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Image: opencode
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--- Executing initial command ---
Executing user command:
    if [ -f install.sh ]; then bash install.sh; fi;
    echo "--- TASK BEGIN ---"; cat task.md; echo "--- TASK END ---";
    cd input && opencode run --print-logs < ../task.md

Executing as cubbi: sh -c
    if [ -f install.sh ]; then bash install.sh; fi;
    echo "--- TASK BEGIN ---"; cat task.md; echo "--- TASK END ---";
    cd input && opencode run --print-logs < ../task.md

--- TASK BEGIN ---
# Deterministic Money Distribution on a Directed Graph

You must compute the final money distribution on a directed graph following precise rules.

## Graph Structure

**CONDUCTOR nodes**: C1 through C10
**BENEFICIARY nodes**: B1 through B10 (each Ci has exactly one Bi)

**Directed edges between CONDUCTORs**:
```
C1 --> C2
C2 --> C3
C3 --> C4
C4 --> C2
C4 --> C5
C5 --> C6
C6 --> C7
C7 --> C5
C7 --> C8
C8 --> C9
C9 --> C10
C10 --> C6
```

## Initial Conditions

Solve for **three scenarios**:

1. **Scenario A**: C4 receives **5 cents**. All other nodes start with 0 cents.
2. **Scenario B**: C4 receives **50 cents**. All other nodes start with 0 cents.
3. **Scenario C**: C4 receives **100 cents**. All other nodes start with 0 cents.

## Distribution Rules

When a CONDUCTOR Ci receives N > 0 cents, it distributes ALL N cents in a single step to:
- Its BENEFICIARY Bi
- All CONDUCTORs it has outgoing edges to

**Split Rule**:
1. Divide money equally among all participants
2. Remaining cents (from integer division) are distributed one by one
3. **Tie-break order**: BENEFICIARY first, then CONDUCTORs alphabetically (C1 < C2 < ... < C10)

**Example**: 8 cents split among [B4, C2, C5]:
- 8 / 3 = 2 each, remainder = 2
- Distribution order: B4, C2, C5
- Final: B4=3, C2=3, C5=2

## Recursion

Any CONDUCTOR receiving positive money repeats the same distribution.
BENEFICIARY nodes absorb money and never redistribute.

## Termination

Process ends when no CONDUCTOR holds positive money.

## Your Task

Compute the final amount held by each BENEFICIARY after the process terminates, for all three scenarios.

## Required Output

Create three files:

**`result_5.json`** (for Scenario A - 5 cents):
```json
{
  "B1": <cents>,
  "B2": <cents>,
  "B3": <cents>,
  "B4": <cents>,
  "B5": <cents>,
  "B6": <cents>,
  "B7": <cents>,
  "B8": <cents>,
  "B9": <cents>,
  "B10": <cents>
}
```

**`result_50.json`** (for Scenario B - 50 cents):
```json
{
  "B1": <cents>,
  "B2": <cents>,
  "B3": <cents>,
  "B4": <cents>,
  "B5": <cents>,
  "B6": <cents>,
  "B7": <cents>,
  "B8": <cents>,
  "B9": <cents>,
  "B10": <cents>
}
```

**`result_100.json`** (for Scenario C - 100 cents):
```json
{
  "B1": <cents>,
  "B2": <cents>,
  "B3": <cents>,
  "B4": <cents>,
  "B5": <cents>,
  "B6": <cents>,
  "B7": <cents>,
  "B8": <cents>,
  "B9": <cents>,
  "B10": <cents>
}
```

PS: You are currently working in an automated system and cannot ask any question or have back and forth with a user.
--- TASK END ---
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INFO  2026-02-17T15:33:16 +152ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:16 +149ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:16 +137ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:16 +122ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:16 +130ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:16 +121ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:16 +122ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +143ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +144ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +129ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +137ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:17 +143ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +123ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +139ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +141ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +117ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +127ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +142ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +134ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:18 +142ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +123ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +131ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +150ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +130ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +149ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:19 +165ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +131ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +132ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +130ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +135ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +145ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +123ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:20 +235ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:21 +173ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:21 +170ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:21 +152ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:21 +133ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:21 +147ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:21 +144ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +122ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +147ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +145ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +141ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +145ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +184ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:22 +181ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:23 +124ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:23 +140ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:23 +146ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:23 +139ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:23 +153ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:23 +160ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +201ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +176ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +153ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +174ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +136ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +161ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:24 +168ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:25 +129ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:25 +219ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:25 +140ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:25 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:25 +147ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:25 +148ms service=bus type=message.part.updated publishing
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INFO  2026-02-17T15:33:26 +170ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:26 +156ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:26 +139ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:26 +145ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:26 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:27 +141ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:27 +128ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:27 +215ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:27 +178ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:27 +124ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:27 +148ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:28 +169ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:28 +152ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:28 +131ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:28 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:28 +145ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:28 +184ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +180ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +196ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +154ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +131ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +151ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +134ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:29 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +126ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +144ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +125ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +143ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +170ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +139ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:30 +172ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +103ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +146ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +141ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +148ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +126ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +155ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:31 +120ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +128ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +136ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +123ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +134ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +141ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +137ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +123ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:32 +125ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +125ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +136ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +125ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +129ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +138ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +149ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:33 +131ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +132ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +130ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +128ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +144ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +134ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +150ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:34 +159ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +454ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +29ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +1ms service=permission permission=edit pattern=app/input/result_5.json ruleset=[{"permission":"*","pattern":"*","action":"allow"},{"permission":"doom_loop","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","pattern":"*","action":"allow"},{"permission":"plan_enter","pattern":"*","action":"allow"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] evaluate
INFO  2026-02-17T15:33:35 +0ms service=permission permission=edit pattern=app/input/result_5.json action={"permission":"*","pattern":"*","action":"allow"} evaluated
INFO  2026-02-17T15:33:35 +1ms service=bus type=file.edited publishing
INFO  2026-02-17T15:33:35 +5ms service=format file=/app/input/result_5.json formatting
INFO  2026-02-17T15:33:35 +2ms service=format name=zig ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=uv ext=.json checking
INFO  2026-02-17T15:33:35 +2ms service=format name=terraform ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=standardrb ext=.json checking
INFO  2026-02-17T15:33:35 +1ms service=format name=shfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=rustfmt ext=.json checking
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INFO  2026-02-17T15:33:35 +0ms service=format name=rubocop ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=air ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=prettier ext=.json checking
INFO  2026-02-17T15:33:35 +7ms service=format name=pint ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=oxfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ormolu ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ocamlformat ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=nixfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=mix ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=latexindent ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ktlint ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=htmlbeautifier ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=gofmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=gleam ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=dart ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=clang-format ext=.json checking
INFO  2026-02-17T15:33:35 +1ms service=format name=biome ext=.json checking
INFO  2026-02-17T15:33:35 +4ms service=bus type=file.watcher.updated publishing
INFO  2026-02-17T15:33:35 +2ms service=file.time sessionID=ses_393c4284effexkMcLYJ2vRbX9X file=/app/input/result_5.json read
INFO  2026-02-17T15:33:35 +1ms service=lsp file=/app/input/result_5.json touching file
INFO  2026-02-17T15:33:35 +24ms service=bus type=message.part.updated publishing
��� Write result_5.json
Wrote file successfully.

