html.hub-math{color-scheme:light;--bg: #fbfefe;--bg-gradient-tint: transparent;--bg-gradient-base: #fbfefe;--surface: #ffffff;--surface-muted: #f2f8f8;--surface-solid: #ffffff;--text: #0f2e33;--muted: #5a7579;--line: #dcebeb;--line-strong: #b8d6d6;--accent: #0b8a84;--accent-strong: #0b6e69;--accent-soft: #e3f4f2;--ink: #0b8a84;--primary: #0b8a84;--primary-hover: #0b6e69;--on-primary: #ffffff;--category-nav-bg: rgb(255 255 255 / 92%);--mh-sans: "IBM Plex Sans", system-ui, sans-serif;--mh-mono: "IBM Plex Mono", ui-monospace, monospace;--mh-fn: #f2f8f8;--mh-fn-ink: #1d4f52;--mh-mod: #d3eeec;--mh-op: #e3f4f2;--mh-op-ink: #0b6e69;--mh-clear: #eef4f4;--mh-ok: #0b8a84;--mh-ok-bg: #d3eeec;--mh-error: #b42318;font-family:var(--mh-sans)}html.hub-math body{background:repeating-linear-gradient(0deg,#e8f3f3 0 1px,transparent 1px 28px),repeating-linear-gradient(90deg,#e8f3f3 0 1px,transparent 1px 28px),var(--bg);color:var(--text)}html.hub-math .site-header a,html.hub-math .site-header-nav a{font-weight:600}html.hub-math a{color:var(--accent-strong)}html.hub-math .site-header>.site-header-inner>a,html.hub-math .site-header-nav a:not([aria-current]){color:var(--text)}html.hub-math .site-header-nav a[aria-current]{color:var(--accent-strong)}html.hub-math :focus-visible{outline:2px solid var(--accent);outline-offset:2px;box-shadow:none}.mh-main{max-width:72rem;margin:0 auto;padding:.5rem 1.25rem 2rem}.mh-crumbs ol{display:flex;flex-wrap:wrap;gap:.35rem;margin:.5rem 0 0;padding:0;list-style:none;font-size:.82rem;color:var(--muted)}.mh-crumbs li+li:before{content:"/";margin-right:.35rem}.mh-main h1{margin:.4rem 0 .35rem;font-size:clamp(1.6rem,3.5vw,2.5rem);font-weight:600;letter-spacing:-.02em;line-height:1.15}.mh-lede{max-width:60ch;margin:0 0 1.25rem;color:var(--muted)}.mh-workspace{display:grid;grid-template-columns:minmax(0,1fr) 18.75rem;gap:2.5rem;align-items:start}.mh-calc{padding:1.5rem;border-radius:14px;background:var(--surface);box-shadow:0 0 0 1px #d5e8e8,0 24px 40px -28px #0b8a8459}.mh-display{position:relative;margin:-1.5rem -1.5rem 1.1rem;padding:1.25rem 1.5rem 1.4rem;border-radius:14px 14px 0 0;border-bottom:1px solid #d6e9e8;background:linear-gradient(180deg,#edf8f7,#fff)}.mh-display:after{content:"";position:absolute;right:1.5rem;bottom:.45rem;left:1.5rem;height:6px;background:repeating-linear-gradient(90deg,#bfdcda 0 1px,transparent 1px 10px)}.mh-modes{display:flex;flex-wrap:wrap;align-items:center;gap:.6rem;font-size:.82rem}.mh-seg{display:inline-flex;padding:3px;border-radius:999px;background:#eaf5f4}.mh-seg button,.mh-digits,.mh-tool,.mh-mem button{border:0;background:none;font:inherit;color:var(--muted);cursor:pointer}.mh-seg button{padding:.2rem .7rem;border-radius:999px;font-weight:500}.mh-seg button[aria-checked=true]{background:var(--accent);color:#fff;font-weight:600}.mh-digits{padding:.2rem .4rem;border-radius:999px}.mh-digits[aria-pressed=true]{color:var(--accent-strong);font-weight:600}.mh-memflag{padding:0 .45rem;border-radius:6px;background:var(--mh-mod);color:var(--accent-strong);font-weight:700}.mh-tools{display:flex;gap:.25rem;margin-left:auto}.mh-tool{padding:.25rem .75rem;border-radius:999px;color:var(--accent-strong);font-weight:600}.mh-tool:hover,.mh-mem