tabular-nums;border-radius:50%;place-items:center;font-size:.78rem;display:grid;position:absolute;translate:-50% -50%;box-shadow:inset 0 0 0 1px #0000001f;box-shadow:inset 0 0 0 1px lab(0% 0 0/.12)}.apples-demo-cell.is-a{box-shadow:inset 0 0 0 2px var(--ad-a)}.apples-demo-cell.is-b{box-shadow:inset 0 0 0 2px var(--ad-b)}.apples-demo-cell.is-now{--s:1.55rem;box-shadow:inset 0 0 0 2px var(--algo-fg);background:#d36a3a;font-weight:600}.apples-demo-cell.is-wait{opacity:.55}.ad-player{background:0 0;border:0;justify-content:flex-end;align-items:center;gap:.15rem;padding:0;display:flex}.ad-player .apples-demo-iconbtn{width:2rem;height:2rem;color:var(--algo-muted);background:0 0;border:0}.ad-player .apples-demo-iconbtn.is-play{color:var(--algo-link)}.ad-player .apples-demo-iconbtn:hover,.ad-player .ad-player-text:hover{color:var(--algo-heading);background:0 0}.ad-player-left,.ad-player-right{align-items:center;gap:.05rem;display:flex}.ad-player-right{margin-inline-start:.25rem}.ad-player-text{font:inherit;font-size:.9rem;font-family:var(--learn-ui);color:var(--algo-muted);cursor:pointer;background:0 0;border:0;border-radius:0;min-height:2rem;padding:0 .4rem}.ad-player-text:active{scale:.96}.apples-demo-toolbar{grid-template-columns:1fr;gap:.75rem;display:grid}.apples-demo-field{color:var(--algo-fg);flex-direction:column;gap:.4rem;font-size:.92rem;display:flex}.apples-demo-field input,.apples-demo-step,.apples-demo-optimal{font:inherit;color:var(--algo-fg);background:var(--ad-box);border:1px solid var(--algo-code-border);border-radius:.35rem}.apples-demo-field input{width:100%;min-height:2.75rem;padding:.55rem 1rem}.apples-demo-step,.apples-demo-optimal{cursor:pointer;min-height:2.75rem}.apples-demo-step:hover,.apples-demo-optimal:hover{background:var(--ad-box)}.apples-demo-step:active,.apples-demo-optimal:active{scale:.96}.apples-demo-step:disabled{opacity:.4;cursor:not-allowed;scale:1}.apples-demo-optimal{width:100%;margin-block-start:.75rem}code.nextra-code>span.is-code-hl{background:#fff3bf;box-shadow:inset 3px 0 #c9a227}html.dark code.nextra-code>span.is-code-hl{background:#3d3420;box-shadow:inset 3px 0 #e2b203}@media (max-width:36rem){.apples-demo:has(>.lang-section){grid-template-columns:minmax(0,1fr)}.apples-demo:has(>.lang-section)>.lang-section>.lang-head{grid-area:2/1;margin-block-end:.25rem}.apples-demo:has(>.lang-section)>.ad-player{grid-area:3/1;justify-content:flex-start;margin-block:0 .65rem}.apples-demo:has(>.lang-section)>.lang-section>.lang-panel{grid-row:4}.apples-demo-stats{grid-template-columns:repeat(2,minmax(0,1fr));gap:.5rem}.apples-demo-toolbar{grid-template-columns:1fr}}.ps1d-cell:focus-visible,.fence-demo-cell:focus-visible,.bs-demo-cell:focus-visible,.fence-demo-who button:focus-visible,.tp-demo-actions button:focus-visible,.ps-demo-step:focus-visible,.rive-stage-hits button:focus-visible,.apples-demo-iconbtn:focus-visible,.ad-player-text:focus-visible,.apples-demo-step:focus-visible,.apples-demo-optimal:focus-visible,.apples-demo-field input:focus-visible{outline:2px solid var(--algo-link);outline-offset:2px}.rive-stage{width:100%;min-height:7rem;margin-block:.45rem;position:relative}.rive-stage-hits{align-items:stretch;display:flex;position:absolute;inset:0}.rive-stage-hits button{cursor:pointer;background:0 