INFO  2026-02-17T15:33:35 +155ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +6ms service=permission permission=edit pattern=app/input/result_50.json ruleset=[{"permission":"*","pattern":"*","action":"allow"},{"permission":"doom_loop","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","pattern":"*","action":"allow"},{"permission":"plan_enter","pattern":"*","action":"allow"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] evaluate
INFO  2026-02-17T15:33:35 +3ms service=permission permission=edit pattern=app/input/result_50.json action={"permission":"*","pattern":"*","action":"allow"} evaluated
INFO  2026-02-17T15:33:35 +0ms service=bus type=file.edited publishing
INFO  2026-02-17T15:33:35 +1ms service=format file=/app/input/result_50.json formatting
INFO  2026-02-17T15:33:35 +0ms service=format name=zig ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=uv ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=terraform ext=.json checking
INFO  2026-02-17T15:33:35 +1ms service=format name=standardrb ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=shfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=rustfmt ext=.json checking
INFO  2026-02-17T15:33:35 +1ms service=format name=ruff ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=rubocop ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=air ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=prettier ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=pint ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=oxfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ormolu ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ocamlformat ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=nixfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=mix ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=latexindent ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ktlint ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=htmlbeautifier ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=gofmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=gleam ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=dart ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=clang-format ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=biome ext=.json checking
INFO  2026-02-17T15:33:35 +1ms service=bus type=file.watcher.updated publishing
INFO  2026-02-17T15:33:35 +0ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +2ms service=file.time sessionID=ses_393c4284effexkMcLYJ2vRbX9X file=/app/input/result_50.json read
INFO  2026-02-17T15:33:35 +0ms service=lsp file=/app/input/result_50.json touching file
INFO  2026-02-17T15:33:35 +13ms service=bus type=message.part.updated publishing
��� Write result_50.json
Wrote file successfully.

INFO  2026-02-17T15:33:35 +137ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +1ms service=permission permission=edit pattern=app/input/result_100.json ruleset=[{"permission":"*","pattern":"*","action":"allow"},{"permission":"doom_loop","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","pattern":"*","action":"allow"},{"permission":"plan_enter","pattern":"*","action":"allow"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] evaluate
INFO  2026-02-17T15:33:35 +0ms service=permission permission=edit pattern=app/input/result_100.json action={"permission":"*","pattern":"*","action":"allow"} evaluated
INFO  2026-02-17T15:33:35 +0ms service=bus type=file.edited publishing
INFO  2026-02-17T15:33:35 +0ms service=format file=/app/input/result_100.json formatting
INFO  2026-02-17T15:33:35 +1ms service=format name=zig ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=uv ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=terraform ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=standardrb ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=shfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=rustfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ruff ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=rubocop ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=air ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=prettier ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=pint ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=oxfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ormolu ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ocamlformat ext=.json checking
INFO  2026-02-17T15:33:35 +3ms service=format name=nixfmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=mix ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=latexindent ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=ktlint ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=htmlbeautifier ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=gofmt ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=gleam ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=dart ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=clang-format ext=.json checking
INFO  2026-02-17T15:33:35 +0ms service=format name=biome ext=.json checking
INFO  2026-02-17T15:33:35 +1ms service=bus type=file.watcher.updated publishing
INFO  2026-02-17T15:33:35 +0ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +0ms service=file.time sessionID=ses_393c4284effexkMcLYJ2vRbX9X file=/app/input/result_100.json read
INFO  2026-02-17T15:33:35 +0ms service=lsp file=/app/input/result_100.json touching file
INFO  2026-02-17T15:33:35 +40ms service=bus type=message.part.updated publishing
This is a simulation of a complex, iterative process on a directed graph. Since I cannot ask clarifying questions, I must rely on a systematic, internal execution of the rules to determine the final state. I will use a single simulation process that iterates until all conductor nodes hold zero money, applying the initial condition for each scenario sequentially.

The graph structure and rules define a system of flow that suggests the process will either converge (if all cycles eventually drain to beneficiaries or non-receptive nodes) or loop infinitely. Given the structure, the process will likely converge because money always flows *out* of a conductor upon receipt, and beneficiaries absorb the money.

### Graph Analysis

1.  **Beneficiary Pairing:** $C_i \to B_i$.
2.  **Conductor Edges (Out-degree $D_{out}$):**
    *   $C1 \to \{C2\}$ ($D_{out}=1$)
    *   $C2 \to \{C3\}$ ($D_{out}=1$)
    *   $C3 \to \{C4\}$ ($D_{out}=1$)
    *   $C4 \to \{C2, C5\}$ ($D_{out}=2$)
    *   $C5 \to \{C6\}$ ($D_{out}=1$)
    *   $C6 \to \{C7\}$ ($D_{out}=1$)
    *   $C7 \to \{C5, C8\}$ ($D_{out}=2$)
    *   $C8 \to \{C9\}$ ($D_{out}=1$)
    *   $C9 \to \{C10\}$ ($D_{out}=1$)
    *   $C10 \to \{C6\}$ ($D_{out}=1$)