button:hover{background:var(--accent-soft)}.mh-expr{display:block;width:100%;box-sizing:border-box;margin-top:1.1rem;padding:.2rem 0;border:0;border-bottom:1px dashed transparent;background:transparent;color:var(--muted);font-family:var(--mh-mono);font-size:1.35rem;caret-color:var(--accent)}.mh-expr:focus,.mh-expr:focus-visible{outline:none;border-bottom-color:var(--line-strong)}.mh-result{display:block;margin-top:.25rem;min-height:1.2em;overflow-wrap:anywhere;font-family:var(--mh-mono);font-size:clamp(1.6rem,4.2vw,3.25rem);font-weight:500;letter-spacing:-.03em;line-height:1.12;text-align:right;color:var(--text)}.mh-result.is-error{font-family:var(--mh-sans);font-size:1.15rem;font-weight:600;letter-spacing:0;color:var(--mh-error)}.mh-eq{margin-right:.8rem;color:var(--accent);font-weight:400}.mh-exact,.mh-hint{margin:.35rem 0 0;text-align:right;font-size:.95rem;color:var(--muted)}.mh-exact math{font-size:1.15rem;color:var(--text)}.mh-suggest{display:block;margin:.5rem 0 0 auto;padding:.3rem .8rem;border:1px solid var(--line-strong);border-radius:999px;background:var(--surface);color:var(--accent-strong);font:inherit;font-weight:600;cursor:pointer}.mh-suggest[hidden],.mh-exact[hidden],.mh-hint[hidden],.mh-memflag[hidden],.mh-tabs,.mh-strip{display:none}.mh-pads{display:grid;grid-template-columns:5fr 4fr;gap:1rem}.mh-pad{display:grid;gap:6px}.mh-pad-fn{grid-template-columns:repeat(5,1fr)}.mh-pad-num{grid-template-columns:repeat(4,1fr)}.mh-k{height:3.1rem;border:0;border-radius:8px;background:var(--mh-fn);color:var(--mh-fn-ink);font:500 .95rem var(--mh-sans);cursor:pointer;transition:background .15s ease;touch-action:manipulation}.mh-k:hover{background:#e6f2f1}.mh-k:active{transform:translateY(1px)}.mh-k-mod{background:var(--mh-mod);color:var(--accent-strong);font-weight:600}.mh-calc.is-second .mh-k-mod{background:var(--accent);color:#fff}.mh-k-num{border:1px solid #d6e7e7;background:#fff;box-shadow:inset 0 -2px #e3efef;color:var(--text);font:500 1.3rem var(--mh-mono)}.mh-k-num:hover{background:#f7fbfb}.mh-k-op{background:var(--mh-op);color:var(--mh-op-ink);font-size:1.2rem}.mh-k-clear{background:var(--mh-clear);color:#2b4a4f;font-weight:600}.mh-k-eq{background:var(--accent);color:#fff;font-size:1.6rem}.mh-k-eq:hover{background:var(--accent-strong)}.mh-mem{display:flex;align-items:center;gap:.35rem;margin-top:.9rem;font-size:.82rem}.mh-mem button{padding:.3rem .75rem;border-radius:999px;color:var(--mh-fn-ink);font-weight:600}.mh-mem .mh-kbd{margin-left:auto;color:var(--muted);font-weight:400}.mh-kbd kbd,.mh-dialog kbd{padding:0 .35rem;border:1px solid var(--line);border-radius:5px;background:var(--surface);font-family:var(--mh-mono)}.mh-dialog{max-width:30rem;border:1px solid var(--line-strong);border-radius:14px;background:var(--surface);color:var(--text)}.mh-dialog::backdrop{background:#0f2e3340}.mh-dialog h2{margin-top:0;font-size:1.15rem}.mh-dialog dl{display:grid;grid-template-columns:auto 1fr;gap:.4rem 1rem}.mh-dialog dt{font-family:var(--mh-mono);font-weight:600}.mh-dialog dd{margin:0}.mh-dialog button{margin-top:1rem;padding:.4rem 1rem;border:0;border-radius:8px;background:var(--accent);color:#fff;font:inherit;cursor:pointer}.mh-history