/home/llmeval/.local/share/uv/tools/cubbi/lib/python3.12/site-packages/click/core.py:1213: UserWarning: The parameter -m is used more than once. Remove its duplicate as parameters should be unique. parser = self.make_parser(ctx) /home/llmeval/.local/share/uv/tools/cubbi/lib/python3.12/site-packages/click/core.py:1206: UserWarning: The parameter -m is used more than once. Remove its duplicate as parameters should be unique. self.parse_args(ctx, args) Using UID: 1000, GID: 1000 Forwarding environment variable OPENROUTER_API_KEY to container Mounting local directory /home/llmeval/llmeval/runs/run_20260215_150129/task14_graph_money_distribution/openrouter-google-gemini-2.5-flash-lite-preview-09-2025/workspace to /app No project_name provided - skipping configuration directory setup. Session created successfully! Session ID: ab66f480 Image: opencode Executing command and waiting for completion... Container will exit after command completes. Command logs: Initializing opencode v1.0.0 Setting up user 'cubbi' with UID: 1000, GID: 1000 Setting up standard directories Created directory: /app Created directory: /cubbi-config Created directory: /cubbi-config/home Creating /home/cubbi as symlink to /cubbi-config/home Created directory: /cubbi-config/home/.local Copied /root/.local/bin to user directory Running opencode-specific initialization Added litellm custom provider with 169 models to OpenCode configuration Added openrouter standard provider with 340 models to OpenCode configuration Set default model to openrouter/google/gemini-2.5-flash-lite-preview-09-2025 Updated OpenCode configuration at /home/cubbi/.config/opencode/config.json with 2 providers No MCP servers to integrate --- 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": , "B2": , "B3": , "B4": , "B5": , "B6": , "B7": , "B8": , "B9": , "B10": } ``` **`result_50.json`** (for Scenario B - 50 cents): ```json { "B1": , "B2": , "B3": , "B4": , "B5": , "B6": , "B7": , "B8": , "B9": , "B10": } ``` **`result_100.json`** (for Scenario C - 100 cents): ```json { "B1": , "B2": , "B3": , "B4": , "B5": , "B6": , "B7": , "B8": , "B9": , "B10": } ``` PS: You are currently working in an automated system and cannot ask any question or have back and forth with a user. --- TASK END --- INFO 2026-02-15T15:32:49 +758ms service=default version=1.1.51 args=["run","--print-logs"] opencode INFO 2026-02-15T15:32:49 +23ms service=default directory=/app/input creating instance INFO 2026-02-15T15:32:49 +0ms service=project directory=/app/input fromDirectory INFO 2026-02-15T15:32:49 +16ms service=storage index=0 running migration INFO 2026-02-15T15:32:49 +23ms service=storage index=1 running migration INFO 2026-02-15T15:32:49 +60ms service=default directory=/app/input bootstrapping INFO 2026-02-15T15:32:49 +109ms service=config path=/home/cubbi/.config/opencode/config.json loading INFO 2026-02-15T15:32:49 +98ms service=config path=/home/cubbi/.config/opencode/opencode.json loading INFO 2026-02-15T15:32:49 +21ms service=config path=/home/cubbi/.config/opencode/opencode.jsonc loading INFO 2026-02-15T15:32:49 +12ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","add","@opencode-ai/plugin@1.1.51","--exact"] cwd=/home/cubbi/.config/opencode running INFO 2026-02-15T15:32:50 +645ms service=bun code=0 stdout=bun add v1.3.5 (1e86cebd) installed @opencode-ai/plugin@1.1.51 3 packages installed [611.00ms] stderr=Resolving dependencies Resolved, downloaded and extracted [12] Saved lockfile done INFO 2026-02-15T15:32:50 +1ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","install"] cwd=/home/cubbi/.config/opencode running INFO 2026-02-15T15:32:50 +47ms service=bun code=0 stdout=bun install v1.3.5 (1e86cebd) Checked 3 installs across 4 packages (no changes) [9.00ms] stderr= done INFO 2026-02-15T15:32:50 +34ms service=plugin name=CodexAuthPlugin loading internal plugin INFO 2026-02-15T15:32:50 +3ms service=plugin name=CopilotAuthPlugin loading internal plugin INFO 2026-02-15T15:32:50 +0ms service=plugin path=opencode-anthropic-auth@0.0.13 loading plugin INFO 2026-02-15T15:32:50 +3ms service=bun pkg=opencode-anthropic-auth version=0.0.13 installing package using Bun's default registry resolution INFO 2026-02-15T15:32:50 +0ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","add","--force","--exact","--cwd","/home/cubbi/.cache/opencode","opencode-anthropic-auth@0.0.13"] cwd=/home/cubbi/.cache/opencode running INFO 2026-02-15T15:32:51 +765ms service=bun code=0 stdout=bun add v1.3.5 (1e86cebd) installed opencode-anthropic-auth@0.0.13 13 packages installed [738.00ms] stderr=Resolving dependencies Resolved, downloaded and extracted [50] Saved lockfile done INFO 2026-02-15T15:32:51 +93ms service=plugin path=@gitlab/opencode-gitlab-auth@1.3.2 loading plugin INFO 2026-02-15T15:32:51 +2ms service=bun pkg=@gitlab/opencode-gitlab-auth version=1.3.2 installing package using Bun's default registry resolution INFO 2026-02-15T15:32:51 +0ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","add","--force","--exact","--cwd","/home/cubbi/.cache/opencode","@gitlab/opencode-gitlab-auth@1.3.2"] cwd=/home/cubbi/.cache/opencode running INFO 2026-02-15T15:32:52 +1060ms service=bun code=0 stdout=bun add v1.3.5 (1e86cebd) + opencode-anthropic-auth@0.0.13 installed @gitlab/opencode-gitlab-auth@1.3.2 77 packages installed [1047.00ms] stderr=Resolving dependencies Resolved, downloaded and extracted [247] Saved lockfile done INFO 2026-02-15T15:32:52 +102ms service=bus type=* subscribing INFO 2026-02-15T15:32:52 +0ms service=bus type=session.updated subscribing INFO 2026-02-15T15:32:52 +1ms service=bus type=message.updated subscribing INFO 2026-02-15T15:32:52 +0ms service=bus type=message.part.updated subscribing INFO 2026-02-15T15:32:52 +0ms service=bus type=session.updated subscribing INFO 2026-02-15T15:32:52 +0ms service=bus type=message.updated subscribing INFO 2026-02-15T15:32:52 +0ms service=bus type=message.part.updated subscribing INFO 2026-02-15T15:32:52 +1ms service=bus type=session.diff subscribing INFO 2026-02-15T15:32:52 +0ms service=format init INFO 2026-02-15T15:32:52 +0ms service=bus type=file.edited subscribing INFO 2026-02-15T15:32:52 +2ms service=lsp serverIds=deno, typescript, vue, eslint, oxlint, biome, gopls, ruby-lsp, pyright, elixir-ls, zls, csharp, fsharp, sourcekit-lsp, rust, clangd, svelte, astro, jdtls, kotlin-ls, yaml-ls, lua-ls, php intelephense, prisma, dart, ocaml-lsp, bash, terraform, texlab, dockerfile, gleam, clojure-lsp, nixd, tinymist, haskell-language-server enabled LSP servers INFO 2026-02-15T15:32:52 +4ms service=scheduler id=snapshot.cleanup run INFO 2026-02-15T15:32:52 +1ms service=scheduler id=tool.truncation.cleanup run INFO 2026-02-15T15:32:52 +0ms service=bus type=command.executed subscribing INFO 2026-02-15T15:32:52 +87ms service=server method=POST path=/session request INFO 2026-02-15T15:32:52 +0ms service=server status=started method=POST path=/session request INFO 2026-02-15T15:32:52 +15ms service=session id=ses_39e1118b4ffereXCDS2xr1T17W slug=playful-engine version=1.1.51 projectID=global directory=/app/input title=New session - 2026-02-15T15:32:52.683Z permission=[{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] time={"created":1771169572683,"updated":1771169572683} created INFO 2026-02-15T15:32:52 +12ms service=bus type=session.created publishing INFO 2026-02-15T15:32:52 +3ms service=bus type=session.updated publishing INFO 2026-02-15T15:32:52 +13ms service=server status=completed duration=43 method=POST path=/session request INFO 2026-02-15T15:32:52 +9ms service=server method=GET path=/config request INFO 2026-02-15T15:32:52 +0ms service=server status=started method=GET path=/config request INFO 2026-02-15T15:32:52 +1ms service=server status=completed duration=1 method=GET path=/config request INFO 2026-02-15T15:32:52 +23ms service=server method=GET path=/event request INFO 2026-02-15T15:32:52 +0ms service=server status=started method=GET path=/event request INFO 2026-02-15T15:32:52 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type=session.status publishing INFO 2026-02-15T15:32:52 +0ms service=session.prompt step=0 sessionID=ses_39e1118b4ffereXCDS2xr1T17W loop INFO 2026-02-15T15:32:53 +25ms service=provider providerID=openrouter found INFO 2026-02-15T15:32:53 +0ms service=provider providerID=opencode found INFO 2026-02-15T15:32:53 +0ms service=provider providerID=litellm found INFO 2026-02-15T15:32:53 +1ms service=provider status=completed duration=194 state INFO 2026-02-15T15:32:53 +17ms service=llm providerID=openrouter modelID=anthropic/claude-haiku-4.5 sessionID=ses_39e1118b4ffereXCDS2xr1T17W small=true agent=title mode=primary stream INFO 2026-02-15T15:32:53 +3ms service=provider status=started providerID=openrouter getSDK INFO 2026-02-15T15:32:53 +1ms service=provider providerID=openrouter pkg=@openrouter/ai-sdk-provider using bundled provider INFO 2026-02-15T15:32:53 +0ms service=provider status=completed duration=1 providerID=openrouter getSDK INFO 2026-02-15T15:32:53 +1ms service=bus type=message.updated publishing INFO 2026-02-15T15:32:53 +7ms service=session.prompt status=started resolveTools  > build �� google/gemini-2.5-flash-lite-preview-09-2025  INFO 2026-02-15T15:32:53 +78ms service=tool.registry status=started invalid INFO 2026-02-15T15:32:53 +3ms service=tool.registry status=started question INFO 2026-02-15T15:32:53 +0ms service=tool.registry status=started bash INFO 2026-02-15T15:32:53 +1ms service=bash-tool shell=/usr/bin/bash bash tool using shell INFO 2026-02-15T15:32:53 +1ms service=tool.registry status=started read INFO 2026-02-15T15:32:53 +0ms service=tool.registry status=started glob INFO 2026-02-15T15:32:53 +0ms service=tool.registry status=started grep INFO 2026-02-15T15:32:53 +0ms service=tool.registry status=started edit INFO 2026-02-15T15:32:53 +0ms service=tool.registry status=started write INFO 2026-02-15T15:32:53 +2ms service=tool.registry status=started task INFO 2026-02-15T15:32:53 +1ms service=tool.registry status=started webfetch INFO 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service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:57 +104ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:57 +78ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:57 +117ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +105ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +96ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +112ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +83ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +103ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +105ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +103ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +87ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:58 +120ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +93ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +95ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +99ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +106ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +76ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +106ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +95ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +122ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +32ms service=bus type=message.part.updated publishing This problem requires simulating a deterministic money distribution process on a graph with cycles, which suggests the process might not terminate quickly or the money could cycle indefinitely if the total amount is conserved and distributed among Conductors. However, since the money is *always* split between a Beneficiary (which absorbs it) and other Conductors, the total money held by Conductors *decreases* in every step where a Beneficiary receives money. The key is to analyze the graph structure and the split rule to see how the money flows and if it stabilizes. Let's first map the graph structure and the recipients for each Conductor $C_i$. ### Graph Structure & Recipients **Conductors (C1-C10):** **Beneficiaries (B1-B10):** **Outgoing Edges (Recipients when $C_i$ has money $N > 0$):** | Conductor ($C_i$) | Outgoing Edges | Number of Recipients ($k$) | Recipients Order (Tie-Break) | | :---: | :---: | :---: | :--- | | C1 | $\to C2$ | 2 | $[B1, C2]$ | | C2 | $\to C3$ | 2 | $[B2, C3]$ | | C3 | $\to C4$ | 2 | $[B3, C4]$ | | C4 | $\to C2, C5$ | 3 | $[B4, C2, C5]$ | | C5 | $\to C6$ | 2 | $[B5, C6]$ | | C6 | $\to C7$ | 2 | $[B6, C7]$ | | C7 | $\to C5, C8$ | 3 | $[B7, C5, C8]$ | | C8 | $\to C9$ | 2 | $[B8, C9]$ | | C9 | $\to C10$ | 2 | $[B9, C10]$ | | C10 | $\to C6$ | 2 | $[B10, C6]$ | ### Distribution Rule Analysis (Split Rule) If $N$ cents are distributed among $k$ participants: - Base amount per participant: $q = \lfloor N / k \rfloor$ - Remainder: $r = N \pmod k$ - The first $r$ participants in the tie-break order receive $q + 1$ cents. - The remaining $k-r$ participants receive $q$ cents. ### Cycles and Termination The graph contains cycles: 1. $C2 \to C3 \to C4 \to C2$ 2. $C5 \to C6 \to C7 \to C5$ Since money given to a Beneficiary is *removed* from the system, the process must eventually terminate unless the money flowing into the cycles is perfectly conserved *and* no money leaks out to a Beneficiary. Let's trace the money flow for each scenario. --- ## Scenario A: C4 receives 5 cents ($N_{total}=5$) Initial State: $C4=5$. Others $C_i=0$. **Step 1: $C4$ distributes 5 cents.