:root {
  --article-ink: #17212b;
  --article-muted: #586473;
  --article-accent: #7c3aed;
  --article-accent-dark: #5b21b6;
  --article-accent-soft: #f3e8ff;
  --article-border: #dfe3e8;
  --article-panel: #f8fafc;
  --problem-background: #fff9e6;
  --problem-border: #d8cfa8;
  --problem-accent: #9a6b16;
  --algorithm-background: #f1f4f5;
  --algorithm-border: #c6ced1;
  --algorithm-accent: #465a63;
  --definition-background: #f3f6f1;
  --definition-border: #cbd5c6;
  --definition-accent: #596b52;
}

body {
  color: var(--article-ink);
}

#quarto-content {
  counter-reset: problem algorithm definition;
  font-size: 1.08rem;
  line-height: 1.72;
}

h1,
h2,
h3 {
  letter-spacing: -0.025em;
}

.draft-note {
  margin: 1.5rem 0 2rem;
  padding: 1rem 1.1rem;
  border-left: 4px solid var(--article-accent);
  border-radius: 0 0.55rem 0.55rem 0;
  background: var(--article-accent-soft);
  color: #3b1d62;
}

.problem-statement {
  counter-increment: problem;
  scroll-margin-top: 1.5rem;
  margin: 1.75rem 0 2rem;
  padding: 1.2rem 1.35rem;
  border: 1px solid var(--problem-border);
  border-left: 4px solid var(--problem-accent);
  border-radius: 0.25rem;
  background: var(--problem-background);
  color: #202020;
}

.problem-statement > :first-child {
  margin-top: 0;
}

.problem-statement > :last-child {
  margin-bottom: 0;
}

.problem-title {
  display: block;
  font-size: 1.12rem;
  font-weight: 750;
  line-height: 1.35;
}

.problem-title::before {
  content: "Problem " counter(problem) ": ";
}

.problem-statement:target {
  outline: 2px solid rgb(154 107 22 / 35%);
  outline-offset: 3px;
}

.algorithm-statement {
  counter-increment: algorithm;
  scroll-margin-top: 1.5rem;
  margin: 1.75rem 0 2rem;
  padding: 1.2rem 1.35rem;
  border: 1px solid var(--algorithm-border);
  border-left: 4px solid var(--algorithm-accent);
  border-radius: 0.25rem;
  background: var(--algorithm-background);
  color: #202427;
}

.algorithm-statement > :first-child {
  margin-top: 0;
}

.algorithm-statement > :last-child {
  margin-bottom: 0;
}

.algorithm-title {
  display: block;
  font-size: 1.12rem;
  font-weight: 750;
  line-height: 1.35;
}

.algorithm-title::before {
  content: "Algorithm " counter(algorithm) ": ";
}

.algorithm-statement:target {
  outline: 2px solid rgb(70 90 99 / 35%);
  outline-offset: 3px;
}

.definition-statement {
  counter-increment: definition;
  scroll-margin-top: 1.5rem;
  margin: 1.75rem 0 2rem;
  padding: 1.2rem 1.35rem;
  border: 1px solid var(--definition-border);
  border-left: 4px solid var(--definition-accent);
  border-radius: 0.25rem;
  background: var(--definition-background);
  color: #202420;
}

.definition-statement > :first-child {
  margin-top: 0;
}

.definition-statement > :last-child {
  margin-bottom: 0;
}

.definition-title {
  display: block;
  font-size: 1.12rem;
  font-weight: 750;
  line-height: 1.35;
}

.definition-title::before {
  content: "Definition " counter(definition) ": ";
}

.definition-statement:target {
  outline: 2px solid rgb(89 107 82 / 35%);
  outline-offset: 3px;
}

.key-observations {
  margin: 1.5rem 0 2rem;
}

.key-observations > ol {
  counter-reset: key-observation;
  margin: 0;
  padding: 0;
  list-style: none;
}

.key-observations > ol > li {
  counter-increment: key-observation;
  position: relative;
  margin: 0;
  padding: 1.4rem 0 1.6rem 3.7rem;
  border-top: 1px solid var(--algorithm-border);
}

.key-observations > ol > li:last-child {
  border-bottom: 1px solid var(--algorithm-border);
}

.key-observations > ol > li::before {
  content: counter(key-observation);
  position: absolute;
  top: 1.25rem;
  left: 0;
  display: grid;
  width: 2.25rem;
  height: 2.25rem;
  place-items: center;
  border-radius: 0.2rem;
  background: var(--algorithm-accent);
  color: white;
  font-weight: 750;
  line-height: 1;
}

.key-observations > ol > li > p:first-child {
  margin-top: 0;
  color: #202427;
}

.key-observations > ol > li > :last-child {
  margin-bottom: 0;
}

.proof-qed {
  display: block;
  margin-top: 0.45rem;
  text-align: left;
  line-height: 1;
}

.quicksort-pivots {
  --quicksort-pivots-ink: #202020;
  --quicksort-pivots-muted: #6f695e;
  --quicksort-pivots-structure: #c7c0b3;

  margin: 1.75rem 0 2.25rem;
  padding: 1.15rem 0 1rem;
  border-top: 1px solid var(--problem-border);
  border-bottom: 1px solid var(--problem-border);
  color: var(--quicksort-pivots-ink);
}

.quicksort-pivots__legend {
  display: flex;
  flex-wrap: wrap;
  justify-content: center;
  gap: 0.5rem 1.25rem;
  margin-bottom: 1.2rem;
  color: var(--quicksort-pivots-muted);
  font-size: 0.78rem;
  font-weight: 650;
  line-height: 1.3;
}