0;border:0;flex:1;margin:0;padding:0}@media (prefers-reduced-motion:no-preference){.ps1d-cell,.tp-demo-cell,.ps-demo-cell{transition-property:background-color,box-shadow;transition-duration:.15s;transition-timing-function:ease-out}.fence-stroke,.bs-window,.apples-demo-beam{transition-property:left,width,transform;transition-duration:.18s;transition-timing-function:ease-out}.apples-demo-cell{transition-property:left,top,width,height,background-color,color,opacity,box-shadow;transition-duration:.28s;transition-timing-function:ease-out}.bs-demo-cell{transition-property:opacity,color;transition-duration:.16s;transition-timing-function:ease-out}}article main a{color:var(--algo-link);text-decoration:none}article main a:hover{color:var(--algo-link-hover)}article main :not(pre)>code{border:1px solid var(--algo-code-border);background:var(--algo-code-bg);border-radius:3px;padding:2px;font-size:.75em}article main pre,article main pre:not([data-theme]){border:1px solid var(--algo-code-border);text-align:start;border-radius:3px;background:var(--algo-code-bg)!important}article main blockquote{color:var(--algo-muted);border-inline-start:.25em solid var(--algo-border);margin:0;padding-inline-start:1em}.nextra-toc{display:none}.nextra-toc a{color:var(--algo-fg);font-weight:400}.nextra-toc a:hover{color:var(--algo-link-hover)}footer,.nextra-footer{display:none!important}article>.x\:mt-16{display:none}article>.nextra-border{width:min(850px,100%);font-family:var(--learn-body);margin-block:auto 1.25rem;margin-inline:auto}article>.nextra-border a{color:var(--algo-link)}article>.nextra-border a:hover{color:var(--algo-link-hover)}.usaco-resources{margin-block:1.5rem;overflow-x:auto}.usaco-resources table{border-collapse:collapse;width:100%}.usaco-resources caption{caption-side:top;text-align:start;letter-spacing:.04em;text-transform:uppercase;color:var(--color-slate-500,#64748b);padding-block-end:.5rem;font-size:.8rem;font-weight:600}.usaco-resources th,.usaco-resources td{text-align:start;vertical-align:top;border-bottom:1px solid var(--color-slate-200,#e2e8f0);padding:.7rem .85rem}@media (prefers-color-scheme:dark){.usaco-resources caption{color:#94a3b8}.usaco-resources th,.usaco-resources td{border-bottom-color:#334155}}.usaco-resources th{letter-spacing:.04em;text-transform:uppercase;font-size:.75rem;font-weight:600}.usaco-resources td:first-child{white-space:nowrap;width:7.5rem;font-weight:600}.usaco-resources td p{margin:0}.usaco-resources-star{color:var(--color-amber-500,#f59e0b)}.lang-section{margin-block:1.25rem}.lang-section>input{clip:rect(0 0 0 0);clip-path:inset(50%);white-space:nowrap;width:1px;height:1px;position:absolute;overflow:hidden}.lang-head{align-items:center;margin-block-end:.85rem;display:flex}.lang-tabs{flex-wrap:wrap;gap:.4rem;display:flex}.lang-head .lang-tabs{margin:0}.lang-tabs label{cursor:pointer;border:0;font-family:var(--learn-ui);color:var(--algo-muted);background:0 0;border-block-end:1px solid #0000;border-radius:0;padding:.2rem .15rem;font-size:.95rem;font-weight:400}.lang-panel{display:none}:is(.lang-section:has(input[value=cpp]:checked) .lang-panel[data-lang=cpp],.lang-section:has(input[value=java]:checked) .lang-panel[data-lang=java],.lang-section:has(input[value=py]:checked) .lang-panel[data-lang=py]){display:block}:is(.lang-section:has(input[value=cpp]:checked) label[for$=-cpp],.lang-section:has(input[value=java]:checked) label[for$=-java],.lang-section:has(input[value=py]:checked) label[for$=-py]){color:var(--algo-heading);border-block-end-color:var(--algo-heading);background:0 