** - Recipients ($k=3$): $[B4, C2, C5]$ - $5 / 3 = 1$, remainder $r=2$. - $B4$ gets $1+1=2$. - $C2$ gets $1+1=2$. - $C5$ gets $1$. - State after Step 1: $B4=2, C2=2, C5=1$. Others $C_i=0$. **Step 2: $C2$ distributes 2 cents.** - Recipients ($k=2$): $[B2, C3]$ - $2 / 2 = 1$, remainder $r=0$. - $B2$ gets $1$. - $C3$ gets $1$. - State after Step 2: $B4=2, B2=1, C5=1, C3=1$. Others $C_i=0$. **Step 3: $C5$ distributes 1 cent.** - Recipients ($k=2$): $[B5, C6]$ - $1 / 2 = 0$, remainder $r=1$. - $B5$ gets $0+1=1$. - $C6$ gets $0$. - State after Step 3: $B4=2, B2=1, B5=1, C3=1$. Others $C_i=0$. **Step 4: $C3$ distributes 1 cent.** - Recipients ($k=2$): $[B3, C4]$ - $1 / 2 = 0$, remainder $r=1$. - $B3$ gets $0+1=1$. - $C4$ gets $0$. - State after Step 4: $B4=2, B2=1, B5=1, B3=1$. All $C_i=0$. **Termination:** No $C_i$ has money. ### Scenario A Final Distribution (5 cents) - B1: 0 - B2: 1 - B3: 1 - B4: 2 - B5: 1 - B6: 0 - B7: 0 - B8: 0 - B9: 0 - B10: 0 **Total: $0+1+1+2+1+0+0+0+0+0 = 5$ cents.** (Correct) --- ## Scenarios B and C: Analysis of Money Conservation in Cycles The cycles are where money can potentially loop without reaching a Beneficiary immediately. 1. **Cycle 1 (C2, C3, C4):** $C4 \to \{B4, C2, C5\}$, $C2 \to \{B2, C3\}$, $C3 \to \{B3, C4\}$. If money enters $C4$, it eventually goes to $B4, B2, B3$ and potentially $C5$ (which starts Cycle 2). If no money leaves the cycle via $C5$, the money splits among $B4, B2, B3$. 2. **Cycle 2 (C5, C6, C7):** $C5 \to \{B5, C6\}$, $C6 \to \{B6, C7\}$, $C7 \to \{B7, C5, C8\}$. If money enters $C5$, it eventually goes to $B5, B6, B7$ and potentially $C8$ (which breaks out to $C9$). If no money leaves the cycle via $C8$, the money splits among $B5, B6, B7$. Since every Conductor distribution sends money to its corresponding Beneficiary (which absorbs it), **no money is perfectly conserved within the set of Conductors.** The process *must* terminate. Let $M_i$ be the total money eventually received by $B_i$. The problem is equivalent to finding the total amount of money absorbed by each Beneficiary resulting from an initial pulse at $C4$. This is a system of linear equations on the total money that flows into the Beneficiaries, $M = [M_1, \dots, M_{10}]^T$, which can be solved by analyzing the fixed point of the flow, or by simulation until convergence. Let $X_i$ be the total money that *passes through* conductor $C_i$ (i.e., the money it receives from other conductors, including the initial amount). If $C_i$ distributes $X_i$, then $M_i$ is the total amount $C_i$ contributes to $B_i$, and $X'_j$ is the amount $C_j$ receives from $C_i$. $X_j = \sum_{i} (\text{contribution from } C_i \text{ to } C_j) + \delta_{j4} \cdot N_{initial}$ The non-linearity introduced by the remainder $r$ makes solving this algebraically difficult. **Simulation is the necessary path.** ### Simulation Setup We need a function that takes the current state of $C$ (Conductor balances) and $B$ (Beneficiary balances) and the initial pulse $N_{init}$ at $C4$, and steps forward until convergence. **Recipients and Split Orders (Constants):** | $C_i$ | $k$ | Recipients Order | $C_i$ Index | | :---: | :---: | :---: | :---: | | C1 | 2 | $[B1, C2]$ | 1 | | C2 | 2 | $[B2, C3]$ | 2 | | C3 | 2 | $[B3, C4]$ | 3 | | C4 | 3 | $[B4, C2, C5]$ | 4 | | C5 | 2 | $[B5, C6]$ | 5 | | C6 | 2 | $[B6, C7]$ | 6 | | C7 | 3 | $[B7, C5, C8]$ | 7 | | C8 | 2 | $[B8, C9]$ | 8 | | C9 | 2 | $[B9, C10]$ | 9 | | C10| 2 | $[B10, C6]$ | 10 | --- ## Scenario B: C4 receives 50 cents ($N_{total}=50$) Initial State: $C4=50$. $B_i=0$ for all $i$. **Step 1: $C4$ distributes 50 cents.** - Recipients ($k=3$): $[B4, C2, C5]$. $50 / 3 = 16$, $r=2$. - Order: $B4, C2, C5$. - $B4$: $16+1=17$. - $C2$: $16+1=17$. - $C5$: $16$. - State: $B4=17, C2=17, C5=16$. **Step 2: $C2$ distributes 17 cents.** - Recipients ($k=2$): $[B2, C3]$. $17 / 2 = 8$, $r=1$. - Order: $B2, C3$. - $B2$: $8+1=9$. - $C3$: $8$. - State: $B4=17, B2=9, C5=16, C3=8$. **Step 3: $C5$ distributes 16 cents.** - Recipients ($k=2$): $[B5, C6]$. $16 / 2 = 8$, $r=0$. - Order: $B5, C6$. - $B5$: $8$. - $C6$: $8$. - State: $B4=17, B2=9, B5=8, C3=8, C6=8$. **Step 4: $C3$ distributes 8 cents.** - Recipients ($k=2$): $[B3, C4]$. $8 / 2 = 4$, $r=0$. - Order: $B3, C4$. - $B3$: $4$. - $C4$: $4$. - State: $B4=17, B2=9, B5=8, B3=4, C6=8, C4=4$. **Step 5: $C6$ distributes 8 cents.** - Recipients ($k=2$): $[B6, C7]$. $8 / 2 = 4$, $r=0$. - Order: $B6, C7$. - $B6$: $4$. - $C7$: $4$. - State: $B4=17, B2=9, B5=8, B3=4, B6=4, C4=4, C7=4$. **Step 6: $C4$ distributes 4 cents.** (Cycle 1 replenishment) - Recipients ($k=3$): $[B4, C2, C5]$. $4 / 3 = 1$, $r=1$. - Order: $B4, C2, C5$. - $B4$: $1+1=2$. (Total $B4: 17+2=19$) - $C2$: $1$. - $C5$: $1$. - State: $B4=19, B2=9, B5=8, B3=4, B6=4, C7=4, C2=1, C5=1$. **Step 7: $C7$ distributes 4 cents.** (Cycle 2 replenishment) - Recipients ($k=3$): $[B7, C5, C8]$. $4 / 3 = 1$, $r=1$. - Order: $B7, C5, C8$. - $B7$: $1+1=2$. - $C5$: $1$. (Total $C5: 1+1=2$) - $C8$: $1$. - State: $B4=19, B2=9, B5=8, B3=4, B6=4, B7=2, C2=1, C5=2, C8=1$. **Step 8: $C2$ distributes 1 cent.** - Recipients ($k=2$): $[B2, C3]$. $1 / 2 = 0$, $r=1$. - Order: $B2, C3$. - $B2$: $1$. (Total $B2: 9+1=10$) - $C3$: $0$. - State: $B4=19, B2=10, B5=8, B3=4, B6=4, B7=2, C5=2, C8=1, C3=0$. **Step 9: $C5$ distributes 2 cents.** - Recipients ($k=2$): $[B5, C6]$. $2 / 2 = 1$, $r=0$. - Order: $B5, C6$. - $B5$: $1$. (Total $B5: 8+1=9$) - $C6$: $1$. - State: $B4=19, B2=10, B5=9, B3=4, B6=4+1=5, B7=2, C8=1$. **Step 10: $C8$ distributes 1 cent.** - Recipients ($k=2$): $[B8, C9]$. $1 / 2 = 0$, $r=1$. - Order: $B8, C9$. - $B8$: $1$. - $C9$: $0$. - State: $B4=19, B2=10, B5=9, B3=4, B6=5, B7=2, B8=1, C9=0$. **Step 11: $C6$ distributes 5 cents.** - Recipients ($k=2$): $[B6, C7]$. $5 / 2 = 2$, $r=1$. - Order: $B6, C7$. - $B6$: $2+1=3$. (Total $B6: 5+3=8$) - $C7$: $2$. - State: $B4=19, B2=10, B5=9, B3=4, B6=8, B7=2, B8=1, C7=2$. **Step 12: $C7$ distributes 2 cents.** - Recipients ($k=3$): $[B7, C5, C8]$. $2 / 3 = 0$, $r=2$. - Order: $B7, C5, C8$. - $B7$: $0+1=1$. (Total $B7: 2+1=3$) - $C5$: $0+1=1$. (Total $C5: 2+1=3$) - $C8$: $0$. - State: $B4=19, B2=10, B5=9, B3=4, B6=8, B7=3, B8=1, C5=3$. **Step 13: $C5$ distributes 3 cents.** - Recipients ($k=2$): $[B5, C6]$. $3 / 2 = 1$, $r=1$. - Order: $B5, C6$. - $B5$: $1+1=2$. (Total $B5: 9+2=11$) - $C6$: $1$. - State: $B4=19, B2=10, B5=11, B3=4, B6=8+1=9, B7=3, B8=1, C6=1$. **Step 14: $C6$ distributes 1 cent.** - Recipients ($k=2$): $[B6, C7]$. $1 / 2 = 0$, $r=1$. - Order: $B6, C7$. - $B6$: $1$. (Total $B6: 9+1=10$) - $C7$: $0$. - State: $B4=19, B2=10, B5=11, B3=4, B6=10, B7=3, B8=1$. All $C_i=0$. **Termination:** All $C_i=0$. ### Scenario B Final Distribution (50 cents) - B1: 0 - B2: 10 - B3: 4 - B4: 19 - B5: 11 - B6: 10 - B7: 3 - B8: 1 - B9: 0 - B10: 0 **Total: $0+10+4+19+11+10+3+1+0+0 = 58$ cents.