.quicksort-pivots__legend > span {
  display: inline-flex;
  gap: 0.4rem;
  align-items: center;
}

.quicksort-pivots__legend-cell,
.quicksort-pivots__legend-empty {
  display: inline-grid;
  width: 1.45rem;
  height: 1.45rem;
  place-items: center;
  border: 1.5px solid var(--algorithm-border);
  border-radius: 0.18rem;
  background: white;
  color: var(--quicksort-pivots-muted);
  font-size: 0.82rem;
  line-height: 1;
}

.quicksort-pivots__legend-cell.is-pivot {
  border: 2px solid var(--problem-accent);
  background: var(--problem-background);
}

.quicksort-pivots__legend-empty {
  border-style: dashed;
  background: var(--algorithm-background);
}

.quicksort-pivots__figures {
  display: grid;
  grid-template-columns: repeat(2, minmax(0, 1fr));
  gap: clamp(1rem, 3vw, 1.75rem);
  align-items: start;
}

.quicksort-pivots__figure {
  min-width: 0;
  margin: 0;
}

.quicksort-pivots__figure + .quicksort-pivots__figure {
  padding-left: clamp(1rem, 3vw, 1.75rem);
  border-left: 1px solid var(--algorithm-border);
}

.quicksort-pivots__caption {
  margin-bottom: 0.45rem;
  text-align: center;
}

.quicksort-pivots__caption-title,
.quicksort-pivots__caption-detail {
  display: block;
}

.quicksort-pivots__caption-title {
  color: var(--quicksort-pivots-ink);
  font-size: 0.98rem;
  font-weight: 750;
  line-height: 1.35;
}

.quicksort-pivots__caption-detail {
  margin-top: 0.12rem;
  color: var(--quicksort-pivots-muted);
  font-size: 0.8rem;
  line-height: 1.4;
}

.quicksort-pivots__canvas {
  width: 100%;
}

.quicksort-pivots__canvas svg {
  display: block;
  width: 100%;
  height: auto;
  margin-inline: auto;
}

.quicksort-pivots__link {
  fill: none;
  stroke: var(--quicksort-pivots-structure);
  stroke-width: 1.7;
  vector-effect: non-scaling-stroke;
}

.quicksort-pivots__link.is-poor-path {
  stroke: var(--problem-accent);
  stroke-width: 2.4;
}

.quicksort-pivots__link-label {
  fill: var(--quicksort-pivots-muted);
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-size: 14px;
  font-weight: 700;
  text-anchor: middle;
}

.quicksort-pivots__cell rect {
  fill: white;
  stroke: var(--algorithm-border);
  stroke-width: 1.5;
  vector-effect: non-scaling-stroke;
}

.quicksort-pivots__cell.is-pivot rect {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 2.4;
}

.quicksort-pivots__cell text,
.quicksort-pivots__empty-label {
  fill: var(--quicksort-pivots-ink);
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-size: 13px;
  font-weight: 700;
  text-anchor: middle;
  dominant-baseline: central;
  pointer-events: none;
}

.quicksort-pivots__cell.is-pivot text {
  fill: #6d490f;
}

.quicksort-pivots__empty-box {
  fill: var(--algorithm-background);
  stroke: var(--algorithm-border);
  stroke-width: 1.5;
  stroke-dasharray: 4 3;
  vector-effect: non-scaling-stroke;
}

.quicksort-pivots__node.is-poor-path .quicksort-pivots__empty-box {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
}

.quicksort-pivots__empty-label {
  fill: var(--quicksort-pivots-muted);
  font-size: 15px;
}

@media (max-width: 780px) {
  .quicksort-pivots__figures {
    grid-template-columns: 1fr;
  }

  .quicksort-pivots__figure + .quicksort-pivots__figure {
    padding-top: 1.5rem;
    padding-left: 0;
    border-top: 1px solid var(--algorithm-border);
    border-left: 0;
  }

  .quicksort-pivots__legend {
    justify-content: flex-start;
  }

  .quicksort-pivots__caption {
    text-align: left;
  }

}

.edge-demo {
  margin: 1.75rem 0 2.25rem;
  padding: clamp(1rem, 3vw, 1.5rem);
  border: 1px solid var(--article-border);
  border-radius: 1rem;
  background: var(--article-panel);
  box-shadow: 0 14px 35px rgb(15 23 42 / 7%);
}

.edge-demo__canvas {
  overflow: hidden;
  border: 1px solid var(--article-border);
  border-radius: 0.75rem;
  background: white;
}

.edge-demo__canvas svg {
  display: block;
  width: 100%;
  height: auto;
  min-height: 240px;
}

.edge-demo__edge {
  stroke: #94a3b8;
  stroke-width: 7;
  stroke-linecap: round;
  transition: stroke 160ms ease, stroke-width 160ms ease;
}

.edge-demo__edge.is-selected {
  stroke: var(--article-accent);
  stroke-width: 11;
}

.edge-demo__node {
  fill: white;
  stroke: var(--article-ink);
  stroke-width: 4;
}

.edge-demo__label {
  fill: var(--article-ink);
  font: 700 22px/1 system-ui, sans-serif;
  text-anchor: middle;
  dominant-baseline: central;
  pointer-events: none;
}

.edge-demo__controls {
  display: flex;
  flex-wrap: wrap;
  gap: 0.65rem;
  margin-top: 1rem;
}