h2{margin:.4rem 0 .5rem;font-size:.8rem;font-weight:600;letter-spacing:.08em;text-transform:uppercase;color:var(--muted)}.mh-history ol{margin:0;padding:0;list-style:none}.mh-history li button{display:flex;flex-direction:column;gap:2px;width:100%;padding:.7rem 0;border:0;border-bottom:1px solid var(--line);background:none;text-align:left;cursor:pointer;font:inherit;color:inherit}.mh-history li span{font-family:var(--mh-mono);font-size:.85rem;color:var(--muted)}.mh-history li b{align-self:flex-end;overflow-wrap:anywhere;font-family:var(--mh-mono);font-size:1.05rem;font-weight:600}.mh-history-empty{color:var(--muted);font-size:.9rem}.mh-history-empty[hidden]{display:none}.mh-clear-history{margin-top:.6rem;padding:0;border:0;background:none;color:var(--accent-strong);font:inherit;font-weight:600;cursor:pointer}.mh-trust{display:flex;flex-wrap:wrap;align-items:center;gap:.6rem;margin:1.4rem 0 0}.mh-tick{display:inline-grid;place-items:center;width:1.5rem;height:1.5rem;border-radius:50%;background:var(--mh-ok-bg);color:var(--mh-ok);font-weight:700;font-size:.8rem}.mh-ad{height:100px;margin-top:1.4rem}.mh-section{max-width:72ch;margin-top:2.25rem}.mh-section.mh-wide{max-width:none}.mh-wide table{min-width:52rem;table-layout:fixed}.mh-wide th:nth-child(1){width:17%}.mh-wide th:nth-child(2){width:7%}.mh-wide th:nth-child(3),.mh-wide th:nth-child(4){width:21%}.mh-wide th:nth-child(5){width:9%}.mh-wide td{white-space:normal;overflow-wrap:anywhere}.mh-section h2{margin:0 0 .6rem;font-size:1.45rem;font-weight:600;letter-spacing:-.01em}.mh-table-wrap{overflow-x:auto}.mh-section table{width:100%;border-collapse:collapse;font-size:.92rem}.mh-section th,.mh-section td{padding:.55rem .6rem;border-bottom:1px solid var(--line);text-align:left;vertical-align:top;white-space:normal;overflow-wrap:anywhere}.mh-section thead th{color:var(--muted);font-weight:600}.mh-mono{font-family:var(--mh-mono)}.mh-pass{color:var(--mh-ok);font-weight:600;white-space:nowrap}.mh-fail{color:var(--mh-error);font-weight:700}.mh-examples{padding:0;list-style:none}.mh-examples li{display:flex;flex-wrap:wrap;justify-content:space-between;gap:.4rem 1rem;padding:.6rem 0;border-bottom:1px solid var(--line)}.mh-examples code{font-family:var(--mh-mono)}.mh-faq details{padding:.7rem 0;border-bottom:1px solid var(--line)}.mh-faq summary{cursor:pointer;font-weight:600}.mh-faq details p{margin:.5rem 0 0;color:#2b4a4f}html.hub-math .mh-feature{display:grid;gap:.4rem;max-width:44rem;padding:1.5rem;border-radius:14px;background:linear-gradient(180deg,#edf8f7,#fff);box-shadow:0 0 0 1px #d5e8e8;color:var(--text);text-decoration:none}.mh-feature-kicker{color:var(--accent-strong);font-size:.85rem;font-weight:600;letter-spacing:.06em;text-transform:uppercase}.mh-feature-title{font-size:1.25rem;font-weight:600}.mh-feature-cta{color:var(--accent-strong);font-weight:600}.mh-links{padding-left:1.1rem}.mh-updated{margin-top:2rem;color:var(--muted);font-size:.85rem}@media(max-width:66rem){.mh-workspace{grid-template-columns:1fr;gap:1.5rem}.mh-history ol{display:grid;grid-template-columns:1fr 1fr;column-gap:1.75rem}}@media(max-width:38.75rem){.mh-main{display:flex;flex-direction:column;padding:.25rem 1rem 2rem}.mh-crumbs{display:none}.mh-main