0}.lang-only-java,.lang-only-py{display:none}body:has(.lang-section input[value=java]:checked) .lang-only-java{display:contents}body:has(.lang-section input[value=java]:checked) .lang-only-cpp{display:none}body:has(.lang-section input[value=py]:checked) .lang-only-py{display:contents}body:has(.lang-section input[value=py]:checked) .lang-only-cpp{display:none}.usaco-quiz{border:1px solid var(--color-slate-200,#e2e8f0);border-radius:.6rem;margin-block:1.5rem;padding:1rem 1.15rem 1.15rem}.usaco-quiz-count{color:var(--color-slate-500,#64748b);margin:0 0 .4rem;font-size:.85rem}.usaco-quiz-prompt{margin:0 0 .85rem;font-size:1.05rem;line-height:1.5}.usaco-quiz-options{flex-direction:column;gap:.5rem;margin-block-end:.85rem;display:flex}.usaco-quiz-option,.usaco-quiz-check,.usaco-quiz-next{font:inherit;cursor:pointer}.usaco-quiz-option{text-align:start;border:1px solid var(--color-slate-300,#cbd5e1);background:0 0;border-radius:.45rem;width:100%;padding:.65rem .85rem;display:block}.usaco-quiz-option code,.usaco-quiz-prompt code{font-family:ui-monospace,SFMono-Regular,Menlo,monospace;font-size:.9em}.usaco-quiz-pre,.usaco-quiz-option pre{text-align:start;tab-size:4;background:var(--algo-code-bg);border:1px solid var(--algo-code-border);margin:.7rem 0 .15rem;padding:0;overflow-x:auto}.usaco-quiz-pre code.nextra-code,.usaco-quiz-option pre code.nextra-code{white-space:pre;tab-size:4;padding-block:.65rem;font-size:.86rem;line-height:1.5;display:grid}.usaco-quiz-pre code.nextra-code>span,.usaco-quiz-option pre code.nextra-code>span{min-height:1.45em;padding-inline:.85rem}.usaco-quiz-option .usaco-quiz-pre{margin:.45rem 0 0}.usaco-quiz-option.is-selected{border-color:var(--color-slate-900,#0f172a);box-shadow:inset 0 0 0 1px var(--color-slate-900,#0f172a)}.usaco-quiz-option.is-correct{background:#f0fdf4;border-color:#15803d}.usaco-quiz-option.is-wrong{background:#fef2f2;border-color:#b91c1c}.usaco-quiz-actions{justify-content:space-between;align-items:center;gap:.75rem;width:100%;display:flex}.usaco-quiz-next{margin-inline-start:auto}.usaco-quiz-check,.usaco-quiz-next{border:1px solid var(--color-slate-900,#0f172a);background:var(--color-slate-900,#0f172a);color:#fff;border-radius:.4rem;padding:.45rem .9rem}.usaco-quiz-check:disabled,.usaco-quiz-next:disabled{opacity:.45;cursor:not-allowed}.usaco-quiz-explain{margin:.85rem 0 0;line-height:1.5}.usaco-quiz-explain.is-correct{color:#166534}.usaco-quiz-explain.is-wrong{color:#991b1b}.usaco-problems{margin-block:1.5rem;overflow-x:auto}.usaco-problems.is-focus table{border:1px solid var(--algo-code-border)}.usaco-problems table{border-collapse:collapse;width:100%}.usaco-problems caption{caption-side:top;text-align:start;padding-block-end:.45rem;font-weight:600}.usaco-problems th,.usaco-problems td{text-align:start;vertical-align:top;border-bottom:1px solid var(--color-slate-200,#e2e8f0);padding:.6rem .75rem}.usaco-problems th{letter-spacing:.04em;text-transform:uppercase;font-size:.75rem;font-weight:600}.usaco-problems-empty{color:var(--color-slate-500,#64748b)}