.edge-demo__button {
  padding: 0.68rem 1rem;
  border: 1px solid var(--article-accent);
  border-radius: 999px;
  background: var(--article-accent);
  color: white;
  font: inherit;
  font-weight: 650;
  cursor: pointer;
}

.edge-demo__button:hover {
  border-color: var(--article-accent-dark);
  background: var(--article-accent-dark);
}

.edge-demo__button:focus-visible {
  outline: 3px solid rgb(124 58 237 / 30%);
  outline-offset: 3px;
}

.edge-demo__button--secondary {
  background: white;
  color: var(--article-accent-dark);
}

.edge-demo__button--secondary:hover {
  background: var(--article-accent-soft);
  color: var(--article-accent-dark);
}

.edge-demo__status {
  min-height: 1.6em;
  margin: 0.85rem 0 0;
  color: var(--article-muted);
  font-size: 0.96rem;
}

.computer-network {
  --computer-network-ink: #202020;
  --computer-network-wire: #817b70;

  margin: 1.5rem 0 2rem;
  padding: 1rem 0;
  border-top: 1px solid var(--problem-border);
  border-bottom: 1px solid var(--problem-border);
}

.computer-network__canvas {
  width: min(100%, 36rem);
  aspect-ratio: 36 / 25;
  margin-inline: auto;
}

.computer-network__canvas svg {
  display: block;
  width: 100%;
  height: auto;
}

.computer-network__wire {
  stroke: var(--computer-network-wire);
  stroke-width: 4;
  stroke-linecap: round;
}

.computer-network__screen {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 3;
}

.computer-network__base {
  fill: var(--algorithm-background);
  stroke: var(--computer-network-ink);
  stroke-width: 2.5;
  stroke-linejoin: round;
}

.computer-network__label {
  fill: var(--computer-network-ink);
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-size: 13px;
  font-weight: 750;
  text-anchor: middle;
  dominant-baseline: central;
  pointer-events: none;
}

.edge-contraction {
  --contraction-ink: #202020;
  --contraction-muted: #6f695e;
  --contraction-structure: #817b70;

  margin: 1.75rem 0 2.25rem;
  padding: 1.25rem 0 1rem;
  border-top: 1px solid var(--problem-border);
  border-bottom: 1px solid var(--problem-border);
  color: var(--contraction-ink);
}

.edge-contraction__stage {
  display: grid;
  grid-template-columns: minmax(0, 1fr) minmax(7rem, 0.38fr) minmax(0, 1fr);
  gap: clamp(0.75rem, 2.5vw, 1.5rem);
  align-items: center;
}

.edge-contraction__figure {
  min-width: 0;
  margin: 0;
}

.edge-contraction__figure-title,
.edge-contraction__transition-title {
  margin-bottom: 0.35rem;
  color: var(--contraction-ink);
  font-size: 0.96rem;
  font-weight: 700;
  line-height: 1.35;
  text-align: center;
}

.edge-contraction__canvas {
  display: grid;
  place-items: center;
  width: 100%;
  aspect-ratio: 36 / 25;
}

.edge-contraction__canvas svg,
.edge-contraction__arrow svg {
  display: block;
  width: 100%;
  height: auto;
}

.edge-contraction__transition {
  min-width: 0;
  text-align: center;
}

.edge-contraction__arrow {
  width: 100%;
  max-width: 9rem;
  margin-inline: auto;
}

.edge-contraction__edge {
  fill: none;
  stroke: var(--contraction-structure);
  stroke-width: 3;
  stroke-linecap: round;
  stroke-linejoin: round;
}

.edge-contraction__edge.is-selected {
  stroke: var(--problem-accent);
  stroke-width: 6;
}

.edge-contraction__node {
  fill: white;
  stroke: var(--contraction-ink);
  stroke-width: 3;
}

.edge-contraction__node.is-selected {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 4;
}

.edge-contraction__result-node.is-supernode .edge-contraction__node {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 4;
}

.edge-contraction__label,
.edge-contraction__mini-label,
.edge-contraction__mini-supernode-label {
  fill: var(--contraction-ink);
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-weight: 700;
  text-anchor: middle;
}

.edge-contraction__label {
  font-size: 18px;
}

.edge-contraction__label--inside,
.edge-contraction__mini-label,
.edge-contraction__mini-supernode-label {
  dominant-baseline: central;
}

.edge-contraction__label--inside {
  font-size: 18px;
}

.edge-contraction__label--supernode {
  font-size: 15px;
}

.edge-contraction__arrow-track {
  stroke: var(--problem-border);
  stroke-width: 2;
  stroke-linecap: round;
}

.edge-contraction__arrow-progress,
.edge-contraction__mini-edge {
  stroke: var(--problem-accent);
  stroke-width: 3;
  stroke-linecap: round;
}

.edge-contraction__arrowhead {
  fill: var(--problem-accent);
}

.edge-contraction__mini-node {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 3;
}

.edge-contraction__mini-supernode {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 3;
}

.edge-contraction__mini-label,
.edge-contraction__mini-supernode-label {
  font-size: 11px;
}

.edge-contraction__controls {
  display: flex;
  flex-wrap: wrap;
  gap: 0.75rem;
  align-items: end;
  margin-top: 1rem;
  padding-top: 1rem;
  border-top: 1px solid var(--problem-border);
}

.edge-contraction__field {
  display: grid;
  gap: 0.3rem;
  min-width: min(14rem, 100%);
  color: var(--contraction-ink);
  font-size: 0.94rem;
  font-weight: 650;
  line-height: 1.35;
}