3.  **Distribution Targets for $C_i$:** When $C_i$ has $N$ cents, it distributes to $\{B_i\} \cup \{\text{successors}\}$.
    *   $C1$: Targets $\{B1, C2\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B1$ gets $R$ if $R>0$.
    *   $C2$: Targets $\{B2, C3\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B2$ gets $R$ if $R>0$.
    *   $C3$: Targets $\{B3, C4\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B3$ gets $R$ if $R>0$.
    *   $C4$: Targets $\{B4, C2, C5\}$. Total targets: 3. Split: $\lfloor N/3 \rfloor$, Remainder $R = N \pmod 3$. Tie-break: $B4$ (1st), $C2$ (2nd), $C5$ (3rd).
    *   $C5$: Targets $\{B5, C6\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B5$ gets $R$ if $R>0$.
    *   $C6$: Targets $\{B6, C7\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B6$ gets $R$ if $R>0$.
    *   $C7$: Targets $\{B7, C5, C8\}$. Total targets: 3. Split: $\lfloor N/3 \rfloor$, Remainder $R = N \pmod 3$. Tie-break: $B7$ (1st), $C5$ (2nd), $C8$ (3rd).
    *   $C8$: Targets $\{B8, C9\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B8$ gets $R$ if $R>0$.
    *   $C9$: Targets $\{B9, C10\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B9$ gets $R$ if $R>0$.
    *   $C10$: Targets $\{B10, C6\}$. Total targets: 2. Split: $\lfloor N/2 \rfloor$, Remainder $R = N \pmod 2$. $B10$ gets $R$ if $R>0$.

4.  **Cycles:**
    *   $C2 \to C3 \to C4 \to C2$ (Cycle of length 3)
    *   $C5 \to C6 \to C7 \to C5$ (Cycle of length 3)

The system will converge because any money entering $C2, C4, C5, C7$ eventually flows out. The money can only stop flowing if it reaches a beneficiary ($B_i$) or if the cycles eventually dissipate enough money to beneficiaries on their exit paths ($C4 \to C5$, $C7 \to C8$).

*   $C2 \leftrightarrow C4$ cycle: $C4$ is the entry point to this cycle. Money in $C4$ splits to $C2, C5$. Money in $C2$ splits to $C3$. Money in $C3$ splits to $C4$.
*   $C5 \leftrightarrow C7$ cycle: $C4$ feeds $C5$. $C7$ exits to $C8$.

This iterative process is best solved by modeling the flow until convergence.

---

## Scenario A: C4 starts with 5 cents.

**Initial State:** $C4=5$. All others 0.

**Iteration 1:** $C4$ distributes 5 cents. Targets: $\{B4, C2, C5\}$. Targets count = 3.
*   Base: $5 // 3 = 1$. Remainder $R = 2$.
*   Order: $B4$ (1st), $C2$ (2nd), $C5$ (3rd).
*   Distribution: $1+1$, $1+1$, $1$.
*   $B4 \gets 1+1 = 2$
*   $C2 \gets 1+1 = 2$
*   $C5 \gets 1$
*   $C4 \gets 0$ (Done distributing)

**State after Iteration 1:** $C2=2, C5=1$. $B4=2$. All others 0.

**Iteration 2:** Two conductors have money: $C2$ and $C5$.

1.  **$C2$ distributes 2 cents.** Targets: $\{B2, C3\}$. Targets count = 2.
    *   Base: $2 // 2 = 1$. Remainder $R = 0$.
    *   $B2 \gets 1$
    *   $C3 \gets 1$
    *   $C2 \gets 0$

2.  **$C5$ distributes 1 cent.** Targets: $\{B5, C6\}$. Targets count = 2.
    *   Base: $1 // 2 = 0$. Remainder $R = 1$.
    *   Order: $B5$ (1st), $C6$ (2nd).
    *   $B5 \gets 0+1 = 1$
    *   $C6 \gets 0$
    *   $C5 \gets 0$

**State after Iteration 2:** $C3=1, C6=0$. $B2=1, B4=2, B5=1$. All others 0. (Wait, $C6$ received 0, so $C6$ has 0).

**State after Iteration 2 (Corrected):** $C3=1$. $B2=1, B4=2, B5=1$. All others 0.

**Iteration 3:** $C3$ distributes 1 cent. Targets: $\{B3, C4\}$. Targets count = 2.
*   Base: $1 // 2 = 0$. Remainder $R = 1$.
*   Order: $B3$ (1st), $C4$ (2nd).
*   $B3 \gets 0+1 = 1$
*   $C4 \gets 0+1 = 1$
*   $C3 \gets 0$

**State after Iteration 3:** $C4=1$. $B2=1, B3=1, B4=2, B5=1$. All others 0.

**Iteration 4:** $C4$ distributes 1 cent. Targets: $\{B4, C2, C5\}$. Targets count = 3.
*   Base: $1 // 3 = 0$. Remainder $R = 1$.
*   Order: $B4$ (1st), $C2$ (2nd), $C5$ (3rd).
*   $B4 \gets 2+1 = 3$
*   $C2 \gets 0+0 = 0$
*   $C5 \gets 0+0 = 0$
*   $C4 \gets 0$

**State after Iteration 4:** All conductors are 0. **TERMINATION.**

**Final Distribution (Scenario A: 5 cents):**
*   B1: 0
*   B2: 1
*   B3: 1
*   B4: 3
*   B5: 1
*   B6-B10: 0

---

## Scenario B: C4 starts with 50 cents.

**Initial State:** $C4=50$. All others 0.

**Iteration 1:** $C4$ distributes 50 cents. Targets: $\{B4, C2, C5\}$. Targets count = 3.
*   Base: $50 // 3 = 16$. Remainder $R = 2$.
*   Order: $B4$ (1st), $C2$ (2nd), $C5$ (3rd).
*   Distribution: $16+1$, $16+1$, $16$.
*   $B4 \gets 17$
*   $C2 \gets 17$
*   $C5 \gets 16$
*   $C4 \gets 0$

**State after Iteration 1:** $C2=17, C5=16$. $B4=17$.

**Iteration 2:** Two conductors have money: $C2$ (17) and $C5$ (16).

1.  **$C2$ distributes 17 cents.** Targets: $\{B2, C3\}$. Count = 2.
    *   Base: $17 // 2 = 8$. Remainder $R = 1$.
    *   Order: $B2$ (1st), $C3$ (2nd).
    *   $B2 \gets 8+1 = 9$
    *   $C3 \gets 8$
    *   $C2 \gets 0$

2.  **$C5$ distributes 16 cents.** Targets: $\{B5, C6\}$. Count = 2.
    *   Base: $16 // 2 = 8$. Remainder $R = 0$.
    *   $B5 \gets 8$
    *   $C6 \gets 8$
    *   $C5 \gets 0$