h1{margin:.15rem 0 .75rem;font-size:1.5rem}.mh-workspace{order:2}.mh-lede{order:3;margin:1.25rem 0 0}.mh-trust{order:4}.mh-ad{order:5}.mh-section,.mh-updated{order:6}.mh-calc{min-width:0;padding:.9rem}.mh-display{margin:-.9rem -.9rem .75rem;padding:.9rem .9rem 1.1rem}.mh-display:after{right:.9rem;left:.9rem}.mh-modes{flex-wrap:nowrap;gap:.35rem;font-size:.75rem}.mh-seg button{padding:.2rem .5rem}.mh-digits,.mh-mem .mh-kbd{display:none}.mh-tools{gap:0}.mh-tool{padding:.15rem .45rem;font-size:0;line-height:1}.mh-tool:before{font-size:1.05rem}.mh-copy:before{content:"\29c9"}.mh-share:before{content:"\2197"}.mh-expr{margin-top:.85rem;font-size:1.05rem}.mh-result{font-size:clamp(1.5rem,8vw,2.1rem);white-space:nowrap;overflow-x:auto}.mh-eq{margin-right:.5rem}.mh-tabs{display:flex;gap:4px;margin-bottom:.75rem;padding:3px;border-radius:999px;background:#eaf5f4}.mh-tabs button{flex:1;padding:.45rem 0;border:0;border-radius:999px;background:none;color:var(--muted);font:600 .9rem var(--mh-sans);cursor:pointer}.mh-tabs button[aria-selected=true]{background:var(--accent);color:#fff}.mh-strip{display:grid;grid-template-columns:repeat(8,1fr);gap:6px;margin-bottom:.6rem}.mh-strip .mh-k{height:2.4rem;padding:0;font-size:.9rem}.mh-pads{grid-template-columns:1fr}.mh-pad-num{gap:8px}.mh-k{height:3.25rem}.mh-pad-fn{display:none}.mh-calc[data-tab=fn] .mh-pad-fn{display:grid}.mh-calc[data-tab=fn] .mh-pad-num,.mh-calc[data-tab=fn] .mh-strip{display:none}.mh-mem{justify-content:space-between}.mh-history ol{grid-template-columns:1fr}}@media(max-width:22.5rem){.mh-modes{flex-wrap:wrap}}.mh-byline,.mh-note{margin:0 0 .5rem;color:var(--muted);font-size:.85rem}.mh-features{display:grid;grid-template-columns:repeat(auto-fill,minmax(17rem,1fr));gap:1rem;max-width:64rem}.mh-features .mh-feature-title{font-size:1.02rem}.mh-panel{max-width:56rem;border-radius:14px;background:var(--surface);box-shadow:0 0 0 1px #d5e8e8,0 24px 40px -28px #0b8a8459}.mh-panel-help{margin:0;padding:1rem 1.4rem 0;color:var(--muted);font-size:.9rem}.mh-chips{display:flex;flex-wrap:wrap;gap:.5rem;padding:.9rem 1.4rem 0}.mh-chip{min-height:2.75rem;padding:.4rem .95rem;border:1px solid var(--line-strong);border-radius:999px;background:var(--surface);color:#2b4a4f;font:500 .9rem var(--mh-sans);cursor:pointer}.mh-chip[aria-checked=true]{border-color:var(--accent);background:var(--accent);color:#fff;font-weight:600}.mh-help{margin:0;padding:0;border:0;background:none;font-size:.88rem;color:#2b4a4f}.mh-help summary{display:inline-flex;align-items:center;gap:.35rem;min-height:2.75rem;color:var(--accent-strong);font-weight:600;cursor:pointer;list-style:none}.mh-help summary::-webkit-details-marker{display:none}.mh-help summary:before{content:"?";display:inline-grid;place-items:center;width:1.25rem;height:1.25rem;border-radius:50%;background:var(--accent-soft);font-size:.75rem}.mh-help[open] summary:before{content:"\2013"}.mh-help p{max-width:62ch;margin:0 0 .6rem}.mh-help-mode{padding:0 1.4rem}.mh-ask{display:flex;flex-wrap:wrap;align-items:center;gap:.6rem .75rem;padding:.9rem 1.4rem .4rem;font-size:clamp(1.15rem,2.4vw,1.6rem);font-weight:500}.mh-ask[hidden],.mh-fieldhelp[hidden],[data-only][hidden],[data-only-not][hidden],[data-only-b][hidden],.mh-issue[hidden]{display:none}.mh-blank{width:5.5ch;min-height:2.75rem;padding:.2rem .6rem;border:0;border-bottom:2px solid var(--accent);border-radius:8px 8px 0 0;background:#f2f8f8;color:var(--text);font:500 1em var(--mh-mono)}.mh-blank-wide{width:8ch}.mh-blank-small{width:3.5ch;font-size:1rem}.mh-blank-select{width:auto;font-family:var(--mh-sans);font-size:.85em}.mh-blank:focus,.mh-frac-box:focus{outline:none;background:#e6f2f1}.mh-blank[aria-invalid=true],.mh-frac-box[aria-invalid=true]{border-color:var(--mh-error)}.mh-fieldhelp{display:flex;flex-wrap:wrap;gap:0 1.25rem;padding:0 1.4rem}.mh-opts{display:flex;flex-wrap:wrap;align-items:center;gap:.25rem 1.25rem;padding:.2rem 1.4rem .6rem;font-size:.9rem;color:#2b4a4f}.mh-check,.mh-places{display:inline-flex;align-items:center;gap:.5rem;min-height:2.75rem}.mh-check input{width:1.2rem;height:1.2rem;accent-color:var(--accent)}.mh-issue{margin:0 1.4rem .6rem;color:var(--mh-error);font-weight:600}.mh-panel.is-stale [data-answer],.mh-panel.is-stale [data-working]{opacity:.45}.mh-answer{position:relative;padding:1.1rem 1.4rem 1.2rem;border-top:1px solid #d6e9e8;background:linear-gradient(180deg,#edf8f7,#fff)}.mh-answer-head{display:flex;align-items:center;justify-content:space-between}.mh-answer-label{color:var(--muted);font-size:.75rem;font-weight:600;letter-spacing:.08em;text-transform:uppercase}.mh-answer .mh-tools{margin-left:0}.mh-answer-sentence{margin:.3rem 0 0;font-size:clamp(1.35rem,3.2vw,2.1rem);font-weight:500}.mh-answer-sentence b,.mh-also b{font-family:var(--mh-mono);font-weight:600}.mh-answer-sentence b{color:var(--accent-strong)}.mh-also{display:flex;flex-wrap:wrap;gap:.4rem 1.2rem;margin:.6rem 0 0;color:#2b4a4f;font-size:.95rem}.mh-bar{max-width:34rem;height:14px;margin-top:.9rem;overflow:hidden;border-radius:7px;background:#e6f2f1}.mh-bar i{display:block;height:100%;border-radius:7px;background:var(--accent)}.mh-bar-legend{margin:.35rem 0 0;color:var(--muted);font-size:.82rem}.mh-use{min-height:2.75rem;margin-top:.4rem;padding:0;border:0;background:none;color:var(--accent-strong);font:600 .92rem var(--mh-sans);text-decoration:underline;cursor:pointer}.mh-use[hidden]{display:none}.mh-working{padding:1rem 1.4rem 1.2rem;border-top:1px solid var(--line)}.mh-working h2{margin:0 0 .5rem;font-size:1rem;font-weight:600}.mh-formula{margin:0 0 .4rem;font-family:var(--mh-mono);color:var(--accent-strong)}.mh-working ol{display:grid;gap:.3rem;margin:0;padding-left:1.4rem;color:#2b4a4f}.mh-working li::marker{color:var(--accent);font-weight:600}.mh-frac-row{display:grid;grid-template-columns:minmax(0,1fr) auto minmax(0,1fr);gap:1rem;align-items:start;padding:.9rem 1.4rem .2rem}.mh-frac-in label,.mh-dec-field{display:block;margin-bottom:.35rem;color:var(--muted);font-size:.82rem;font-weight:600}.mh-frac-box{box-sizing:border-box;width:100%;min-height:3.1rem;padding:.4rem .8rem;border:1.5px solid var(--line-strong);border-radius:10px;background:var(--surface);color:var(--text);font:500 1.4rem var(--mh-mono)}.mh-frac-box:focus{border-color:var(--accent)}.mh-frac-box-small{max-width:10rem;font-size:1.1rem}.mh-frac-preview{display:flex;align-items:center;gap:.6rem;min-height:3.5rem;margin-top:.4rem;color:#2b4a4f}.mh-words{color:var(--muted);font-size:.85rem}.mh-ops{display:grid;gap:6px;padding-top:1.55rem}.mh-op{width:3rem;height:2.75rem;border:1px