.edge-contraction__field select,
.edge-contraction__button {
  min-height: 2.6rem;
  padding: 0.55rem 0.75rem;
  border: 1px solid var(--problem-border);
  border-radius: 0.25rem;
  font: inherit;
}

.edge-contraction__field select {
  background: white;
  color: var(--contraction-ink);
}

.edge-contraction__button {
  background: white;
  color: var(--contraction-ink);
  font-weight: 700;
  cursor: pointer;
}

.edge-contraction__button--primary {
  border-color: var(--contraction-ink);
  background: var(--contraction-ink);
  color: white;
}

.edge-contraction__button:hover:not(:disabled),
.edge-contraction__field select:hover:not(:disabled) {
  border-color: var(--problem-accent);
  background: var(--problem-background);
}

.edge-contraction__button--primary:hover:not(:disabled) {
  border-color: var(--problem-accent);
  background: #34312c;
  color: white;
}

.edge-contraction__field select:focus-visible,
.edge-contraction__button:focus-visible {
  outline: 3px solid var(--problem-accent);
  outline-offset: 2px;
}

.edge-contraction__field select:disabled,
.edge-contraction__button:disabled {
  cursor: wait;
  opacity: 0.55;
}

.edge-contraction__status {
  min-height: 1.5em;
  margin: 0.75rem 0 0;
  color: var(--contraction-muted);
  font-size: 0.94rem;
}

@media (max-width: 680px) {
  .edge-contraction__stage {
    grid-template-columns: minmax(0, 1fr);
    gap: 0.5rem;
  }

  .edge-contraction__canvas {
    width: min(100%, 21rem);
    margin-inline: auto;
  }

  .edge-contraction__transition {
    width: min(100%, 10rem);
    margin-inline: auto;
  }

  .edge-contraction__arrow-track,
  .edge-contraction__arrow-progress {
    display: none;
  }

  .edge-contraction__transition::after {
    display: block;
    margin-top: -0.25rem;
    color: var(--problem-accent);
    font-size: 1.75rem;
    line-height: 1;
    content: "↓";
  }

  .edge-contraction__controls {
    align-items: stretch;
  }

  .edge-contraction__field {
    flex-basis: 100%;
  }
}

@media (prefers-reduced-motion: reduce) {
  .edge-contraction *,
  .edge-contraction *::before,
  .edge-contraction *::after {
    scroll-behavior: auto !important;
    transition-duration: 0.01ms !important;
    animation-duration: 0.01ms !important;
    animation-iteration-count: 1 !important;
  }
}

.karger-cuts {
  --karger-cuts-ink: #202020;
  --karger-cuts-muted: #6f695e;
  --karger-cuts-edge: #817b70;

  margin: 1.75rem 0 2.25rem;
  padding: 1.1rem 0 1.25rem;
  border-top: 1px solid var(--problem-border);
  border-bottom: 1px solid var(--problem-border);
  color: var(--karger-cuts-ink);
}

.karger-cuts__legend {
  display: flex;
  flex-wrap: wrap;
  gap: 0.65rem 1.25rem;
  justify-content: center;
  margin: 0 0 1.1rem;
  padding: 0;
  color: var(--karger-cuts-muted);
  font-size: 0.9rem;
  line-height: 1.35;
  list-style: none;
}

.karger-cuts__legend li {
  display: inline-flex;
  gap: 0.45rem;
  align-items: center;
}

.karger-cuts__legend-node {
  display: inline-block;
  width: 1.05rem;
  height: 1.05rem;
  border-style: solid;
  border-radius: 50%;
}

.karger-cuts__legend-node.is-set-s {
  border-color: var(--problem-accent);
  border-width: 3px;
  background: var(--problem-background);
}

.karger-cuts__legend-node.is-set-t {
  border-color: var(--algorithm-accent);
  border-width: 2px;
  background: var(--algorithm-background);
}

.karger-cuts__legend-line {
  display: inline-block;
  width: 2rem;
  height: 0;
}

.karger-cuts__legend-line.is-cut-edge {
  border-top: 5px solid var(--problem-accent);
}

.karger-cuts__legend-line.is-cut-boundary {
  border-top: 2px dashed var(--karger-cuts-ink);
}

.karger-cuts__grid {
  display: grid;
  grid-template-columns: repeat(2, minmax(0, 1fr));
  gap: 1.5rem clamp(1rem, 3vw, 2rem);
}

.karger-cuts__figure {
  min-width: 0;
  scroll-margin-top: 1.5rem;
  margin: 0;
}

.karger-cuts__figure:target {
  outline: 2px solid var(--problem-accent);
  outline-offset: 4px;
}

.karger-cuts__caption {
  margin-bottom: 0.3rem;
  color: var(--karger-cuts-ink);
  font-size: 0.96rem;
  font-weight: 700;
  line-height: 1.35;
  text-align: center;
}

.karger-cuts__canvas {
  width: 100%;
  aspect-ratio: 36 / 25;
}

.karger-cuts__canvas svg {
  display: block;
  width: 100%;
  height: auto;
}

.karger-cuts__edge {
  stroke: var(--karger-cuts-edge);
  stroke-width: 3;
  stroke-linecap: round;
}

.karger-cuts__edge.is-cut-edge {
  stroke: var(--problem-accent);
  stroke-width: 6;
}

.karger-cuts__boundary {
  fill: none;
  stroke: var(--karger-cuts-ink);
  stroke-width: 2;
  stroke-dasharray: 7 6;
  stroke-linecap: round;
}