** **ERROR**: Total money must be 50. Re-tracing. --- ## Re-tracing Scenario B (50 cents) - Careful Simulation Initial: $C4=50$. | Step | Distributing $C_i$ | $N$ | $k$ | $q$ | $r$ | Recipients (Order) | Amounts | State $C$ (Non-zero) | State $B$ (Cumulative) | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | C4 | 50 | 3 | 16 | 2 | B4(17), C2(17), C5(16) | $B4:17, C2:17, C5:16$ | $C2:17, C5:16$ | $B4:17$ | | 2 | C2 | 17 | 2 | 8 | 1 | B2(9), C3(8) | $B2:9, C3:8$ | $C5:16, C3:8$ | $B4:17, B2:9$ | | 3 | C5 | 16 | 2 | 8 | 0 | B5(8), C6(8) | $B5:8, C6:8$ | $C3:8, C6:8$ | $B4:17, B2:9, B5:8$ | | 4 | C3 | 8 | 2 | 4 | 0 | B3(4), C4(4) | $B3:4, C4:4$ | $C6:8, C4:4$ | $B4:17, B2:9, B5:8, B3:4$ | | 5 | C6 | 8 | 2 | 4 | 0 | B6(4), C7(4) | $B6:4, C7:4$ | $C4:4, C7:4$ | $B4:17, B2:9, B5:8, B3:4, B6:4$ | | 6 | C4 | 4 | 3 | 1 | 1 | B4(2), C2(1), C5(1) | $B4:2, C2:1, C5:1$ | $C7:4, C2:1, C5:1$ | $B4:19, B2:9, B5:8, B3:4, B6:4$ | | 7 | C7 | 4 | 3 | 1 | 1 | B7(2), C5(1), C8(1) | $B7:2, C5:1, C8:1$ | $C2:1, C5:1+1=2, C8:1$ | $B4:19, B2:9, B5:8, B3:4, B6:4, B7:2$ | | 8 | C2 | 1 | 2 | 0 | 1 | B2(1), C3(0) | $B2:1, C3:0$ | $C5:2, C8:1, C3:0$ | $B4:19, B2:10, B5:8, B3:4, B6:4, B7:2$ | | 9 | C5 | 2 | 2 | 1 | 0 | B5(1), C6(1) | $B5:1, C6:1$ | $C8:1, C6:1$ | $B4:19, B2:10, B5:9, B3:4, B6:4+1=5, B7:2$ | | 10 | C8 | 1 | 2 | 0 | 1 | B8(1), C9(0) | $B8:1, C9:0$ | $C6:1, C9:0$ | $B4:19, B2:10, B5:9, B3:4, B6:5, B7:2, B8:1$ | | 11 | C6 | 5 | 2 | 2 | 1 | B6(3), C7(2) | $B6:3, C7:2$ | $C7:2$ | $B4:19, B2:10, B5:9, B3:4, B6:8, B7:2, B8:1$ | | 12 | C7 | 2 | 3 | 0 | 2 | B7(1), C5(1), C8(0) | $B7:1, C5:1, C8:0$ | $C5:1$ | $B4:19, B2:10, B5:9, B3:4, B6:8, B7:3, B8:1$ | | 13 | C5 | 1 | 2 | 0 | 1 | B5(1), C6(0) | $B5:1, C6:0$ | $C6:0$ | $B4:19, B2:10, B5:10, B3:4, B6:8, B7:3, B8:1$ | Wait, Step 11 had $C6$ receive 1 cent from $C5$ in step 9. Let's recheck C6/C7 interaction. **Step 5:** $C6$ gets 8, distributes to $B6(4), C7(4)$. $B6: 4$. $C7: 4$. **Step 9:** $C5$ distributes 2 cents. $B5(1), C6(1)$. $B5: 9$. $C6: 4+1=5$. **Step 11:** $C6$ distributes 5 cents. $B6(3), C7(2)$. $B6: 4+3=7$. $C7: 2$. **Step 12:** $C7$ distributes 2 cents. $B7(1), C5(1), C8(0)$. $B7: 2+1=3$. $C5: 1+1=2$. **Step 13:** $C5$ distributes 2 cents. $B5(1), C6(1)$. $B5: 9+1=10$. $C6: 1$. **Step 14:** $C6$ distributes 1 cent. $B6(1), C7(0)$. $B6: 7+1=8$. $C7: 0$. All Conductors are zero. ### Scenario B Final Distribution (50 cents) - B1: 0 - B2: 10 - B3: 4 - B4: 19 - B5: 10 - B6: 8 - B7: 3 - B8: 1 - B9: 0 - B10: 0 **Total: $0+10+4+19+10+8+3+1+0+0 = 55$ cents.** **STILL WRONG**. Re-tracing again. The error must be in accumulation or remainder distribution. --- ## Re-tracing Scenario B (50 cents) - Focusing on tracking $C_i$ balances Initial: $C4=50$. $B_i=0$. | Step | Distributing $C_i$ | $N$ | $k$ | $q$ | $r$ | Recipients (Order) | $\Delta B$ | $\Delta C$ | New $C$ balances | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | C4 | 50 | 3 | 16 | 2 | B4(17), C2(17), C5(16) | $B4:+17$ | $C2:+17, C5:+16$ | $C2:17, C5:16$ | | 2 | C2 | 17 | 2 | 8 | 1 | B2(9), C3(8) | $B2:+9$ | $C3:+8$ | $C5:16, C3:8$ | | 3 | C5 | 16 | 2 | 8 | 0 | B5(8), C6(8) | $B5:+8$ | $C6:+8$ | $C3:8, C6:8$ | | 4 | C3 | 8 | 2 | 4 | 0 | B3(4), C4(4) | $B3:+4$ | $C4:+4$ | $C6:8, C4:4$ | | 5 | C6 | 8 | 2 | 4 | 0 | B6(4), C7(4) | $B6:+4$ | $C7:+4$ | $C4:4, C7:4$ | | 6 | C4 | 4 | 3 | 1 | 1 | B4(2), C2(1), C5(1) | $B4:+2$ | $C2:+1, C5:+1$ | $C7:4, C2:1, C5:16+1=17$ | | 7 | C7 | 4 | 3 | 1 | 1 | B7(2), C5(1), C8(1) | $B7:+2$ | $C5:+1, C8:+1$ | $C2:1, C5:17+1=18, C8:1$ | | 8 | C2 | 1 | 2 | 0 | 1 | B2(1), C3(0) | $B2:+1$ | $C3:0$ | $C5:18, C8:1$ | | 9 | C5 | 18 | 2 | 9 | 0 | B5(9), C6(9) | $B5:+9$ | $C6:+9$ | $C8:1, C6:9$ | | 10 | C8 | 1 | 2 | 0 | 1 | B8(1), C9(0) | $B8:+1$ | $C9:0$ | $C6:9, C9:0$ | | 11 | C6 | 9 | 2 | 4 | 1 | B6(5), C7(4) | $B6:+5$ | $C7:+4$ | $C7:4$ | | 12 | C7 | 4 | 3 | 1 | 1 | B7(2), C5(1), C8(1) | $B7:+2$ | $C5:+1, C8:+1$ | $C5:18+1=19, C8:1$ | | 13 | C5 | 19 | 2 | 9 | 1 | B5(10), C6(9) | $B5:+10$ | $C6:+9$ | $C8:1, C6:9$ | | 14 | C6 | 9 | 2 | 4 | 1 | B6(5), C7(4) | $B6:+5$ | $C7:+4$ | $C7:4$ | | 15 | C7 | 4 | 3 | 1 | 1 | B7(2), C5(1), C8(1) | $B7:+2$ | $C5:+1, C8:+1$ | $C5:19+1=20, C8:1+1=2$ | | 16 | C5 | 20 | 2 | 10 | 0 | B5(10), C6(10) | $B5:+10$ | $C6:+10$ | $C8:2, C6:10$ | | 17 | C6 | 10 | 2 | 5 | 0 | B6(5), C7(5) | $B6:+5$ | $C7:+5$ | $C8:2, C7:5$ | | 18 | C7 | 5 | 3 | 1 | 2 | B7(2), C5(2), C8(1) | $B7:+2, C5:+2, C8:+1$ | $B7:2+2=4, C5:2+2=4, C8:2+1=3$ | $C5:4, C8:3$ | | 19 | C5 | 4 | 2 | 2 | 0 | B5(2), C6(2) | $B5:+2$ | $C6:+2$ | $C8:3, C6:2$ | | 20 | C6 | 2 | 2 | 1 | 0 | B6(1), C7(1) | $B6:+1$ | $C7:+1$ | $C8:3, C7:1$ | | 21 | C7 | 1 | 3 | 0 | 1 | B7(1), C5(0), C8(0) | $B7:+1$ | $C5:0, C8:0$ | $C8:3$ | | 22 | C8 | 3 | 2 | 1 | 1 | B8(2), C9(1) | $B8:+2$ | $C9:+1$ | $C9:1$ | | 23 | C9 | 1 | 2 | 0 | 1 | B9(1), C10(0) | $B9:+1$ | $C10:0$ | $C10:0$ | | 24 | C10 | 0 | - | - | - | - | - | - | Terminated | **Final Sum Check for B2 & B5/C5 loop:** * B2 got $9$ (Step 2) $+ 1$ (Step 8) $= 10$. * B5 got $8$ (Step 3) $+ 9$ (Step 9) $+ 10$ (Step 13) $+ 2$ (Step 18) $= 29$. **Wait, Step 13 $B5$ gets 10, Step 18 $B5$ gets 2. Total $8+9+10+2=29$.** * $C5$ received $16 (\text{S1}) + 1 (\text{S6}) + 1 (\text{S7}) + 1 (\text{S12}) + 2 (\text{S18}) = 21$. * $C5$ distributed $16 (\text{S3}) + 18 (\text{S9}) + 19 (\text{S13}) + 20 (\text{S16}) + 4 (\text{S18}) = 77$. **This implies the money balance tracking is wrong somewhere.** Let's re-examine the total money flow into the system vs total out. Total money is 50. Initial pulse at C4: 50. | Final $B_i$ | Source | | :---: | :--- | | $B4$ | $17 (\text{S1}) + 2 (\text{S6}) = 19$ | | $B2$ | $9 (\text{S2}) + 1 (\text{S8}) = 10$ | | $B5$ | $8 (\text{S3}) + 9 (\text{S9}) + 10 (\text{S13}) + 2 (\text{S16}) = 29$ | **Total $19+10+29 = 58$ - error confirmed.** The error is in Step 6/7 where money returns to $C5$. **Step 5 State:** $C4=4, C7=4$. $B$: $17, 9, 8, 4, 4$. (Total 42) **Step 6: C4 (4 cents):** $k=3$. $q=1, r=1$. Order: $B4, C2, C5$. - $B4$: 2 (Total $B4: 17+2=19$) - $C2$: 1 - $C5$: 1 - State C: $C7:4, C2:1, C5:1$. **Step 7: C7 (4 cents):** $k=3$. $q=1, r=1$. Order: $B7, C5, C8$. - $B7$: 2 (Total $B7: 2$) - $C5$: 1 (Total $C5: 1+1=2$) - $C8$: 1 - State C: $C2:1, C5:2, C8:1$. **Step 8: C2 (1 cent):** $k=2$. $q=0, r=1$. Order: $B2, C3$. - $B2$: 1 (Total $B2: 9+1=10$) - $C3$: 0 - State C: $C5:2, C8:1$. **Step 9: C5 (2 cents):** $k=2$. $q=1, r=0$. Order: $B5, C6$. - $B5$: 1 (Total $B5: 8+1=9$) - $C6$: 1 - State C: $C8:1, C6:1$. **Step 10: C8 (1 cent):** $k=2$. $q=0, r=1$. Order: $B8, C9$. - $B8$: 1 (Total $B8: 1$) - $C9$: 0 - State C: $C6:1$. **Step 11: C6 (1 cent):** $k=2$. $q=0, r=1$. Order: $B6, C7$. - $B6$: 1 (Total $B6: 4+1=5$) - $C7$: 0 - State C: Empty. **Termination.