solid var(--line-strong);border-radius:10px;background:var(--surface);color:#2b4a4f;font:600 1.25rem var(--mh-sans);cursor:pointer}.mh-op.is-on{border-color:var(--accent);background:var(--accent);color:#fff}.mh-vs{padding-top:2.4rem;color:var(--muted);font-size:.9rem}.mh-dec-row{display:flex;flex-wrap:wrap;gap:.5rem 1.5rem;padding:.9rem 1.4rem .4rem}.mh-dec-field .mh-frac-box{margin-top:.35rem}.mh-dec-row .mh-help{flex-basis:100%}.mh-stack{display:inline-flex;flex-direction:column;align-items:center;font-family:var(--mh-mono);font-weight:600;line-height:1.05;vertical-align:middle}.mh-stack-n{padding:0 .2em;border-bottom:2px solid currentColor}.mh-stack-d{padding:0 .2em}.mh-drawn{display:inline-flex;align-items:center;gap:.15em}.mh-whole{font-family:var(--mh-mono);font-weight:600}.mh-frac-headline{display:flex;flex-wrap:wrap;align-items:center;gap:.5rem;margin:.4rem 0 0;font-size:clamp(1.4rem,3.4vw,2.1rem)}.mh-op-sign{color:var(--muted);font-weight:500}.mh-result-frac{color:var(--accent-strong)}.mh-answer-words{margin:.5rem 0 0;font-size:1.05rem;font-weight:500}.mh-forms{display:grid;grid-template-columns:repeat(auto-fit,minmax(8rem,1fr));gap:.6rem 0;margin-top:1rem}.mh-form{display:grid;gap:.3rem;padding:.2rem 1rem;border-left:1px solid var(--line-strong)}.mh-form:first-child{padding-left:0;border-left:0}.mh-form-k{color:var(--muted);font-size:.72rem;font-weight:600;letter-spacing:.06em;text-transform:uppercase}.mh-form-v{font-family:var(--mh-mono);font-size:1.3rem;font-weight:600}.mh-fbars{display:flex;flex-wrap:wrap;gap:.9rem 2rem;margin-top:1.1rem}.mh-fbar{display:grid;gap:.3rem}.mh-fbar-label{color:var(--muted);font-size:.8rem}.mh-fbar-row{display:flex;flex-wrap:wrap;gap:4px}.mh-seg{--unit: 9rem;display:inline-flex;gap:2px;width:calc(var(--unit) * var(--pieces) / var(--d));max-width:100%}.mh-seg i{flex:1;height:14px;border-radius:3px;background:#e6f2f1}.mh-seg i.on{background:var(--accent)}.mh-main .deep-section{max-width:72ch;margin-top:2.25rem}.mh-main .deep-section h2{margin:0 0 .6rem;font-size:1.45rem;font-weight:600}.mh-main .deep-section table{width:100%;border-collapse:collapse;font-size:.92rem}.mh-main .deep-section th,.mh-main .deep-section td{padding:.5rem .6rem;border-bottom:1px solid var(--line);text-align:left}.mh-main .calc-embed{margin-top:2rem}.mh-embed-page .mh-main{padding-top:1rem}.mh-embed-credit{margin-top:.75rem;font-size:.85rem}@media(max-width:38.75rem){.mh-chips{flex-wrap:nowrap;overflow-x:auto;padding:.8rem 1rem 0;scrollbar-width:none}.mh-chip{flex:0 0 auto;white-space:nowrap}.mh-panel-help,.mh-help-mode,.mh-fieldhelp,.mh-opts,.mh-answer,.mh-working{padding-right:1rem;padding-left:1rem}.mh-ask{padding:.8rem 1rem .3rem;font-size:1.15rem}.mh-issue{margin:0 1rem .6rem}.mh-frac-row{grid-template-columns:1fr;padding:.8rem 1rem .2rem}.mh-ops{grid-auto-flow:column;justify-content:start;padding-top:0}.mh-vs{padding-top:0}.mh-dec-row{padding:.8rem 1rem .3rem}.mh-forms{grid-template-columns:1fr 1fr}.mh-form:nth-child(odd){padding-left:0;border-left:0}.mh-seg{--unit: 7rem}}