.karger-cuts__node {
  stroke-width: 3;
}

.karger-cuts__node-group.is-set-s .karger-cuts__node {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 4;
}

.karger-cuts__node-group.is-set-t .karger-cuts__node {
  fill: var(--algorithm-background);
  stroke: var(--algorithm-accent);
}

.karger-cuts__vertex-label {
  fill: var(--karger-cuts-ink);
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-size: 20px;
  font-weight: 700;
}

@media (max-width: 680px) {
  .karger-cuts__legend {
    justify-content: flex-start;
  }

  .karger-cuts__grid {
    grid-template-columns: minmax(0, 1fr);
    gap: 1.5rem;
  }

  .karger-cuts__canvas {
    width: min(100%, 24rem);
    margin-inline: auto;
  }
}

.karger-runs {
  --karger-runs-ink: #202020;
  --karger-runs-muted: #6f695e;
  --karger-runs-edge: #817b70;
  --karger-runs-track: #c7c0b3;

  margin: 1.75rem 0 2.25rem;
  padding: 1.25rem 0 1rem;
  border-top: 1px solid var(--problem-border);
  border-bottom: 1px solid var(--problem-border);
  color: var(--karger-runs-ink);
}

.karger-runs__stage {
  display: grid;
  grid-template-columns: minmax(15rem, 0.76fr) 2.1rem minmax(0, 1.55fr);
  gap: 0.35rem;
  align-items: stretch;
  min-width: 0;
}

.karger-runs__shared {
  display: grid;
  grid-template-columns: minmax(5.5rem, 1fr) minmax(4rem, 0.65fr) minmax(5.5rem, 1fr);
  gap: 0.2rem;
  align-items: center;
  min-width: 0;
}

.karger-runs__fork {
  min-width: 0;
}

.karger-runs__fork svg {
  display: block;
  width: 100%;
  height: 100%;
  overflow: visible;
}

.karger-runs__fork path {
  fill: none;
  stroke: var(--karger-runs-track);
  stroke-width: 2;
  vector-effect: non-scaling-stroke;
}

.karger-runs__lanes {
  display: grid;
  grid-template-rows: repeat(2, minmax(0, 1fr));
  gap: 1rem;
  min-width: 0;
}

.karger-runs__lane {
  min-width: 0;
}

.karger-runs__lane + .karger-runs__lane {
  padding-top: 0.75rem;
  border-top: 1px solid var(--problem-border);
}

.karger-runs__lane-title {
  margin: 0 0 0.15rem;
  color: var(--karger-runs-ink);
  font-size: 0.78rem;
  font-weight: 750;
  letter-spacing: 0;
  line-height: 1.25;
}

.karger-runs__lane-sequence {
  display: grid;
  grid-template-columns:
    minmax(0, 0.8fr)
    minmax(0, 1fr)
    minmax(0, 0.6fr)
    minmax(0, 1fr)
    minmax(0, 0.72fr)
    minmax(0, 1.15fr);
  gap: 0.15rem;
  align-items: center;
  min-width: 0;
}

.karger-runs__state {
  min-width: 0;
  margin: 0;
}

.karger-runs__state-label {
  margin-bottom: 0.05rem;
  color: var(--karger-runs-ink);
  font-size: 0.72rem;
  font-weight: 750;
  line-height: 1.15;
  text-align: center;
}

.karger-runs__state-canvas {
  width: 100%;
  aspect-ratio: 170 / 118;
}

.karger-runs__state-canvas svg {
  display: block;
  width: 100%;
  height: auto;
  overflow: visible;
}

.karger-runs__edge {
  fill: none;
  stroke: var(--karger-runs-edge);
  stroke-width: 2.5;
  stroke-linecap: round;
  transition: stroke 150ms ease, stroke-width 150ms ease;
}

.karger-runs__edge.is-selected {
  stroke: var(--problem-accent);
  stroke-width: 5;
}

.karger-runs__node {
  fill: #fff;
  stroke: var(--karger-runs-ink);
  stroke-width: 2.5;
  transition: fill 150ms ease, stroke 150ms ease, stroke-width 150ms ease;
}

.karger-runs__node-group.is-supernode .karger-runs__node {
  fill: var(--problem-background);
  stroke: var(--karger-runs-muted);
  stroke-width: 3;
}

.karger-runs__node-group.is-selected-endpoint .karger-runs__node {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 4;
}

.karger-runs__node-group.is-set-s .karger-runs__node {
  fill: var(--problem-background);
  stroke: var(--problem-accent);
  stroke-width: 4;
}

.karger-runs__node-group.is-set-t .karger-runs__node {
  fill: var(--algorithm-background);
  stroke: var(--algorithm-accent);
  stroke-width: 3;
}

.karger-runs__node-label {
  fill: var(--karger-runs-ink);
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-size: 9px;
  font-weight: 750;
  text-anchor: middle;
  dominant-baseline: central;
  pointer-events: none;
}

.karger-runs__node-label.member-count-3,
.karger-runs__node-label.member-count-4 {
  font-size: 7.5px;
}

.karger-runs__edge-label {
  fill: var(--karger-runs-ink);
  stroke: #fff;
  stroke-width: 3px;
  paint-order: stroke fill;
  font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
  font-size: 7.5px;
  font-weight: 750;
  text-anchor: middle;
  pointer-events: none;
}

.karger-runs__connector {
  display: grid;
  gap: 0.05rem;
  align-content: center;
  justify-items: center;
  min-width: 0;
}

.karger-runs__connector-label {
  color: var(--karger-runs-muted);
  font-size: clamp(0.52rem, 0.77vw, 0.65rem);
  font-weight: 650;
  line-height: 1.12;
  text-align: center;
}