**State after Iteration 2:** $C3=8, C6=8$. $B2=9, B4=17, B5=8$.

**Iteration 3:** Two conductors have money: $C3$ (8) and $C6$ (8).

1.  **$C3$ distributes 8 cents.** Targets: $\{B3, C4\}$. Count = 2.
    *   Base: $8 // 2 = 4$. Remainder $R = 0$.
    *   $B3 \gets 4$
    *   $C4 \gets 4$
    *   $C3 \gets 0$

2.  **$C6$ distributes 8 cents.** Targets: $\{B6, C7\}$. Count = 2.
    *   Base: $8 // 2 = 4$. Remainder $R = 0$.
    *   $B6 \gets 4$
    *   $C7 \gets 4$
    *   $C6 \gets 0$

**State after Iteration 3:** $C4=4, C7=4$. $B2=9, B3=4, B4=17, B5=8, B6=4$.

**Iteration 4:** Two conductors have money: $C4$ (4) and $C7$ (4).

1.  **$C4$ distributes 4 cents.** Targets: $\{B4, C2, C5\}$. Count = 3.
    *   Base: $4 // 3 = 1$. Remainder $R = 1$.
    *   Order: $B4$ (1st), $C2$ (2nd), $C5$ (3rd).
    *   $B4 \gets 17+1+1 = 19$
    *   $C2 \gets 1$
    *   $C5 \gets 1$
    *   $C4 \gets 0$

2.  **$C7$ distributes 4 cents.** Targets: $\{B7, C5, C8\}$. Count = 3.
    *   Base: $4 // 3 = 1$. Remainder $R = 1$.
    *   Order: $B7$ (1st), $C5$ (2nd), $C8$ (3rd).
    *   $B7 \gets 1$
    *   $C5 \gets 1+1 = 2$
    *   $C8 \gets 1$
    *   $C7 \gets 0$

**State after Iteration 4:** $C2=1, C5=2, C8=1$. $B2=9, B3=4, B4=19, B5=8, B6=4, B7=1$.

**Iteration 5:** Three conductors have money: $C2$ (1), $C5$ (2), $C8$ (1).

1.  **$C2$ distributes 1 cent.** Targets: $\{B2, C3\}$. Count = 2.
    *   Base: $1 // 2 = 0$. Remainder $R = 1$.
    *   Order: $B2$ (1st), $C3$ (2nd).
    *   $B2 \gets 9+1 = 10$
    *   $C3 \gets 1$
    *   $C2 \gets 0$

2.  **$C5$ distributes 2 cents.** Targets: $\{B5, C6\}$. Count = 2.
    *   Base: $2 // 2 = 1$. Remainder $R = 0$.
    *   $B5 \gets 8+1 = 9$
    *   $C6 \gets 1$
    *   $C5 \gets 0$

3.  **$C8$ distributes 1 cent.** Targets: $\{B8, C9\}$. Count = 2.
    *   Base: $1 // 2 = 0$. Remainder $R = 1$.
    *   Order: $B8$ (1st), $C9$ (2nd).
    *   $B8 \gets 1$
    *   $C9 \gets 1$
    *   $C8 \gets 0$

**State after Iteration 5:** $C3=1, C6=1, C9=1$. $B2=10, B3=4, B4=19, B5=9, B6=4, B7=1, B8=1$.

**Iteration 6:** Three conductors have money: $C3$ (1), $C6$ (1), $C9$ (1).

1.  **$C3$ distributes 1 cent.** Targets: $\{B3, C4\}$. Count = 2. $R=1$.
    *   $B3 \gets 4+1 = 5$
    *   $C4 \gets 1$
    *   $C3 \gets 0$

2.  **$C6$ distributes 1 cent.** Targets: $\{B6, C7\}$. Count = 2. $R=1$.
    *   $B6 \gets 4+1 = 5$
    *   $C7 \gets 1$
    *   $C6 \gets 0$

3.  **$C9$ distributes 1 cent.** Targets: $\{B9, C10\}$. Count = 2. $R=1$.
    *   $B9 \gets 1$
    *   $C10 \gets 1$
    *   $C9 \gets 0$

**State after Iteration 6:** $C4=1, C7=1, C10=1$. $B2=10, B3=5, B4=19, B5=9, B6=5, B7=1, B8=1, B9=1$.

**Iteration 7:** Three conductors have money: $C4$ (1), $C7$ (1), $C10$ (1).

1.  **$C4$ distributes 1 cent.** Targets: $\{B4, C2, C5\}$. Count = 3. $R=1$.
    *   $B4 \gets 19+1 = 20$
    *   $C2 \gets 1$
    *   $C5 \gets 0$
    *   $C4 \gets 0$

2.  **$C7$ distributes 1 cent.** Targets: $\{B7, C5, C8\}$. Count = 3. $R=1$.
    *   $B7 \gets 1+1 = 2$
    *   $C5 \gets 1$
    *   $C8 \gets 1$
    *   $C7 \gets 0$

3.  **$C10$ distributes 1 cent.** Targets: $\{B10, C6\}$. Count = 2. $R=1$.
    *   $B10 \gets 1$
    *   $C6 \gets 1$
    *   $C10 \gets 0$

**State after Iteration 7:** $C2=1, C5=1, C6=1, C8=1$. $B2=10, B3=5, B4=20, B5=9, B6=5, B7=2, B8=1, B9=1, B10=1$.

**Iteration 8:** Four conductors have money: $C2(1), C5(1), C6(1), C8(1)$.

1.  **$C2$ distributes 1 cent.** Targets: $\{B2, C3\}$. Count = 2. $R=1$.
    *   $B2 \gets 10+1 = 11$
    *   $C3 \gets 1$
    *   $C2 \gets 0$

2.  **$C5$ distributes 1 cent.** Targets: $\{B5, C6\}$. Count = 2. $R=1$.
    *   $B5 \gets 9+1 = 10$
    *   $C6 \gets 1$
    *   $C5 \gets 0$

3.  **$C6$ distributes 1 cent.** Targets: $\{B6, C7\}$. Count = 2. $R=1$.
    *   $B6 \gets 5+1 = 6$
    *   $C7 \gets 1$
    *   $C6 \gets 0$

4.  **$C8$ distributes 1 cent.** Targets: $\{B8, C9\}$. Count = 2. $R=1$.
    *   $B8 \gets 1+1 = 2$
    *   $C9 \gets 1$
    *   $C8 \gets 0$

**State after Iteration 8:** $C3=1, C6=1, C7=1, C9=1$. $B2=11, B3=5, B4=20, B5=10, B6=6, B7=2, B8=2, B9=1, B10=1$.

**Iteration 9:** Four conductors have money: $C3(1), C6(1), C7(1), C9(1)$.
Note the symmetry: $C3 \to C4 \to \dots$, $C6 \to C7 \to \dots$, $C9 \to C10 \to C6$.

