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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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This is a complex simulation task that requires implementing the specified graph structure and distribution logic. Since this is a self-contained computational task, I will implement the logic in Python to perform the simulation for all three scenarios and then write the results to the requested JSON files.

The logic needs to handle:
1.  The graph structure (Conductors and their edges).
2.  The initial conditions (Scenarios A, B, C).
3.  The recursive distribution process until all Conductors have 0 cents.
4.  The specific Split Rule (equal division + remainder distribution using the tie-break order).

First, I will define the graph structure and distribution logic.

### Graph and Distribution Setup

The graph structure is:
- C1 -> C2
- C2 -> C3
- C3 -> C4
- C4 -> C2, C5
- C5 -> C6
- C6 -> C7
- C7 -> C5, C8
- C8 -> C9
- C9 -> C10
- C10 -> C6

Each $C_i$ has a beneficiary $B_i$.
The participants in the split are always $B_i$ and the outgoing $C_j$'s.
The tie-break order for remainder is: $B_i$, then $C_j$'s in alphabetical order ($C_2 < C_5 < \dots$).

I will implement the simulation in a Python script.

### Plan:

1.  **Define Graph**: A dictionary mapping each conductor to its beneficiaries (always one) and its outgoing conductor edges.
2.  **Define Split Function**: A function that takes the current money $N$ and the list of participants, and returns the distributed amounts according to the rules.
3.  **Define Simulation Function**: A function that takes the initial money at C4, runs the distribution process recursively, and returns the final beneficiary sums.
4.  **Execute Scenarios**: Run the simulation for 5, 50, and 100 cents.
5.  **Write Results**: Create the three JSON files.

Since I cannot write and execute a file in separate steps and need to output the final tool calls, I will prepare a single Python script and use the `bash` tool to execute it. Then I will use the `write` tool to create the final JSON files.

The Python script `money_distribution.py` will contain the entire logic.

```python
import json
from collections import deque

# 1. Define the graph structure
GRAPH = {
    'C1': ['C2'],
    'C2': ['C3'],
    'C3': ['C4'],
    'C4': ['C2', 'C5'],
    'C5': ['C6'],
    'C6': ['C7'],
    'C7': ['C5', 'C8'],
    'C8': ['C9'],
    'C9': ['C10'],
    'C10': ['C6'],
}

def get_participants(conductor):
    """
    Returns the list of participants (beneficiary + other conductors)
    and the tie-break order.
    """
    i = conductor[1:]
    beneficiary = f'B{i}'
    outgoing_conductors = GRAPH.get(conductor, [])

    # Tie-break order: Beneficiary first, then Conductors alphabetically
    participants = [beneficiary] + sorted(outgoing_conductors)
    return participants

def split_money(money, participants):
    """
    Implements the Split Rule and Tie-break order.
    Returns a dictionary of {participant: amount}.
    """
    num_participants = len(participants)
    if num_participants == 0:
        return {}

    base_amount = money // num_participants
    remainder = money % num_participants

    distribution = {p: base_amount for p in participants}

    # Distribute remainder based on tie-break order
    for i in range(remainder):
        participant_to_receive = participants[i]
        distribution[participant_to_receive] += 1

    return distribution

def simulate_distribution(initial_c4_cents):
    """
    Simulates the entire recursive distribution process.
    """
    conductor_money = {f'C{i}': 0 for i in range(1, 11)}
    beneficiary_money = {f'B{i}': 0 for i in range(1, 11)}

    # Set initial condition
    conductor_money['C4'] = initial_c4_cents

    # Queue for conductors that need to distribute
    # We start with C4 as it is the only one with money initially
    active_conductors = deque(['C4'])

    while active_conductors:
        current_conductor = active_conductors.popleft()

        N = conductor_money[current_conductor]

        # Only distribute if N > 0
        if N > 0:
            # Clear the money from the current conductor before distribution
            conductor_money[current_conductor] = 0

            participants = get_participants(current_conductor)
            distribution = split_money(N, participants)

            for participant, amount in distribution.items():
                if amount > 0:
                    if participant.startswith('B'):
                        # Money absorbed by Beneficiary
                        beneficiary_money[participant] += amount
                    elif participant.startswith('C'):
                        # Money received by another Conductor
                        conductor_money[participant] += amount
                        # Add to the queue if it now holds money (or had money already)
                        if participant not in active_conductors:
                            active_conductors.append(participant)

    # Return only the final beneficiary distribution
    return beneficiary_money

# --- Execution ---

scenarios = {
    '5': 5,
    '50': 50,
    '100': 100,
}

results = {}

for suffix, initial_cents in scenarios.items():
    result = simulate_distribution(initial_cents)
    # The output format requires B1 to B10 keys only
    final_output = {f'B{i}': result[f'B{i}'] for i in range(1, 11)}
    results[suffix] = final_output

# Output JSON files will be written by the tool
json_outputs = {}
for suffix, data in results.items():
    json_outputs[f'result_{suffix}.json'] = json.dumps(data, indent=2)

# Print JSON outputs in a format easy to copy/paste into write calls
for filename, content in json_outputs.items():
    print(f"--- {filename} ---\n{content}\n--- End {filename} ---\n")
```

I will now write the Python script to the file system and execute it to get the final results. I will use a temporary file `money_distribution.py` to store and run the script.

INFO  2026-01-16T15:31:12 +18ms service=bus type=message.part.updated publishing
INFO  2026-01-16T15:31:12 +1ms service=bus type=message.updated publishing
INFO  2026-01-16T15:31:12 +20ms service=bus type=message.updated publishing
INFO  2026-01-16T15:31:12 +1ms service=bus type=session.status publishing
INFO  2026-01-16T15:31:12 +0ms service=session.prompt step=1 sessionID=ses_4389190daffeIsqZJJXPSXyPKU loop
INFO  2026-01-16T15:31:12 +16ms service=bus type=message.updated publishing
INFO  2026-01-16T15:31:12 +1ms service=bus type=session.updated publishing
INFO  2026-01-16T15:31:12 +1ms service=bus type=session.diff publishing
INFO  2026-01-16T15:31:12 +3ms service=session.prompt sessionID=ses_4389190daffeIsqZJJXPSXyPKU exiting loop
INFO  2026-01-16T15:31:12 +1ms service=session.compaction pruning
INFO  2026-01-16T15:31:12 +21ms service=session.prompt sessionID=ses_4389190daffeIsqZJJXPSXyPKU cancel
INFO  2026-01-16T15:31:12 +0ms service=bus type=session.status publishing
INFO  2026-01-16T15:31:12 +1ms service=bus type=session.idle publishing
INFO  2026-01-16T15:31:12 +2ms service=default directory=/app/input disposing instance
INFO  2026-01-16T15:31:12 +1ms service=state key=/app/input waiting for state disposal to complete
INFO  2026-01-16T15:31:12 +3ms 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.