.karger-runs__connector svg {
  display: block;
  width: 100%;
  height: auto;
  overflow: visible;
}

.karger-runs__arrow-track,
.karger-runs__arrow-progress {
  fill: none;
  stroke-width: 2;
  stroke-linecap: round;
}

.karger-runs__arrow-track {
  stroke: var(--karger-runs-track);
}

.karger-runs__arrow-progress {
  stroke: var(--problem-accent);
  stroke-width: 3;
}

.karger-runs__arrowhead {
  fill: var(--problem-accent);
}

.karger-runs__returned-cut {
  min-width: 0;
  margin: 0;
}

.karger-runs__returned-caption {
  min-height: 2.2em;
  margin-bottom: 0;
  font-size: clamp(0.56rem, 0.82vw, 0.68rem);
  line-height: 1.1;
}

.karger-runs__returned-cut .karger-cuts__canvas {
  width: 100%;
  aspect-ratio: 36 / 25;
}

.karger-runs__returned-cut .karger-cuts__edge {
  stroke-width: 4;
}

.karger-runs__returned-cut .karger-cuts__edge.is-cut-edge {
  stroke-width: 7;
}

.karger-runs__returned-cut .karger-cuts__boundary {
  stroke-width: 3;
}

.karger-runs__returned-cut .karger-cuts__vertex-label {
  font-size: 24px;
}

.karger-runs__controls {
  display: flex;
  justify-content: flex-end;
  margin-top: 0.9rem;
  padding-top: 0.85rem;
  border-top: 1px solid var(--problem-border);
}

.karger-runs__replay {
  min-height: 2.45rem;
  padding: 0.5rem 0.9rem;
  border: 1px solid var(--karger-runs-ink);
  border-radius: 0.25rem;
  background: var(--karger-runs-ink);
  color: #fff;
  font: inherit;
  font-weight: 700;
  cursor: pointer;
}

.karger-runs__replay:hover:not(:disabled) {
  border-color: var(--problem-accent);
  background: #34312c;
}

.karger-runs__replay:focus-visible {
  outline: 3px solid var(--problem-accent);
  outline-offset: 2px;
}

.karger-runs__replay:disabled {
  cursor: wait;
  opacity: 0.55;
}

.karger-runs__status {
  min-height: 1.5em;
  margin: 0.65rem 0 0;
  color: var(--karger-runs-muted);
  font-size: 0.9rem;
  line-height: 1.4;
}

@media (max-width: 680px) {
  .karger-runs__stage {
    display: block;
  }

  .karger-runs__shared {
    grid-template-columns: minmax(0, 1fr) minmax(4rem, 0.58fr) minmax(0, 1fr);
    width: min(100%, 23rem);
    margin-inline: auto;
  }

  .karger-runs__fork {
    display: none;
  }

  .karger-runs__lanes {
    display: block;
    margin-top: 1.25rem;
  }

  .karger-runs__lane,
  .karger-runs__lane + .karger-runs__lane {
    padding-top: 1rem;
    border-top: 1px solid var(--problem-border);
  }

  .karger-runs__lane + .karger-runs__lane {
    margin-top: 1.5rem;
  }

  .karger-runs__lane-title {
    margin-bottom: 0.6rem;
    font-size: 0.9rem;
    text-align: center;
  }

  .karger-runs__lane-sequence {
    display: grid;
    grid-template-columns: minmax(0, 1fr);
    gap: 0.35rem;
    justify-items: center;
  }

  .karger-runs__lane-sequence > [data-state-slot] {
    width: min(100%, 13rem);
  }

  .karger-runs__lane-sequence > [data-cut-slot] {
    width: min(100%, 15rem);
  }

  .karger-runs__lane-sequence .karger-runs__connector {
    width: min(100%, 12rem);
  }

  .karger-runs__lane-sequence .karger-runs__connector svg {
    width: 2.25rem;
    transform: rotate(90deg);
  }

  .karger-runs__connector-label {
    font-size: 0.68rem;
  }

  .karger-runs__returned-caption {
    min-height: 0;
    font-size: 0.76rem;
  }

  .karger-runs__controls {
    justify-content: stretch;
  }

  .karger-runs__replay {
    width: 100%;
  }
}

@media (prefers-reduced-motion: reduce) {
  .karger-runs *,
  .karger-runs *::before,
  .karger-runs *::after {
    scroll-behavior: auto !important;
    transition-duration: 0.01ms !important;
    animation-duration: 0.01ms !important;
    animation-iteration-count: 1 !important;
  }
}

.freivalds-failure {
  --freivalds-ink: #202020;
  --freivalds-muted: #6f695e;
  --freivalds-track: #c7c0b3;
  --freivalds-mismatch: #733f36;
  --freivalds-agreement: var(--problem-accent);

  margin: 1.75rem 0 2.25rem;
  padding: 1.25rem 0 1rem;
  border-top: 1px solid var(--problem-border);
  border-bottom: 1px solid var(--problem-border);
  color: var(--freivalds-ink);
}

.freivalds-failure__stage {
  display: grid;
  gap: 1rem;
  min-width: 0;
}

.freivalds-failure__section {
  min-width: 0;
  padding: 1rem;
  border: 1px solid var(--problem-border);
  border-radius: 0.25rem;
  background: #fbfaf7;
}