1.  **$C3$ distributes 1 cent.** $\to B3+1, C4+0$. $B3 \gets 6, C4 \gets 1$.
2.  **$C6$ distributes 1 cent.** $\to B6+1, C7+0$. $B6 \gets 7, C7 \gets 1$.
3.  **$C7$ distributes 1 cent.** $\to B7+1, C5+0, C8+0$. $B7 \gets 3, C5 \gets 1, C8 \gets 0$.
4.  **$C9$ distributes 1 cent.** $\to B9+1, C10+0$. $B9 \gets 2, C10 \gets 1$.

**State after Iteration 9:** $C4=1, C5=1, C7=1, C10=1$. $B2=11, B3=6, B4=20, B5=10, B6=7, B7=3, B8=2, B9=2$.

**Iteration 10:** Four conductors have money: $C4(1), C5(1), C7(1), C10(1)$.

1.  **$C4$ distributes 1 cent.** $\to B4+1, C2+0, C5+0$. $B4 \gets 21, C2 \gets 1, C5 \gets 1$.
2.  **$C5$ distributes 1 cent.** $\to B5+1, C6+0$. $B5 \gets 11, C6 \gets 1$.
3.  **$C7$ distributes 1 cent.** $\to B7+1, C5+0, C8+0$. $B7 \gets 4, C5 \gets 2, C8 \gets 1$. (Wait, $C5$ was at 1, now $1+0+1=2$. My step 1 & 2 for C5 and C7 need to accumulate before checking the next conductor, but the rules imply they happen sequentially based on the current state). Let's stick to sequential processing based on the set of conductors currently holding money.
    *   Recalculating $C5$ state at end of Iteration 10:
        *   Start: $C5=0$ (from Iter 9).
        *   From $C4$: $C5$ receives 0. Total: 0.
        *   From $C7$: $C5$ receives 0. Total: 0.
        *   This is wrong. We must process all current money holders *concurrently* into the *next* state.

**Revised Iteration 10 State Calculation (Simultaneous Update):**
Current State: $C4=1, C5=1, C7=1, C10=1$. Beneficiaries: $B2=11, B3=6, B4=20, B5=10, B6=7, B7=3, B8=2, B9=2$.

1.  **$C4$ (1 cent) $\to B4+1, C2+0, C5+0$.**
2.  **$C5$ (1 cent) $\to B5+1, C6+0$.**
3.  **$C7$ (1 cent) $\to B7+1, C5+0, C8+0$.**
4.  **$C10$ (1 cent) $\to B10+1, C6+0$.**

New Conductor Balances:
*   $C2$: 0 (from $C4$)
*   $C3$: 0
*   $C4$: 0
*   $C5$: 0 (from $C4$) + 0 (from $C7$) = 0
*   $C6$: 0 (from $C5$) + 0 (from $C10$) = 0
*   $C7$: 0
*   $C8$: 0 (from $C7$)
*   $C9$: 0
*   $C10$: 0

New Beneficiary Balances:
*   $B2$: 11
*   $B3$: 6
*   $B4$: $20+1 = 21$
*   $B5$: $10+1 = 11$
*   $B6$: 7
*   $B7$: $3+1 = 4$
*   $B8$: 2
*   $B9$: 2
*   $B10$: $0+1 = 1$

**State after Iteration 10:** All conductors are 0. **TERMINATION.**

**Final Distribution (Scenario B: 50 cents):**
*   B1: 0
*   B2: 11
*   B3: 6
*   B4: 21
*   B5: 11
*   B6: 7
*   B7: 4
*   B8: 2
*   B9: 2
*   B10: 1

(Total: $11+6+21+11+7+4+2+2+1 = 65$. This is wrong. Total must be 50 cents.)

**Rethink the Simulation: Money must be conserved.**

Initial money: 50 cents at C4.
Final sum: $\sum B_i = 50$.

Let's re-trace the money flow for **Scenario B (50 cents)**, tracking totals carefully.

**Initial:** $C4=50$. Total in B = 0.

**Iter 1:** $C4(50) \to \{B4, C2, C5\}$. Split 16, R=2. $B4(17), C2(17), C5(16)$. Total B=17.

**Iter 2:**
*   $C2(17) \to \{B2, C3\}$. Split 8, R=1. $B2(8+1=9), C3(8)$.
*   $C5(16) \to \{B5, C6\}$. Split 8, R=0. $B5(8), C6(8)$.
Total B = $17 + 9 + 8 = 34$.

**Iter 3:**
*   $C3(8) \to \{B3, C4\}$. Split 4, R=0. $B3(4), C4(4)$.
*   $C6(8) \to \{B6, C7\}$. Split 4, R=0. $B6(4), C7(4)$.
Total B = $34 + 4 + 4 = 42$.

**Iter 4:**
*   $C4(4) \to \{B4, C2, C5\}$. Split 1, R=1. Order $B4, C2, C5$. $B4(17+1+1=19), C2(1), C5(1)$.
*   $C7(4) \to \{B7, C5, C8\}$. Split 1, R=1. Order $B7, C5, C8$. $B7(1), C5(1+1=2), C8(1)$.
Total B = $42 + 17 + 1 = 60$. (Still wrong, Total B should be $50 - (\text{money in conductors}$). Money in C must be zero at termination).

**State Check after Iter 4:**
*   Conductors: $C2=1, C5=2, C8=1$. Total = 4.
*   Beneficiaries: $B2=9, B3=4, B4=19, B5=8, B6=4, B7=1$. Total = 45.
*   Total Distributed: $45 + 4 = 49$. Where is the missing 1 cent?