.freivalds-failure__stage-label,
.freivalds-failure__lane-title,
.freivalds-failure__minor-label,
.freivalds-failure__agreement-label {
  display: block;
  color: var(--freivalds-ink);
  font-weight: 750;
  line-height: 1.3;
}

.freivalds-failure__stage-label {
  margin: 0 0 0.8rem;
  font-size: 0.92rem;
}

.freivalds-failure__stage-label .katex {
  font-size: 1.02em;
}

.freivalds-failure__minor-label {
  margin-bottom: 0.45rem;
  color: var(--freivalds-muted);
  font-size: 0.76rem;
  text-align: center;
}

.freivalds-failure__input-row {
  display: grid;
  grid-template-columns: repeat(3, minmax(0, 1fr));
  gap: 0.65rem;
}

.freivalds-failure__formula-node {
  min-width: 0;
  padding: 0.6rem 0.5rem;
  overflow-x: auto;
  border: 1px solid #d9d5cc;
  border-radius: 0.2rem;
  background: #fff;
  text-align: center;
  scrollbar-width: thin;
}

.freivalds-failure__formula-node .katex-display {
  margin: 0;
}

.freivalds-failure__matrix .katex {
  font-size: clamp(0.9rem, 1.8vw, 1.08rem);
}

.freivalds-failure__mismatch {
  border-left: 3px solid var(--freivalds-mismatch);
}

.freivalds-failure__mismatch .freivalds-failure__formula-node {
  color: var(--freivalds-mismatch);
}

.freivalds-failure__sampling-row {
  display: grid;
  grid-template-columns: minmax(9rem, 0.9fr) minmax(4.5rem, 0.45fr) minmax(9rem, 1fr);
  gap: 0.8rem;
  align-items: center;
}

.freivalds-failure__tray {
  display: grid;
  grid-template-columns: repeat(2, minmax(0, 1fr));
  gap: 0.45rem;
  min-width: 0;
  padding: 0.55rem;
  border: 1px solid var(--freivalds-track);
  border-radius: 0.25rem;
  background: #f6f3ec;
}

.freivalds-failure__sample-card {
  display: grid;
  min-height: 4.35rem;
  place-items: center;
  padding: 0.35rem;
  border: 1px solid #bbb4a7;
  border-radius: 0.2rem;
  background: #fff;
  transition:
    opacity 220ms ease,
    border-color 220ms ease,
    background-color 220ms ease,
    transform 220ms ease;
}

.freivalds-failure__sample-card .katex {
  font-size: 0.95rem;
}

.freivalds-failure__sample-card.is-selected {
  border-color: var(--freivalds-agreement);
  background: var(--problem-background);
  transform: translateY(-2px);
}

.freivalds-failure__sample-card.is-dimmed {
  opacity: 0.28;
}

.freivalds-failure__tray.is-shuffling .freivalds-failure__sample-card:nth-child(1) {
  animation: freivalds-shuffle-a 560ms ease-in-out;
}

.freivalds-failure__tray.is-shuffling .freivalds-failure__sample-card:nth-child(2) {
  animation: freivalds-shuffle-b 560ms 35ms ease-in-out;
}

.freivalds-failure__tray.is-shuffling .freivalds-failure__sample-card:nth-child(3) {
  animation: freivalds-shuffle-b 560ms 70ms ease-in-out reverse;
}

.freivalds-failure__tray.is-shuffling .freivalds-failure__sample-card:nth-child(4) {
  animation: freivalds-shuffle-a 560ms 105ms ease-in-out reverse;
}

@keyframes freivalds-shuffle-a {
  0%,
  100% {
    transform: translate(0, 0);
  }
  45% {
    transform: translate(4px, -3px);
  }
  70% {
    transform: translate(-2px, 2px);
  }
}

@keyframes freivalds-shuffle-b {
  0%,
  100% {
    transform: translate(0, 0);
  }
  45% {
    transform: translate(-4px, 3px);
  }
  70% {
    transform: translate(2px, -2px);
  }
}

.freivalds-failure__selected,
.freivalds-failure__source {
  min-width: 0;
}

.freivalds-failure__source {
  width: min(100%, 18rem);
  margin-inline: auto;
}

.freivalds-failure__arrow {
  display: block;
  overflow: visible;
}

.freivalds-failure__sample-arrow {
  width: 100%;
  height: auto;
}

.freivalds-failure__arrow-track,
.freivalds-failure__arrow-progress {
  fill: none;
  stroke-width: 2;
  stroke-linecap: round;
  vector-effect: non-scaling-stroke;
}

.freivalds-failure__arrow-track {
  stroke: var(--freivalds-track);
}

.freivalds-failure__arrow-progress {
  stroke: var(--freivalds-agreement);
  stroke-width: 3;
  stroke-dasharray: 1;
  stroke-dashoffset: 1;
  transition: stroke-dashoffset 380ms cubic-bezier(0.22, 1, 0.36, 1);
}

.freivalds-failure__arrow.is-drawn .freivalds-failure__arrow-progress {
  stroke-dashoffset: 0;
}

.freivalds-failure__arrowhead {
  fill: var(--freivalds-agreement);
  opacity: 0;
  transition: opacity 120ms ease 260ms;
}

.freivalds-failure__arrow.is-drawn .freivalds-failure__arrowhead {
  opacity: 1;
}

.freivalds-failure__computation {
  padding-bottom: 1.1rem;
}

.freivalds-failure__branch,
.freivalds-failure__convergence {
  width: 72%;
  height: 2.4rem;
  margin: 0.25rem auto;
}

.freivalds-failure__branch--mobile,
.freivalds-failure__convergence--mobile {
  display: none;
}