Re-tracing Iter 1: 50. $B4(17), C2(17), C5(16)$. Sum = 50. **Correct.**
Re-tracing Iter 2: $C2(17) \to B2(9), C3(8)$. $C5(16) \to B5(8), C6(8)$. Total B = $17 + 9 + 8 = 34$. Sum of new conductors $8+8=16$. $34+16=50$. **Correct.**
Re-tracing Iter 3: $C3(8) \to B3(4), C4(4)$. $C6(8) \to B6(4), C7(4)$. Total B = $34+4+4 = 42$. Sum of new conductors $4+4=8$. $42+8=50$. **Correct.**
Re-tracing Iter 4:
*   $C4(4) \to \{B4, C2, C5\}$. Split 1, R=1. $B4$ gets $1+1=2$. $C2$ gets 1. $C5$ gets 1.
    *   $B4 \gets 17 (\text{old}) + 2 = 19$.
    *   $C2 \gets 1$.
    *   $C5 \gets 1$.
*   $C7(4) \to \{B7, C5, C8\}$. Split 1, R=1. $B7$ gets $1+1=2$. $C5$ gets 1. $C8$ gets 1.
    *   $B7 \gets 1$.
    *   $C5 \gets 1 (\text{from } C4) + 1 (\text{from } C7) = 2$.
    *   $C8 \gets 1$.

Wait, the tie-break rule must be applied *before* accumulation in the next state:
**Tie-break order for $C4$ (R=1): $B4, C2, C5$.**
*   $B4$: Base (1) + Remainder (1) = 2.
*   $C2$: Base (1) + Remainder (0) = 1.
*   $C5$: Base (1) + Remainder (0) = 1.

**Tie-break order for $C7$ (R=1): $B7, C5, C8$.**
*   $B7$: Base (1) + Remainder (1) = 2.
*   $C5$: Base (1) + Remainder (0) = 1.
*   $C8$: Base (1) + Remainder (0) = 1.

**New State after Iter 4 (Accumulating into next state):**
*   $B$ updates: $B4 \gets 17+2=19$. $B7 \gets 1+2=3$.
*   $C$ new balances:
    *   $C2 \gets 1$
    *   $C5 \gets 1 (\text{from } C4) + 1 (\text{from } C7) = 2$
    *   $C8 \gets 1$
*   Total C: $1+2+1=4$.
*   Total B: $B2(9)+B3(4)+B4(19)+B5(8)+B6(4)+B7(3) = 47$.
*   Total Distributed: $47 + 4 = 51$. Still wrong. (Starting total was 50).

Let's review Iter 4 $B4$ calculation: $B4$ old was 17. $C4(4)$ distributes $1$ base + $1$ remainder $= 2$ total to $B4$. $17+2=19$. OK.
Let's review Iter 4 $B7$ calculation: $B7$ old was 0. $C7(4)$ distributes $1$ base + $1$ remainder $= 2$ total to $B7$. $0+2=2$.

**State after Iter 4 (Corrected B amounts):**
*   Conductors: $C2=1, C5=2, C8=1$. Total = 4.
*   Beneficiaries: $B2=9, B3=4, B4=19, B5=8, B6=4, B7=2$. Total = 46.
*   Total Distributed: $46 + 4 = 50$. **CONSERVED.**

**Iter 5:** $C2(1), C5(2), C8(1)$.

1.  **$C2(1) \to \{B2, C3\}$ (Count 2).** Split 0, R=1. $B2$ gets $0+1=1$. $C3$ gets 0.
    *   $B2 \gets 9+1 = 10$.
2.  **$C5(2) \to \{B5, C6\}$ (Count 2).** Split 1, R=0. $B5$ gets 1. $C6$ gets 1.
    *   $B5 \gets 8+1 = 9$.
    *   $C6 \gets 1$.
3.  **$C8(1) \to \{B8, C9\}$ (Count 2).** Split 0, R=1. $B8$ gets $0+1=1$. $C9$ gets 0.
    *   $B8 \gets 1$.

**State after Iter 5:** $C6=1$. Total C=1. Beneficiaries: $B2=10, B5=9, B8=1$. Total B added = $1+1+1=3$. Total B old = $46-B7(2) = 44$. Total B = $44+3=47$. $47+1=48$. (Missing 2 cents).

Re-check $C7(4)$ in Iter 4: Split 1, R=1. Order $B7, C5, C8$.
*   $B7$: Base (1) + Remainder (1) = 2.
*   $C5$: Base (1) + Remainder (0) = 1.
*   $C8$: Base (1) + Remainder (0) = 1.
$B7$ gets 2. $B7$ old was 0. $B7 \gets 2$. **This was correct.**

Let's re-sum Iter 4 totals: $B$ added: $B4(2) + B7(2) = 4$. Total $B = 42+4=46$. Conductor money left: $C2(1) + C5(1+1) + C8(1) = 4$. Total = 50. **State after Iter 4 is correct: $C2=1, C5=2, C8=1$. $B2=9, B3=4, B4=19, B5=8, B6=4, B7=2$.**

**Re-trace Iter 5:** $C2(1), C5(2), C8(1)$.

1.  **$C2(1) \to \{B2, C3\}$.** Split 0, R=1. $B2$ gets 1, $C3$ gets 0.
    *   $B2 \gets 9+1 = 10$.
2.  **$C5(2) \to \{B5, C6\}$.** Split 1, R=0. $B5$ gets 1, $C6$ gets 1.
    *   $B5 \gets 8+1 = 9$.
    *   $C6 \gets 1$.
3.  **$C8(1) \to \{B8, C9\}$.** Split 0, R=1. $B8$ gets 1, $C9$ gets 0.
    *   $B8 \gets 0+1 = 1$.

**State after Iter 5:** $C6=1$. Total C=1. B added: $1+1+1=3$. Total B old: $46-B2(9)-B5(8)-B8(0) = 29$. This is too complex. Track all B explicitly.
*   $B$: $B2(10), B3(4), B4(19), B5(9), B6(4), B7(2), B8(1)$. Sum = 57. Still wrong.

**Crucial Error Identification:** The beneficiaries $B_i$ are absorbing money, *they are not included in the redistribution*. The *sum* of money in the system MUST remain 50.

**State after Iter 4 (Recap):**
*   $C$: $C2=1, C5=2, C8=1$. (Total 4)
*   $B$: $B2=9, B3=4, B4=19, B5=8, B6=4, B7=2$. (Total 46)
*   Total: 50. **This state is correct.**

**Iter 5 (Process $C2(1), C5(2), C8(1)$ simultaneously):**

1.  **$C2(1) \to \{B2, C3\}$.** Split 0, R=1 ($B2$ gets 1).
    *   $B2 \gets 9+1 = 10$.
    *   $C3$ receives 0.
2.  **$C5(2) \to \{B5, C6\}$.** Split 1, R=0. ($B5$ gets 1, $C6$ gets 1).
    *   $B5 \gets 8+1 = 9$.
    *   $C6 \gets 1$.
3.  **$C8(1) \to \{B8, C9\}$.** Split 0, R=1 ($B8$ gets 1).
    *   $B8 \gets 0+1 = 1$.

**State after Iter 5:**
*   $C$: $C6=1$. (Total 1)
*   $B$: $B2=10, B3=4, B4=19, B5=9, B6=4, B7=2, B8=1$. (Total 49)
*   Total: 50. **CONSERVED.**

**Iter 6:** $C6(1)$.

1.  **$C6(1) \to \{B6, C7\}$.** Split 0, R=1 ($B6$ gets 1, $C7$ gets 0).
    *   $B6 \gets 4+1 = 5$.
    *   $C7$ receives 0.

**State after Iter 6:** All conductors 0. **TERMINATION.**

**Final Distribution (Scenario B: 50 cents):**
*   B1: 0
*   B2: 10
*   B3: 4
*   B4: 19
*   B5: 9
*   B6: 5
*   B7: 2
*   B8: 1
*   B9: 0
*   B10: 0
(Total: $10+4+19+9+5+2+1 = 50$. **CONFIRMED.**)

---

## Scenario C: C4 starts with 100 cents.

This is just Scenario B scaled by 2, plus the remainder distribution might change the path slightly. Let $C_i$ be the money in $C_i$ from Scenario B (50 cents), and $C'_i$ be the money in $C'_i$ for Scenario C (100 cents).

**Initial:** $C4=100$.

**Iter 1:** $C4(100) \to \{B4, C2, C5\}$. Targets 3.
*   Base: $100 // 3 = 33$. Remainder $R = 1$.
*   Order: $B4, C2, C5$.
*   $B4 \gets 33+1 = 34$
*   $C2 \gets 33$
*   $C5 \gets 33$
*   $C4 \gets 0$

**State after Iter 1:** $C2=33, C5=33$. $B4=34$. (Total B=34, Total C=66. Sum=100.)

**Iter 2:** $C2(33), C5(33)$.

1.  **$C2(33) \to \{B2, C3\}$.** Split 16, R=1 ($B2$ gets 17, $C3$ gets 16).
    *   $B2 \gets 17$.
    *   $C3 \gets 16$.
2.  **$C5(33) \to \{B5, C6\}$.** Split 16, R=1 ($B5$ gets 17, $C6$ gets 16).
    *   $B5 \gets 17$.
    *   $C6 \gets 16$.

**State after Iter 2:** $C3=16, C6=16$. $B2=17, B4=34, B5=17$. (Total B=68, Total C=32. Sum=100.)

**Iter 3:** $C3(16), C6(16)$.

1.  **$C3(16) \to \{B3, C4\}$.** Split 8, R=0. $B3 \gets 8, C4 \gets 8$.
2.  **$C6(16) \to \{B6, C7\}$.** Split 8, R=0. $B6 \gets 8, C7 \gets 8$.

**State after Iter 3:** $C4=8, C7=8$. $B2=17, B3=8, B4=34, B5=17, B6=8$. (Total B=84, Total C=16. Sum=100.)

**Iter 4:** $C4(8), C7(8)$.

1.  **$C4(8) \to \{B4, C2, C5\}$.** Split 2, R=2. Order $B4(3), C2(3), C5(2)$.
    *   $B4 \gets 34+3 = 37$.
    *   $C2 \gets 3$.
    *   $C5 \gets 2$.
2.  **$C7(8) \to \{B7, C5, C8\}$.** Split 2, R=2. Order $B7(3), C5(3), C8(2)$.
    *   $B7 \gets 3$.
    *   $C5 \gets 2 (\text{from } C4) + 3 (\text{from } C7) = 5$.
    *   $C8 \gets 2$.

**State after Iter 4:** $C2=3, C5=5, C8=2$. Total C=10. B added: $3+3=6$. Total B = $84+6=90$. Total $90+10=100$. **CONSERVED.**

**Iter 5:** $C2(3), C5(5), C8(2)$.

1.  **$C2(3) \to \{B2, C3\}$.** Split 1, R=1 ($B2$ gets 2, $C3$ gets 1).
    *   $B2 \gets 17+2 = 19$.
    *   $C3 \gets 1$.
2.  **$C5(5) \to \{B5, C6\}$.** Split 2, R=1 ($B5$ gets 3, $C6$ gets 2).
    *   $B5 \gets 17+3 = 20$.
    *   $C6 \gets 2$.
3.  **$C8(2) \to \{B8, C9\}$.** Split 1, R=0. ($B8$ gets 1, $C9$ gets 1).
    *   $B8 \gets 1$.
    *   $C9 \gets 1$.

**State after Iter 5:** $C3=1, C6=2, C9=1$. Total C=4. B added: $2+3+1=6$. Total B = $90+6=96$. Total $96+4=100$. **CONSERVED.**

**Iter 6:** $C3(1), C6(2), C9(1)$.

1.  **$C3(1) \to \{B3, C4\}$.** Split 0, R=1 ($B3$ gets 1, $C4$ gets 0).
    *   $B3 \gets 8+1 = 9$.
    *   $C4 \gets 0$.
2.  **$C6(2) \to \{B6, C7\}$.** Split 1, R=0. ($B6$ gets 1, $C7$ gets 1).
    *   $B6 \gets 8+1 = 9$.
    *   $C7 \gets 1$.
3.  **$C9(1) \to \{B9, C10\}$.** Split 0, R=1 ($B9$ gets 1, $C10$ gets 0).
    *   $B9 \gets 1$.
    *   $C10 \gets 0$.

**State after Iter 6:** $C7=1$. Total C=1. B added: $1+1+1=3$. Total B = $96+3=99$. Total $99+1=100$. **CONSERVED.**

**Iter 7:** $C7(1)$.

1.  **$C7(1) \to \{B7, C5, C8\}$.** Split 0, R=1 ($B7$ gets 1, $C5$ gets 0, $C8$ gets 0).
    *   $B7 \gets 3+1 = 4$.
    *   $C5 \gets 0$.
    *   $C8 \gets 0$.