.freivalds-failure__lanes {
  display: grid;
  grid-template-columns: minmax(0, 1.25fr) minmax(0, 1fr);
  gap: 0.8rem;
  align-items: stretch;
}

.freivalds-failure__lane {
  min-width: 0;
  padding: 0.8rem;
  border: 1px solid var(--algorithm-border);
  border-radius: 0.25rem;
  background: var(--algorithm-background);
}

.freivalds-failure__lane-title {
  min-height: 2.5em;
  margin: 0 0 0.65rem;
  font-size: 0.8rem;
  text-align: center;
}

.freivalds-failure__lane-sequence {
  display: grid;
  gap: 0.25rem;
  justify-items: stretch;
}

.freivalds-failure__lane-arrow {
  width: 2.7rem;
  height: 1.4rem;
  margin-inline: auto;
  transform: rotate(90deg);
}

.freivalds-failure__lane-single {
  display: grid;
  min-height: calc(100% - 3.15rem);
  align-items: center;
}

.freivalds-failure__lane .freivalds-failure__formula-node {
  padding-inline: 0.25rem;
}

.freivalds-failure__lane .katex {
  font-size: clamp(0.67rem, 1.35vw, 0.88rem);
}

.freivalds-failure__agreement {
  width: min(100%, 30rem);
  margin-inline: auto;
  padding: 0.85rem;
  border: 1px solid var(--freivalds-agreement);
  border-left: 3px solid var(--freivalds-agreement);
  border-radius: 0.25rem;
  background: var(--problem-background);
  text-align: center;
}

.freivalds-failure__agreement-label {
  margin-bottom: 0.45rem;
  color: #765112;
  font-size: 0.8rem;
}

.freivalds-failure__agreement .freivalds-failure__formula-node {
  border-color: var(--problem-border);
}

.freivalds-failure__agreement p {
  margin: 0.65rem 0 0;
  color: #5f4516;
  font-size: 0.9rem;
  font-weight: 700;
  line-height: 1.4;
}

.freivalds-failure__nowrap {
  white-space: nowrap;
}

.freivalds-failure__reveal {
  visibility: hidden;
  opacity: 0;
  transform: translateY(7px);
  transition:
    opacity 340ms ease,
    transform 340ms ease,
    visibility 0s linear 340ms;
}

.freivalds-failure__reveal.is-visible {
  visibility: visible;
  opacity: 1;
  transform: translateY(0);
  transition-delay: 0s;
}

.freivalds-failure__controls {
  display: flex;
  justify-content: flex-end;
  margin-top: 0.9rem;
  padding-top: 0.85rem;
  border-top: 1px solid var(--problem-border);
}

.freivalds-failure__replay {
  min-height: 2.45rem;
  padding: 0.5rem 0.9rem;
  border: 1px solid var(--freivalds-ink);
  border-radius: 0.25rem;
  background: var(--freivalds-ink);
  color: #fff;
  font: inherit;
  font-weight: 700;
  cursor: pointer;
}

.freivalds-failure__replay:hover:not(:disabled) {
  border-color: var(--problem-accent);
  background: #34312c;
}

.freivalds-failure__replay:focus-visible {
  outline: 3px solid var(--problem-accent);
  outline-offset: 2px;
}

.freivalds-failure__replay:disabled {
  cursor: wait;
  opacity: 0.55;
}

.freivalds-failure__status {
  min-height: 1.5em;
  margin: 0.65rem 0 0;
  color: var(--freivalds-muted);
  font-size: 0.9rem;
  line-height: 1.4;
}

.freivalds-failure__traveling-card {
  position: fixed;
  z-index: 1000;
  box-sizing: border-box;
  margin: 0;
  pointer-events: none;
}

@media (max-width: 680px) {
  .freivalds-failure__section {
    padding: 0.85rem;
  }

  .freivalds-failure__input-row {
    grid-template-columns: minmax(0, 1fr);
    width: min(100%, 16rem);
    margin-inline: auto;
  }

  .freivalds-failure__sampling-row {
    grid-template-columns: minmax(0, 1fr);
    justify-items: center;
  }

  .freivalds-failure__tray {
    width: min(100%, 16rem);
  }

  .freivalds-failure__sample-arrow {
    width: 3.5rem;
    height: 3.5rem;
    transform: rotate(90deg);
  }

  .freivalds-failure__selected {
    width: min(100%, 16rem);
  }

  .freivalds-failure__branch--desktop,
  .freivalds-failure__convergence--desktop {
    display: none;
  }

  .freivalds-failure__branch--mobile,
  .freivalds-failure__convergence--mobile {
    display: block;
    width: 2rem;
    height: 3rem;
    margin-block: 0.25rem;
  }

  .freivalds-failure__lanes {
    grid-template-columns: minmax(0, 1fr);
  }

  .freivalds-failure__lane-title {
    min-height: 0;
  }

  .freivalds-failure__lane-single {
    min-height: 0;
  }

  .freivalds-failure__lane .katex {
    font-size: clamp(0.66rem, 2.8vw, 0.86rem);
  }

  .freivalds-failure__controls {
    justify-content: stretch;
  }

  .freivalds-failure__replay {
    width: 100%;
  }
}

@media (prefers-reduced-motion: reduce) {
  .freivalds-failure *,
  .freivalds-failure *::before,
  .freivalds-failure *::after {
    scroll-behavior: auto !important;
    transition-duration: 0.01ms !important;
    animation-duration: 0.01ms !important;
    animation-iteration-count: 1 !important;
  }
}