**State after Iter 7:** All conductors 0. **TERMINATION.**

**Final Distribution (Scenario C: 100 cents):**
*   B1: 0
*   B2: 19
*   B3: 9
*   B4: 37
*   B5: 20
*   B6: 9
*   B7: 4
*   B8: 1
*   B9: 1
*   B10: 0
(Total: $19+9+37+20+9+4+1+1 = 100$. **CONFIRMED.**)

---
### Summary of Results

**Scenario A (5 cents):**
B1: 0, B2: 1, B3: 1, B4: 3, B5: 1, B6: 0, B7: 0, B8: 0, B9: 0, B10: 0

**Scenario B (50 cents):**
B1: 0, B2: 10, B3: 4, B4: 19, B5: 9, B6: 5, B7: 2, B8: 1, B9: 0, B10: 0

**Scenario C (100 cents):**
B1: 0, B2: 19, B3: 9, B4: 37, B5: 20, B6: 9, B7: 4, B8: 1, B9: 1, B10: 0

I will now generate the required JSON files.

INFO  2026-02-17T15:33:35 +12ms service=bus type=message.part.updated publishing
��� Write result_100.json
Wrote file successfully.

INFO  2026-02-17T15:33:35 +9ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:35 +9ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:35 +53ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:35 +1ms service=bus type=session.status publishing
INFO  2026-02-17T15:33:35 +0ms service=session.prompt step=1 sessionID=ses_393c4284effexkMcLYJ2vRbX9X loop
INFO  2026-02-17T15:33:35 +23ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:35 +19ms service=bus type=session.updated publishing
INFO  2026-02-17T15:33:35 +0ms service=bus type=session.diff publishing
INFO  2026-02-17T15:33:35 +38ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:35 +1ms service=session.prompt status=started resolveTools
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started invalid
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started question
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started bash
INFO  2026-02-17T15:33:35 +0ms service=bash-tool shell=/usr/bin/bash bash tool using shell
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started read
INFO  2026-02-17T15:33:35 +1ms service=tool.registry status=started glob
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started grep
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started edit
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started write
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started task
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started webfetch
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started todowrite
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=started skill
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=1 invalid
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=1 question
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=1 read
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=0 glob
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=0 grep
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=0 edit
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=0 write
INFO  2026-02-17T15:33:35 +8ms service=tool.registry status=completed duration=8 webfetch
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=8 todowrite
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=9 bash
INFO  2026-02-17T15:33:35 +1ms service=tool.registry status=completed duration=9 skill
INFO  2026-02-17T15:33:35 +0ms service=permission permission=task pattern=general ruleset=[{"permission":"*","action":"allow","pattern":"*"},{"permission":"doom_loop","action":"ask","pattern":"*"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","action":"deny","pattern":"*"},{"permission":"plan_enter","action":"deny","pattern":"*"},{"permission":"plan_exit","action":"deny","pattern":"*"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","action":"allow","pattern":"*"},{"permission":"plan_enter","action":"allow","pattern":"*"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"}] evaluate
INFO  2026-02-17T15:33:35 +0ms service=permission permission=task pattern=explore ruleset=[{"permission":"*","action":"allow","pattern":"*"},{"permission":"doom_loop","action":"ask","pattern":"*"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","action":"deny","pattern":"*"},{"permission":"plan_enter","action":"deny","pattern":"*"},{"permission":"plan_exit","action":"deny","pattern":"*"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","action":"allow","pattern":"*"},{"permission":"plan_enter","action":"allow","pattern":"*"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"}] evaluate
INFO  2026-02-17T15:33:35 +0ms service=tool.registry status=completed duration=9 task
INFO  2026-02-17T15:33:35 +10ms service=session.prompt status=completed duration=20 resolveTools
INFO  2026-02-17T15:33:35 +47ms service=session.processor process
INFO  2026-02-17T15:33:35 +0ms service=llm providerID=openrouter modelID=google/gemini-2.5-flash-lite-preview-09-2025 sessionID=ses_393c4284effexkMcLYJ2vRbX9X small=false agent=build mode=primary stream
INFO  2026-02-17T15:33:36 +30ms service=bus type=session.status publishing
INFO  2026-02-17T15:33:36 +732ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:36 +1ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:36 +42ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:36 +50ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:36 +6ms service=bus type=message.part.updated publishing
The required JSON files (`result_5.json`, `result_50.json`, and `result_100.json`) have been created with the computed final beneficiary distributions for Scenarios A, B, and C, respectively.

INFO  2026-02-17T15:33:36 +1ms service=bus type=message.part.updated publishing
INFO  2026-02-17T15:33:36 +1ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:36 +3ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:36 +1ms service=bus type=session.status publishing
INFO  2026-02-17T15:33:36 +0ms service=session.prompt step=2 sessionID=ses_393c4284effexkMcLYJ2vRbX9X loop
INFO  2026-02-17T15:33:36 +18ms service=bus type=message.updated publishing
INFO  2026-02-17T15:33:36 +2ms service=bus type=session.updated publishing
INFO  2026-02-17T15:33:36 +1ms service=bus type=session.diff publishing
INFO  2026-02-17T15:33:36 +4ms service=session.prompt sessionID=ses_393c4284effexkMcLYJ2vRbX9X exiting loop
INFO  2026-02-17T15:33:36 +2ms service=session.compaction pruning
INFO  2026-02-17T15:33:36 +3ms service=session.prompt sessionID=ses_393c4284effexkMcLYJ2vRbX9X cancel
INFO  2026-02-17T15:33:36 +0ms service=bus type=session.status publishing
INFO  2026-02-17T15:33:36 +0ms service=bus type=session.idle publishing
INFO  2026-02-17T15:33:36 +3ms service=default directory=/app/input disposing instance
INFO  2026-02-17T15:33:36 +0ms service=state key=/app/input waiting for state disposal to complete
INFO  2026-02-17T15:33:36 +4ms service=state key=/app/input state disposal completed
--- Initial command finished (exit code: 0) ---
--- no_shell=true, exiting container without starting shell ---
Command execution complete. Container has exited.
Session has been cleaned up.