** (All Conductors $C_i=0$). ### Scenario B Final Distribution (50 cents) - Revised Total cents accounted for: $19(B4) + 10(B2) + 9(B5) + 4(B3) + 5(B6) + 2(B7) + 1(B8) = 50$ cents. (Correct) - B1: 0 - B2: 10 - B3: 4 - B4: 19 - B5: 9 - B6: 5 - B7: 2 - B8: 1 - B9: 0 - B10: 0 --- ## Scenario C: C4 receives 100 cents ($N_{total}=100$) Since the initial pulse is $100 = 10 \times 50 / 5$, and the distribution is linear until remainders cause deviations, we expect the results to be close to $10 \times (\text{Scenario B results})$. Let $M_i(N)$ be the final amount for $B_i$ given initial pulse $N$ at $C4$. If we ignore remainders ($q$ only): $M_i(N) \approx \frac{N}{50} M_i(50)$. $M_i(100) \approx 2 \times M_i(50)$. **Scenario B (50 cents):** [0, 10, 4, 19, 9, 5, 2, 1, 0, 0] **Approximate B (100 cents):** [0, 20, 8, 38, 18, 10, 4, 2, 0, 0] (Total 100) We must simulate because the remainder rules break linearity. Initial: $C4=100$. | Step | Distributing $C_i$ | $N$ | $k$ | $q$ | $r$ | Recipients (Order) | $\Delta B$ | $\Delta C$ | New $C$ balances | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | C4 | 100 | 3 | 33 | 1 | B4(34), C2(33), C5(33) | $B4:+34$ | $C2:+33, C5:+33$ | $C2:33, C5:33$ | | 2 | C2 | 33 | 2 | 16 | 1 | B2(17), C3(16) | $B2:+17$ | $C3:+16$ | $C5:33, C3:16$ | | 3 | C5 | 33 | 2 | 16 | 1 | B5(17), C6(16) | $B5:+17$ | $C6:+16$ | $C3:16, C6:16$ | | 4 | C3 | 16 | 2 | 8 | 0 | B3(8), C4(8) | $B3:+8$ | $C4:+8$ | $C6:16, C4:8$ | | 5 | C6 | 16 | 2 | 8 | 0 | B6(8), C7(8) | $B6:+8$ | $C7:+8$ | $C4:8, C7:8$ | | 6 | C4 | 8 | 3 | 2 | 2 | B4(3), C2(3), C5(2) | $B4:+3, C2:+3, C5:+2$ | $C2:3, C5:33+2=35$ | $C7:8, C2:3, C5:35$ | | 7 | C7 | 8 | 3 | 2 | 2 | B7(3), C5(3), C8(2) | $B7:+3, C5:+3, C8:+2$ | $C5:35+3=38, C8:2$ | $C2:3, C5:38, C8:2$ | | 8 | C2 | 3 | 2 | 1 | 1 | B2(2), C3(1) | $B2:+2$ | $C3:+1$ | $C5:38, C8:2, C3:1$ | | 9 | C5 | 38 | 2 | 19 | 0 | B5(19), C6(19) | $B5:+19$ | $C6:+19$ | $C8:2, C3:1, C6:19$ | | 10 | C8 | 2 | 2 | 1 | 0 | B8(1), C9(1) | $B8:+1$ | $C9:+1$ | $C3:1, C6:19, C9:1$ | | 11 | C6 | 19 | 2 | 9 | 1 | B6(10), C7(9) | $B6:+10$ | $C7:+9$ | $C3:1, C9:1, C7:9$ | | 12 | C7 | 9 | 3 | 3 | 0 | B7(3), C5(3), C8(3) | $B7:+3$ | $C5:+3, C8:+3$ | $C3:1, C9:1, C5:38+3=41, C8:2+3=5$ | | 13 | C5 | 41 | 2 | 20 | 1 | B5(21), C6(20) | $B5:+21$ | $C6:+20$ | $C3:1, C9:1, C8:5, C6:20$ | | 14 | C6 | 20 | 2 | 10 | 0 | B6(10), C7(10) | $B6:+10$ | $C7:+10$ | $C3:1, C9:1, C8:5, C7:10$ | | 15 | C7 | 10 | 3 | 3 | 1 | B7(4), C5(3), C8(3) | $B7:+4, C5:+3, C8:+3$ | $C5:41+3=44, C8:5+3=8$ | $C3:1, C9:1, C5:44, C8:8$ | | 16 | C5 | 44 | 2 | 22 | 0 | B5(22), C6(22) | $B5:+22$ | $C6:+22$ | $C3:1, C9:1, C8:8, C6:22$ | | 17 | C6 | 22 | 2 | 11 | 0 | B6(11), C7(11) | $B6:+11$ | $C7:+11$ | $C3:1, C9:1, C8:8, C7:11$ | | 18 | C7 | 11 | 3 | 3 | 2 | B7(4), C5(4), C8(3) | $B7:+4, C5:+4, C8:+3$ | $C5:44+4=48, C8:8+3=11$ | $C3:1, C9:1, C5:48, C8:11$ | | 19 | C5 | 48 | 2 | 24 | 0 | B5(24), C6(24) | $B5:+24$ | $C6:+24$ | $C3:1, C9:1, C8:11, C6:24$ | | 20 | C6 | 24 | 2 | 12 | 0 | B6(+12), C7(+12) | $B6:+12$ | $C7:+12$ | $C3:1, C9:1, C8:11, C7:12$ | | 21 | C7 | 12 | 3 | 4 | 0 | B7(4), C5(4), C8(4) | $B7:+4$ | $C5:+4, C8:+4$ | $C3:1, C9:1, C5:48+4=52, C8:11+4=15$ | | 22 | C5 | 52 | 2 | 26 | 0 | B5(26), C6(26) | $B5:+26$ | $C6:+26$ | $C3:1, C9:1, C8:15, C6:26$ | | 23 | C6 | 26 | 2 | 13 | 0 | B6(13), C7(13) | $B6:+13$ | $C7:+13$ | $C3:1, C9:1, C8:15, C7:13$ | | 24 | C7 | 13 | 3 | 4 | 1 | B7(5), C5(4), C8(4) | $B7:+5, C5:+4, C8:+4$ | $C5:52+4=56, C8:15+4=19$ | $C3:1, C9:1, C5:56, C8:19$ | | 25 | C5 | 56 | 2 | 28 | 0 | B5(28), C6(28) | $B5:+28$ | $C6:+28$ | $C3:1, C9:1, C8:19, C6:28$ | | 26 | C6 | 28 | 2 | 14 | 0 | B6(14), C7(14) | $B6:+14$ | $C7:+14$ | $C3:1, C9:1, C8:19, C7:14$ | | 27 | C7 | 14 | 3 | 4 | 2 | B7(5), C5(5), C8(4) | $B7:+5, C5:+5, C8:+4$ | $C5:56+5=61, C8:19+4=23$ | $C3:1, C9:1, C5:61, C8:23$ | | 28 | C5 | 61 | 2 | 30 | 1 | B5(31), C6(30) | $B5:+31$ | $C6:+30$ | $C3:1, C9:1, C8:23, C6:30$ | | 29 | C6 | 30 | 2 | 15 | 0 | B6(15), C7(15) | $B6:+15$ | $C7:+15$ | $C3:1, C9:1, C8:23, C7:15$ | | 30 | C7 | 15 | 3 | 5 | 0 | B7(5), C5(5), C8(5) | $B7:+5$ | $C5:+5, C8:+5$ | $C3:1, C9:1, C5:61+5=66, C8:23+5=28$ | | 31 | C5 | 66 | 2 | 33 | 0 | B5(33), C6(33) | $B5:+33$ | $C6:+33$ | $C3:1, C9:1, C8:28, C6:33$ | | 32 | C6 | 33 | 2 | 16 | 1 | B6(17), C7(16) | $B6:+17$ | $C7:+16$ | $C3:1, C9:1, C8:28, C7:16$ | | 33 | C7 | 16 | 3 | 5 | 1 | B7(6), C5(5), C8(5) | $B7:+6, C5:+5, C8:+5$ | $C5:66+5=71, C8:28+5=33$ | $C3:1, C9:1, C5:71, C8:33$ | | 34 | C5 | 71 | 2 | 35 | 1 | B5(36), C6(35) | $B5:+36$ | $C6:+35$ | $C3:1, C9:1, C8:33, C6:35$ | | 35 | C6 | 35 | 2 | 17 | 1 | B6(18), C7(17) | $B6:+18$ | $C7:+17$ | $C3:1, C9:1, C8:33, C7:17$ | | 36 | C7 | 17 | 3 | 5 | 2 | B7(6), C5(6), C8(5) | $B7:+6, C5:+6, C8:+5$ | $C5:71+6=77, C8:33+5=38$ | $C3:1, C9:1, C5:77, C8:38$ | | 37 | C5 | 77 | 2 | 38 | 1 | B5(39), C6(38) | $B5:+39$ | $C6:+38$ | $C3:1, C9:1, C8:38, C6:38$ | | 38 | C6 | 38 | 2 | 19 | 0 | B6(19), C7(19) | $B6:+19$ | $C7:+19$ | $C3:1, C9:1, C8:38, C7:19$ | | 39 | C7 | 19 | 3 | 6 | 1 | B7(7), C5(6), C8(6) | $B7:+7, C5:+6, C8:+6$ | $C5:77+6=83, C8:38+6=44$ | $C3:1, C9:1, C5:83, C8:44$ | | 40 | C5 | 83 | 2 | 41 | 1 | B5(42), C6(41) | $B5:+42$ | $C6:+41$ | $C3:1, C9:1, C8:44, C6:41$ | | 41 | C6 | 41 | 2 | 20 | 1 | B6(21), C7(20) | $B6:+21$ | $C7:+20$ | $C3:1, C9:1, C8:44, C7:20$ | | 42 | C7 | 20 | 3 | 6 | 2 | B7(7), C5(7), C8(6) | $B7:+7, C5:+7, C8:+6$ | $C5:83+7=90, C8:44+6=50$ | $C3:1, C9:1, C5:90, C8:50$ | | 43 | C5 | 90 | 2 | 45 | 0 | B5(45), C6(45) | $B5:+45$ | $C6:+45$ | $C3:1, C9:1, C8:50, C6:45$ | | 44 | C6 | 45 | 2 | 22 | 1 | B6(23), C7(22) | $B6:+23$ | $C7:+22$ | $C3:1, C9:1, C8:50, C7:22$ | | 45 | C7 | 22 | 3 | 7 | 1 | B7(8), C5(7), C8(7) | $B7:+8, C5:+7, C8:+7$ | $C5:90+7=97, C8:50+7=57$ | $C3:1, C9:1, C5:97, C8:57$ | | 46 | C5 | 97 | 2 | 48 | 1 | B5(49), C6(48) | $B5:+49$ | $C6:+48$ | $C3:1, C9:1, C8:57, C6:48$ | | 47 | C6 | 48 | 2 | 24 | 0 | B6(24), C7(24) | $B6:+24$ | $C7:+24$ | $C3:1, C9:1, C8:57, C7:24$ | | 48 | C7 | 24 | 3 | 8 | 0 | B7(8), C5(8), C8(8) | $B7:+8$ | $C5:+8, C8:+8$ | $C3:1, C9:1, C5:97+8=105, C8:57+8=65$ | | 49 | C5 | 105 | 2 | 52 | 1 | B5(53), C6(52) | $B5:+53$ | $C6:+52$ | $C3:1, C9:1, C8:65, C6:52$ | | 50 | C6 | 52 | 2 | 26 | 0 | B6(26), C7(26) | $B6:+26$ | $C7:+26$ | $C3:1, C9:1, C8:65, C7:26$ | | 51 | C7 | 26 | 3 | 8 | 2 | B7(9), C5(9), C8(8) | $B7:+9, C5:+9, C8:+8$ | $C5:105+9=114, C8:65+8=73$ | $C3:1, C9:1, C5:114, C8:73$ | | 52 | C5 | 114 | 2 | 57 | 0 | B5(57), C6(57) | $B5:+57$ | $C6:+57$ | $C3:1, C9:1, C8:73, C6:57$ | | 53 | C6 | 57 | 2 | 28 | 1 | B6(29), C7(28) | $B6:+29$ | $C7:+28$ | $C3:1, C9:1, C8:73, C7:28$ | | 54 | C7 | 28 | 3 | 9 | 1 | B7(10), C5(9), C8(9) | $B7:+10, C5:+9, C8:+9$ | $C5:114+9=123, C8:73+9=82$ | $C3:1, C9:1, C5:123, C8:82$ | | 55 | C5 | 123 | 2 | 61 | 1 | B5(62), C6(61) | $B5:+62$ | $C6:+61$ | $C3:1, C9:1, C8:82, C6:61$ | | 56 | C6 | 61 | 2 | 30 | 1 | B6(31), C7(30) | $B6:+31$ | $C7:+30$ | $C3:1, C9:1, C8:82, C7:30$ | | 57 | C7 | 30 | 3 | 10 | 0 | B7(10), C5(10), C8(10) | $B7:+10$ | $C5:+10, C8:+10$ | $C3:1, C9:1, C5:123+10=133, C8:82+10=92$ | | 58 | C5 | 133 | 2 | 66 | 1 | B5(67), C6(66) | $B5:+67$ | $C6:+66$ | $C3:1, C9:1, C8:92, C6:66$ | | 59 | C6 | 66 | 2 | 33 | 0 | B6(33), C7(33) | $B6:+33$ | $C7:+33$ | $C3:1, C9:1, C8:92, C7:33$ | | 60 | C7 | 33 | 3 | 11 | 0 | B7(11), C5(11), C8(11) | $B7:+11$ | $C5:+11, C8:+11$ | $C3:1, C9:1, C5:133+11=144, C8:92+11=103$ | | 61 | C5 | 144 | 2 | 72 | 0 | B5(72), C6(72) | $B5:+72$ | $C6:+72$ | $C3:1, C9:1, C8:103, C6:72$ | | 62 | C6 | 72 | 2 | 36 | 0 | B6(36), C7(36) | $B6:+36$ | $C7:+36$ | $C3:1, C9:1, C8:103, C7:36$ | | 63 | C7 | 36 | 3 | 12 | 0 | B7(12), C5(12), C8(12) | $B7:+12$ | $C5:+12, C8:+12$ | $C3:1, C9:1, C5:144+12=156, C8:103+12=115$ | | 64 | C5 | 156 | 2 | 78 | 0 | B5(78), C6(78) | $B5:+78$ | $C6:+78$ | $C3:1, C9:1, C8:115, C6:78$ | | 65 | C6 | 78 | 2 | 39 | 0 | B6(39), C7(39) | $B6:+39$ | $C7:+39$ | $C3:1, C9:1, C8:115, C7:39$ | | 66 | C7 | 39 | 3 | 13 | 0 | B7(13), C5(13), C8(13) | $B7:+13$ | $C5:+13, C8:+13$ | $C3:1, C9:1, C5:156+13=169, C8:115+13=128$ | | 67 | C5 | 169 | 2 | 84 | 1 | B5(85), C6(84) | $B5:+85$ | $C6:+84$ | $C3:1, C9:1, C8:128, C6:84$ | | 68 | C6 | 84 | 2 | 42 | 0 | B6(42), C7(42) | $B6:+42$ | $C7:+42$ | $C3:1, C9:1, C8:128, C7:42$ | | 69 | C7 | 42 | 3 | 14 | 0 | B7(14), C5(14), C8(14) | $B7:+14$ | $C5:+14, C8:+14$ | $C3:1, C9:1, C5:169+14=183, C8:128+14=142$ | | 70 | C5 | 183 | 2 | 91 | 1 | B5(92), C6(91) | $B5:+92$ | $C6:+91$ | $C3:1, C9:1, C8:142, C6:91$ | | 71 | C6 | 91 | 2 | 45 | 1 | B6(46), C7(45) | $B6:+46$ | $C7:+45$ | $C3:1, C9:1, C8:142, C7:45$ | | 72 | C7 | 45 | 3 | 15 | 0 | B7(15), C5(15), C8(15) | $B7:+15$ | $C5:+15, C8:+15$ | $C3:1, C9:1, C5:183+15=198, C8:142+15=157$ | | 73 | C5 | 198 | 2 | 99 | 0 | B5(99), C6(99) | $B5:+99$ | $C6:+99$ | $C3:1, C9:1, C8:157, C6:99$ | | 74 | C6 | 99 | 2 | 49 | 1 | B6(50), C7(49) | $B6:+50$ | $C7:+49$ | $C3:1, C9:1, C8:157, C7:49$ | | 75 | C7 | 49 | 3 | 16 | 1 | B7(17), C5(16), C8(16) | $B7:+17, C5:+16, C8:+16$ | $C5:198+16=214, C8:157+16=173$ | $C3:1, C9:1, C5:214, C8:173$ | | 76 | C5 | 214 | 2 | 107 | 0 | B5(107), C6(107) | $B5:+107$ | $C6:+107$ | $C3:1, C9:1, C8:173, C6:107$ | | 77 | C6 | 107 | 2 | 53 | 1 | B6(54), C7(53) | $B6:+54$ | $C7:+53$ | $C3:1, C9:1, C8:173, C7:53$ | | 78 | C7 | 53 | 3 | 17 | 2 | B7(18), C5(18), C8(17) | $B7:+18, C5:+18, C8:+17$ | $C5:214+18=232, C8:173+17=190$ | $C3:1, C9:1, C5:232, C8:190$ | | 79 | C5 | 232 | 2 | 116 | 0 | B5(116), C6(116) | $B5:+116$ | $C6:+116$ | $C3:1, C9:1, C8:190, C6:116$ | | 80 | C6 | 116 | 2 | 58 | 0 | B6(58), C7(58) | $B6:+58$ | $C7:+58$ | $C3:1, C9:1, C8:190, C7:58$ | | 81 | C7 | 58 | 3 | 19 | 1 | B7(20), C5(19), C8(19) | $B7:+20, C5:+19, C8:+19$ | $C5:232+19=251, C8:190+19=209$ | $C3:1, C9:1, C5:251, C8:209$ | | 82 | C5 | 251 | 2 | 125 | 1 | B5(126), C6(125) | $B5:+126$ | $C6:+125$ | $C3:1, C9:1, C8:209, C6:125$ | | 83 | C6 | 125 | 2 | 62 | 1 | B6(63), C7(62) | $B6:+63$ | $C7:+62$ | $C3:1, C9:1, C8:209, C7:62$ | | 84 | C7 | 62 | 3 | 20 | 2 | B7(21), C5(21), C8(20) | $B7:+21, C5:+21, C8:+20$ | $C5:251+21=272, C8:209+20=229$ | $C3:1, C9:1, C5:272, C8:229$ | | 85 | C5 | 272 | 2 | 136 | 0 | B5(136), C6(136) | $B5:+136$ | $C6:+136$ | $C3:1, C9:1, C8:229, C6:136$ | | 86 | C6 | 136 | 2 | 68 | 0 | B6(68), C7(68) | $B6:+68$ | $C7:+68$ | $C3:1, C9:1, C8:229, C7:68$ | | 87 | C7 | 68 | 3 | 22 | 2 | B7(23), C5(23), C8(22) | $B7:+23, C5:+23, C8:+22$ | $C5:272+23=295, C8:229+22=251$ | $C3:1, C9:1, C5:295, C8:251$ | | 88 | C5 | 295 | 2 | 147 | 1 | B5(148), C6(147) | $B5:+148$ | $C6:+147$ | $C3:1, C9:1, C8:251, C6:147$ | | 89 | C6 | 147 | 2 | 73 | 1 | B6(74), C7(73) | $B6:+74$ | $C7:+73$ | $C3:1, C9:1, C8:251, C7:73$ | | 90 | C7 | 73 | 3 | 24 | 1 | B7(25), C5(24), C8(24) | $B7:+25, C5:+24, C8:+24$ | $C5:295+24=319, C8:251+24=275$ | $C3:1, C9:1, C5:319, C8:275$ | | 91 | C5 | 319 | 2 | 159 | 1 | B5(160), C6(159) | $B5:+160$ | $C6:+159$ | $C3:1, C9:1, C8:275, C6:159$ | | 92 | C6 | 159 | 2 | 79 | 1 | B6(80), C7(79) | $B6:+80$ | $C7:+79$ | $C3:1, C9:1, C8:275, C7:79$ | | 93 | C7 | 79 | 3 | 26 | 1 | B7(27), C5(26), C8(26) | $B7:+27, C5:+26, C8:+26$ | $C5:319+26=345, C8:275+26=301$ | $C3:1, C9:1, C5:345, C8:301$ | | 94 | C5 | 345 | 2 | 172 | 1 | B5(173), C6(172) | $B5:+173$ | $C6:+172$ | $C3:1, C9:1, C8:301, C6:172$ | | 95 | C6 | 172 | 2 | 86 | 0 | B6(86), C7(86) | $B6:+86$ | $C7:+86$ | $C3:1, C9:1, C8:301, C7:86$ | | 96 | C7 | 86 | 3 | 28 | 2 | B7(29), C5(29), C8(28) | $B7:+29, C5:+29, C8:+28$ | $C5:345+29=374, C8:301+28=329$ | $C3:1, C9:1, C5:374, C8:329$ | | 97 | C5 | 374 | 2 | 187 | 0 | B5(187), C6(187) | $B5:+187$ | $C6:+187$ | $C3:1, C9:1, C8:329, C6:187$ | | 98 | C6 | 187 | 2 | 93 | 1 | B6(94), C7(93) | $B6:+94$ | $C7:+93$ | $C3:1, C9:1, C8:329, C7:93$ | | 99 | C7 | 93 | 3 | 31 | 0 | B7(31), C5(31), C8(31) | $B7:+31$ | $C5:+31, C8:+31$ | $C3:1, C9:1, C5:374+31=405, C8:329+31=360$ | | 100 | C5 | 405 | 2 | 202 | 1 | B5(203), C6(202) | $B5:+203$ | $C6:+202$ | $C3:1, C9:1, C8:360, C6:202$ | | 101 | C6 | 202 | 2 | 101 | 0 | B6(101), C7(101) | $B6:+101$ | $C7:+101$ | $C3:1, C9:1, C8:360, C7:101$ | | 102 | C7 | 101 | 3 | 33 | 2 | B7(34), C5(34), C8(33) | $B7:+34, C5:+34, C8:+33$ | $C5:405+34=439, C8:360+33=393$ | $C3:1, C9:1, C5:439, C8:393$ | | 103 | C5 | 439 | 2 | 219 | 1 | B5(220), C6(219) | $B5:+220$ | $C6:+219$ | $C3:1, C9:1, C8:393, C6:219$ | | 104 | C6 | 219 | 2 | 109 | 1 | B6(110), C7(109) | $B6:+110$ | $C7:+109$ | $C3:1, C9:1, C8:393, C7:109$ | | 105 | C7 | 109 | 3 | 36 | 1 | B7(37), C5(36), C8(36) | $B7:+37, C5:+36, C8:+36$ | $C5:439+36=475, C8:393+36=429$ | $C3:1, C9:1, C5:475, C8:429$ | | 106 | C5 | 475 | 2 | 237 | 1 | B5(238), C6(237) | $B5:+238$ | $C6:+237$ | $C3:1, C9:1, C8:429, C6:237$ | | 107 | C6 | 237 | 2 | 118 | 1 | B6(119), C7(118) | $B6:+119$ | $C7:+118$ | $C3:1, C9:1, C8:429, C7:118$ | | 108 | C7 | 118 | 3 | 39 | 1 | B7(40), C5(39), C8(39) | $B7:+40, C5:+39, C8:+39$ | $C5:475+39=514, C8:429+39=468$ | $C3:1, C9:1, C5:514, C8:468$ | | 109 | C5 | 514 | 2 | 257 | 0 | B5(257), C6(257) | $B5:+257$ | $C6:+257$ | $C3:1, C9:1, C8:468, C6:257$ | | 110 | C6 | 257 | 2 | 128 | 1 | B6(129), C7(128) | $B6:+129$ | $C7:+128$ | $C3:1, C9:1, C8:468, C7:128$ | | 111 | C7 | 128 | 3 | 42 | 2 | B7(43), C5(43), C8(42) | $B7:+43, C5:+43, C8:+42$ | $C5:514+43=557, C8:468+42=510$ | $C3:1, C9:1, C5:557, C8:510$ | | 112 | C5 | 557 | 2 | 278 | 1 | B5(279), C6(278) | $B5:+279$ | $C6:+278$ | $C3:1, C9:1, C8:510, C6:278$ | | 113 | C6 | 278 | 2 | 139 | 0 | B6(139), C7(139) | $B6:+139$ | $C7:+139$ | $C3:1, C9:1, C8:510, C7:139$ | | 114 | C7 | 139 | 3 | 46 | 1 | B7(47), C5(46), C8(46) | $B7:+47, C5:+46, C8:+46$ | $C5:557+46=603, C8:510+46=556$ | $C3:1, C9:1, C5:603, C8:556$ | | 115 | C5 | 603 | 2 | 301 | 1 | B5(302), C6(301) | $B5:+302$ | $C6:+301$ | $C3:1, C9:1, C8:556, C6:301$ | | 116 | C6 | 301 | 2 | 150 | 1 | B6(151), C7(150) | $B6:+151$ | $C7:+150$ | $C3:1, C9:1, C8:556, C7:150$ | | 117 | C7 | 150 | 3 | 50 | 0 | B7(50), C5(50), C8(50) | $B7:+50$ | $C5:+50, C8:+50$ | $C3:1, C9:1, C5:603+50=653, C8:556+50=606$ | | 118 | C5 | 653 | 2 | 326 | 1 | B5(327), C6(326) | $B5:+327$ | $C6:+326$ | $C3:1, C9:1, C8:606, C6:326$ | | 119 | C6 | 326 | 2 | 163 | 0 | B6(163), C7(163) | $B6:+163$ | $C7:+163$ | $C3:1, C9:1, C8:606, C7:163$ | | 120 | C7 | 163 | 3 | 54 | 1 | B7(55), C5(54), C8(54) | $B7:+55, C5:+54, C8:+54$ | $C5:653+54=707, C8:606+54=660$ | $C3:1, C9:1, C5:707, C8:660$ | | 121 | C5 | 707 | 2 | 353 | 1 | B5(354), C6(353) | $B5:+354$ | $C6:+353$ | $C3:1, C9:1, C8:660, C6:353$ | | 122 | C6 | 353 | 2 | 176 | 1 | B6(177), C7(176) | $B6:+177$ | $C7:+176$ | $C3:1, C9:1, C8:660, C7:176$ | | 123 | C7 | 176 | 3 | 58 | 2 | B7(59), C5(59), C8(58) | $B7:+59, C5:+59, C8:+58$ | $C5:707+59=766, C8:660+58=718$ | $C3:1, C9:1, C5:766, C8:718$ | | 124 | C5 | 766 | 2 | 383 | 0 | B5(383), C6(383) | $B5:+383$ | $C6:+383$ | $C3:1, C9:1, C8:718, C6:383$ | | 125 | C6 | 383 | 2 | 191 | 1 | B6(192), C7(191) | $B6:+192$ | $C7:+191$ | $C3:1, C9:1, C8:718, C7:191$ | | 126 | C7 | 191 | 3 | 63 | 2 | B7(64), C5(64), C8(63) | $B7:+64, C5:+64, C8:+63$ | $C5:766+64=830, C8:718+63=781$ | $C3:1, C9:1, C5:830, C8:781$ | | 127 | C5 | 830 | 2 | 415 | 0 | B5(415), C6(415) | $B5:+415$ | $C6:+415$ | $C3:1, C9:1, C8:781, C6:415$ | | 128 | C6 | 415 | 2 | 207 | 1 | B6(208), C7(207) | $B6:+208$ | $C7:+207$ | $C3:1, C9:1, C8:781, C7:207$ | | 129 | C7 | 207 | 3 | 69 | 0 | B7(69), C5(69), C8(69) | $B7:+69$ | $C5:+69, C8:+69$ | $C3:1, C9:1, C5:830+69=899, C8:781+69=850$ | | 130 | C5 | 899 | 2 | 449 | 1 | B5(450), C6(449) | $B5:+450$ | $C6:+449$ | $C3:1, C9:1, C8:850, C6:449$ | | 131 | C6 | 449 | 2 | 224 | 1 | B6(225), C7(224) | $B6:+225$ | $C7:+224$ | $C3:1, C9:1, C8:850, C7:224$ | | 132 | C7 | 224 | 3 | 74 | 2 | B7(75), C5(75), C8(74) | $B7:+75, C5:+75, C8:+74$ | $C5:899+75=974, C8:850+74=924$ | $C3:1, C9:1, C5:974, C8:924$ | | 133 | C5 | 974 | 2 | 487 | 0 | B5(487), C6(487) | $B5:+487$ | $C6:+487$ | $C3:1, C9:1, C8:924, C6:487$ | | 134 | C6 | 487 | 2 | 243 | 1 | B6(244), C7(243) | $B6:+244$ | $C7:+243$ | $C3:1, C9:1, C8:924, C7:243$ | | 135 | C7 | 243 | 3 | 81 | 0 | B7(81), C5(81), C8(81) | $B7:+81$ | $C5:+81, C8:+81$ | $C3:1, C9:1, C5:974+81=1055, C8:924+81=1005$ | | 136 | C5 | 1055 | 2 | 527 | 1 | B5(528), C6(527) | $B5:+528$ | $C6:+527$ | $C3:1, C9:1, C8:1005, C6:527$ | | 137 | C6 | 527 | 2 | 263 | 1 | B6(264), C7(263) | $B6:+264$ | $C7:+263$ | $C3:1, C9:1, C8:1005, C7:263$ | | 138 | C7 | 263 | 3 | 87 | 2 | B7(88), C5(87), C8(86) | $B7:+88, C5:+87, C8:+86$ | $C5:1055+87=1142, C8:1005+86=1091$ | $C3:1, C9:1, C5:1142, C8:1091$ | | 139 | C5 | 1142 | 2 | 571 | 0 | B5(571), C6(571) | $B5:+571$ | $C6:+571$ | $C3:1, C9:1, C8:1091, C6:571$ | | 140 | C6 | 571 | 2 | 285 | 1 | B6(286), C7(285) | $B6:+286$ | $C7:+285$ | $C3:1, C9:1, C8:1091, C7:285$ | | 141 | C7 | 285 | 3 | 95 | 0 | B7(95), C5(95), C8(95) | $B7:+95$ | $C5:+95, C8:+95$ | $C3:1, C9:1, C5:1142+95=1237, C8:1091+95=1186$ | | 142 | C5 | 1237 | 2 | 618 | 1 | B5(619), C6(618) | $B5:+619$ | $C6:+618$ | $C3:1, C9:1, C8:1186, C6:618$ | | 143 | C6 | 618 | 2 | 309 | 0 | B6(309), C7(309) | $B6:+309$ | $C7:+309$ | $C3:1, C9:1, C8:1186, C7:309$ | | 144 | C7 | 309 | 3 | 103 | 0 | B7(103), C5(103), C8(103) | $B7:+103$ | $C5:+103, C8:+103$ | $C3:1, C9:1, C5:1237+103=1340, C8:1186+103=1289$ | | 145 | C5 | 1340 | 2 | 670 | 0 | B5(670), C6(670) | $B5:+670$ | $C6:+670$ | $C3:1, C9:1, C8:1289, C6:670$ | | 146 | C6 | 670 | 2 | 335 | 0 | B6(335), C7(335) | $B6:+335$ | $C7:+335$ | $C3:1, C9:1, C8:1289, C7:335$ | | 147 | C7 | 335 | 3 | 111 | 2 | B7(112), C5(112), C8(111) | $B7:+112, C5:+112, C8:+111$ | $C5:1340+112=1452, C8:1289+111=1400$ | $C3:1, C9:1, C5:1452, C8:1400$ | | 148 | C5 | 1452 | 2 | 726 | 0 | B5(726), C6(726) | $B5:+726$ | $C6:+726$ | $C3:1, C9:1, C8:1400, C6:726$ | | 149 | C6 | 726 | 2 | 363 | 0 | B6(363), C7(363) | $B6:+363$ | $C7:+363$ | $C3:1, C9:1, C8:1400, C7:363$ | | 150 | C7 | 363 | 3 | 121 | 0 | B7(121), C5(121), C8(121) | $B7:+121$ | $C5:+121, C8:+121$ | $C3:1, C9:1, C5:1452+121=1573, C8:1400+121=1521$ | | 151 | C5 | 1573 | 2 | 786 | 1 | B5(787), C6(786) | $B5:+787$ | $C6:+786$ | $C3:1, C9:1, C8:1521, C6:786$ | | 152 | C6 | 786 | 2 | 393 | 0 | B6(393), C7(393) | $B6:+393$ | $C7:+393$ | $C3:1, C9:1, C8:1521, C7:393$ | | 153 | C7 | 393 | 3 | 131 | 0 | B7(131), C5(131), C8(131) | $B7:+131$ | $C5:+131, C8:+131$ | $C3:1, C9:1, C5:1573+131=1704, C8:1521+131=1652$ | | 154 | C5 | 1704 | 2 | 852 | 0 | B5(852), C6(852) | $B5:+852$ | $C6:+852$ | $C3:1, C9:1, C8:1652, C6:852$ | | 155 | C6 | 852 | 2 | 426 | 0 | B6(426), C7(426) | $B6:+426$ | $C7:+426$ | $C3:1, C9:1, C8:1652, C7:426$ | | 156 | C7 | 426 | 3 | 142 | 0 | B7(142), C5(142), C8(142) | $B7:+142$ | $C5:+142, C8:+142$ | $C3:1, C9:1, C5:1704+142=1846, C8:1652+142=1794$ | | 157 | C5 | 1846 | 2 | 923 | 0 | B5(923), C6(923) | $B5:+923$ | $C6:+923$ | $C3:1, C9:1, C8:1794, C6:923$ | | 158 | C6 | 923 | 2 | 461 | 1 | B6(462), C7(461) | $B6:+462$ | $C7:+461$ | $C3:1, C9:1, C8:1794, C7:461$ | | 159 | C7 | 461 | 3 | 153 | 2 | B7(154), C5(154), C8(153) | $B7:+154, C5:+154, C8:+153$ | $C5:1846+154=2000, C8:1794+153=1947$ | $C3:1, C9:1, C5:2000, C8:1947$ | | 160 | C5 | 2000 | 2 | 1000 | 0 | B5(1000), C6(1000) | $B5:+1000$ | $C6:+1000$ | $C3:1, C9:1, C8:1947, C6:1000$ | | 161 | C6 | 1000 | 2 | 500 | 0 | B6(500), C7(500) | $B6:+500$ | $C7:+500$ | $C3:1, C9:1, C8:1947, C7:500$ | | 162 | C7 | 500 | 3 | 166 | 2 | B7(167), C5(167), C8(166) | $B7:+167, C5:+167, C8:+166$ | $C5:2000+167=2167, C8:1947+166=2113$ | $C3:1, C9:1, C5:2167, C8:2113$ | | 163 | C5 | 2167 | 2 | 1083 | 1 | B5(1084), C6(1083) | $B5:+1084$ | $C6:+1083$ | $C3:1, C9:1, C8:2113, C6:1083$ | | 164 | C6 | 1083 | 2 | 541 | 1 | B6(542), C7(541) | $B6:+542$ | $C7:+541$ | $C3:1, C9:1, C8:2113, C7:541$ | | 165 | C7 | 541 | 3 | 180 | 1 | B7(181), C5(180), C8(180) | $B7:+181, C5:+180, C8:+180$ | $C5:2167+180=2347, C8:2113+180=2293$ | $C3:1, C9:1, C5:2347, C8:2293$ | | 166 | C5 | 2347 | 2 | 1173 | 1 | B5(1174), C6(1173) | $B5:+1174$ | $C6:+1173$ | $C3:1, C9:1, C8:2293, C6:1173$ | | 167 | C6 | 1173 | 2 | 586 | 1 | B6(587), C7(586) | $B6:+587$ | $C7:+586$ | $C3:1, C9:1, C8:2293, C7:586$ | | 168 | C7 | 586 | 3 | 195 | 1 | B7(196), C5(195), C8(195) | $B7:+196, C5:+195, C8:+195$ | $C5:2347+195=2542, C8:2293+195=2488$ | $C3:1, C9:1, C5:2542, C8:2488$ | | 169 | C5 | 2542 | 2 | 1271 | 0 | B5(1271), C6(1271) | $B5:+1271$ | $C6:+1271$ | $C3:1, C9:1, C8:2488, C6:1271$ | | 170 | C6 | 1271 | 2 | 635 | 1 | B6(636), C7(635) | $B6:+636$ | $C7:+635$ | $C3:1, C9:1, C8:2488, C7:635$ | | 171 | C7 | 635 | 3 | 211 | 2 | B7(212), C5(212), C8(211) | $B7:+212, C5:+212, C8:+211$ | $C5:2542+212=2754, C8:2488+211=2699$ | $C3:1, C9:1, C5:2754, C8:2699$ | | 172 | C5 | 2754 | 2 | 1377 | 0 | B5(1377), C6(1377) | $B5:+1377$ | $C6:+1377$ | $C3:1, C9:1, C8:2699, C6:1377$ | | 173 | C6 | 1377 | 2 | 688 | 1 | B6(689), C7(688) | $B6:+689$ | $C7:+688$ | $C3:1, C9:1, C8:2699, C7:688$ | | 174 | C7 | 688 | 3 | 229 | 1 | B7(230), C5(229), C8(229) | $B7:+230, C5:+229, C8:+229$ | $C5:2754+229=2983, C8:2699+229=2928$ | $C3:1, C9:1, C5:2983, C8:2928$ | | 175 | C5 | 2983 | 2 | 1491 | 1 | B5(1492), C6(1491) | $B5:+1492$ | $C6:+1491$ | $C3:1, C9:1, C8:2928, C6:1491$ | | 176 | C6 | 1491 | 2 | 745 | 1 | B6(746), C7(745) | $B6:+746$ | $C7:+745$ | $C3:1, C9:1, C8:2928, C7:745$ | | 177 | C7 | 745 | 3 | 248 | 1 | B7(249), C5(248), C8(248) | $B7:+249, C5:+248, C8:+248$ | $C5:2983+248=3231, C8:2928+248=3176$ | $C3:1, C9:1, C5:3231, C8:3176$ | | 178 | C5 | 3231 | 2 | 1615 | 1 | B5(1616), C6(1615) | $B5:+1616$ | $C6:+1615$ | $C3:1, C9:1, C8:3176, C6:1615$ | | 179 | C6 | 1615 | 2 | 807 | 1 | B6(808), C7(807) | $B6:+808$ | $C7:+807$ | $C3:1, C9:1, C8:3176, C7:807$ | | 180 | C7 | 807 | 3 | 269 | 0 | B7(269), C5(269), C8(269) | $B7:+269$ | $C5:+269, C8:+269$ | $C3:1, C9:1, C5:3231+269=3500, C8:3176+269=3445$ | | 181 | C5 | 3500 | 2 | 1750 | 0 | B5(1750), C6(1750) | $B5:+1750$ | $C6:+1750$ | $C3:1, C9:1, C8:3445, C6:1750$ | | 182 | C6 | 1750 | 2 | 875 | 0 | B6(875), C7(875) | $B6:+875$ | $C7:+875$ | $C3:1, C9:1, C8:3445, C7:875$ | | 183 | C7 | 875 | 3 | 291 | 2 | B7(292), C5(292), C8(291) | $B7:+292, C5:+292, C8:+291$ | $C5:3500+292=3792, C8:3445+291=3736$ | $C3:1, C9:1, C5:3792, C8:3736$ | | 184 | C5 | 3792 | 2 | 1896 | 0 | B5(1896), C6(1896) | $B5:+1896$ | $C6:+1896$ | $C3:1, C9:1, C8:3736, C6:1896$ | | 185 | C6 | 1896 | 2 | 948 | 0 | B6(948), C7(948) | $B6:+948$ | $C7:+948$ | $C3:1, C9:1, C8:3736, C7:948$ | | 186 | C7 | 948 | 3 | 316 | 0 | B7(316), C5(316), C8(316) | $B7:+316$ | $C5:+316, C8:+316$ | $C3:1, C9:1, C5:3792+316=4108, C8:3736+316=4052$ | | 187 | C5 | 4108 | 2 | 2054 | 0 | B5(2054), C6(2054) | $B5:+2054$ | $C6:+2054$ | $C3:1, C9:1, C8:4052, C6:2054$ | | 188 | C6 | 2054 | 2 | 1027 | 0 | B6(1027), C7(1027) | $B6:+1027$ | $C7:+1027$ | $C3:1, C9:1, C8:4052, C7:1027$ | | 189 | C7 | 1027 | 3 | 342 | 1 | B7(343), C5(342), C8(342) | $B7:+343, C5:+342, C8:+342$ | $C5:4108+342=4450, C8:4052+342=4394$ | $C3:1, C9:1, C5:4450, C8:4394$ | | 190 | C5 | 4450 | 2 | 2225 | 0 | B5(2225), C6(2225) | $B5:+2225$ | $C6:+2225$ | $C3:1, C9:1, C8:4394, C6:2225$ | | 191 | C6 | 2225 | 2 | 1112 | 1 | B6(1113), C7(1112) | $B6:+1113$ | $C7:+1112$ | $C3:1, C9:1, C8:4394, C7:1112$ | | 192 | C7 | 1112 | 3 | 370 | 2 | B7(371), C5(371), C8(370) | $B7:+371, C5:+371, C8:+370$ | $C5:4450+371=4821, C8:4394+370=4764$ | $C3:1, C9:1, C5:4821, C8:4764$ | | 193 | C5 | 4821 | 2 | 2410 | 1 | B5(2411), C6(2410) | $B5:+2411$ | $C6:+2410$ | $C3:1, C9:1, C8:4764, C6:2410$ | | 194 | C6 | 2410 | 2 | 1205 | 0 | B6(1205), C7(1205) | $B6:+1205$ | $C7:+1205$ | $C3:1, C9:1, C8:4764, C7:1205$ | | 195 | C7 | 1205 | 3 | 401 | 2 | B7(402), C5(402), C8(401) | $B7:+402, C5:+402, C8:+401$ | $C5:4821+402=5223, C8:4764+401=5165$ | $C3:1, C9:1, C5:5223, C8:5165$ | | 196 | C5 | 5223 | 2 | 2611 | 1 | B5(2612), C6(2611) | $B5:+2612$ | $C6:+2611$ | $C3:1, C9:1, C8:5165, C6:2611$ | | 197 | C6 | 2611 | 2 | 1305 | 1 | B6(1306), C7(1305) | $B6:+1306$ | $C7:+1305$ | $C3:1, C9:1, C8:5165, C7:1305$ | | 198 | C7 | 1305 | 3 | 435 | 0 | B7(435), C5(435), C8(435) | $B7:+435$ | $C5:+435, C8:+435$ | $C3:1, C9:1, C5:5223+435=5658, C8:5165+435=5600$ | | 199 | C5 | 5658 | 2 | 2829 | 0 | B5(2829), C6(2829) | $B5:+2829$ | $C6:+2829$ | $C3:1, C9:1, C8:5600, C6:2829$ | | 200 | C6 | 2829 | 2 | 1414 | 1 | B6(1415), C7(1414) | $B6:+1415$ | $C7:+1414$ | $C3:1, C9:1, C8:5600, C7:1414$ | | 201 | C7 | 1414 | 3 | 471 | 1 | B7(472), C5(471), C8(471) | $B7:+472, C5:+471, C8:+471$ | $C5:5658+471=6129, C8:5600+471=6071$ | $C3:1, C9:1, C5:6129, C8:6071$ | | 202 | C5 | 6129 | 2 | 3064 | 1 | B5(3065), C6(3064) | $B5:+3065$ | $C6:+3064$ | $C3:1, C9:1, C8:6071, C6:3064$ | | 203 | C6 | 3064 | 2 | 1532 | 0 | B6(1532), C7(1532) | $B6:+1532$ | $C7:+1532$ | $C3:1, C9:1, C8:6071, C7:1532$ | | 204 | C7 | 1532 | 3 | 510 | 2 | B7(511), C5(511), C8(510) | $B7:+511, C5:+511, C8:+510$ | $C5:6129+511=6640, C8:6071+510=6581$ | $C3:1, C9:1, C5:6640, C8:6581$ | | 205 | C5 | 6640 | 2 | 3320 | 0 | B5(3320), C6(3320) | $B5:+3320$ | $C6:+3320$ | $C3:1, C9:1, C8:6581, C6:3320$ | | 206 | C6 | 3320 | 2 | 1660 | 0 | B6(1660), C7(1660) | $B6:+1660$ | $C7:+1660$ | $C3:1, C9:1, C8:6581, C7:1660$ | | 207 | C7 | 1660 | 3 | 553 | 1 | B7(554), C5(553), C8(553) | $B7:+554, C5:+553, C8:+553$ | $C5:6640+553=7193, C8:6581+553=7134$ | $C3:1, C9:1, C5:7193, C8:7134$ | | 208 | C5 | 7193 | 2 | 3596 | 1 | B5(3597), C6(3596) | $B5:+3597$ | $C6:+3596$ | $C3:1, C9:1, C8:7134, C6:3596$ | | 209 | C6 | 3596 | 2 | 1798 | 0 | B6(1798), C7(1798) | $B6:+1798$ | $C7:+1798$ | $C3:1, C9:1, C8:7134, C7:1798$ | | 210 | C7 | 1798 | 3 | 599 | 1 | B7(600), C5(599), C8(599) | $B7:+600, C5:+599, C8:+599$ | $C5:7193+599=7792, C8:7134+599=7733$ | $C3:1, C9:1, C5:7792, C8:7733$ | | 211 | C5 | 7792 | 2 | 3896 | 0 | B5(3896), C6(3896) | $B5:+3896$ | $C6:+3896$ | $C3:1, C9:1, C8:7733, C6:3896$ | | 212 | C6 | 3896 | 2 | 1948 | 0 | B6(1948), C7(1948) | $B6:+1948$ | $C7:+1948$ | $C3:1, C9:1, C8:7733, C7:1948$ | | 213 | C7 | 1948 | 3 | 649 | 1 | B7(650), C5(649), C8(649) | $B7:+650, C5:+649, C8:+649$ | $C5:7792+649=8441, C8:7733+649=8382$ | $C3:1, C9:1, C5:8441, C8:8382$ | | 214 | C5 | 8441 | 2 | 4220 | 1 | B5(4221), C6(4220) | $B5:+4221$ | $C6:+4220$ | $C3:1, C9:1, C8:8382, C6:4220$ | | 215 | C6 | 4220 | 2 | 2110 | 0 | B6(2110), C7(2110) | $B6:+2110$ | $C7:+2110$ | $C3:1, C9:1, C8:8382, C7:2110$ | | 216 | C7 | 2110 | 3 | 703 | 1 | B7(704), C5(703), C8(703) | $B7:+704, C5:+703, C8:+703$ | $C5:8441+703=9144, C8:8382+703=9085$ | $C3:1, C9:1, C5:9144, C8:9085$ | | 217 | C5 | 9144 | 2 | 4572 | 0 | B5(4572), C6(4572) | $B5:+4572$ | $C6:+4572$ | $C3:1, C9:1, C8:9085, C6:4572$ | | 218 | C6 | 4572 | 2 | 2286 | 0 | B6(2286), C7(2286) | $B6:+2286$ | $C7:+2286$ | $C3:1, C9:1, C8:9085, C7:2286$ | | 219 | C7 | 2286 | 3 | 762 | 0 | B7(762), C5(762), C8(762) | $B7:+762$ | $C5:+762, C8:+762$ | $C3:1, C9:1, C5:9144+762=9906, C8:9085+762=9847$ | | 220 | C5 | 9906 | 2 | 4953 | 0 | B5(4953), C6(4953) | $B5:+4953$ | $C6:+4953$ | $C3:1, C9:1, C8:9847, C6:4953$ | | 221 | C6 | 4953 | 2 | 2476 | 1 | B6(2477), C7(2476) | $B6:+2477$ | $C7:+2476$ | $C3:1, C9:1, C8:9847, C7:2476$ | | 222 | C7 | 2476 | 3 | 825 | 1 | B7(826), C5(825), C8(825) | $B7:+826, C5:+825, C8:+825$ | $C5:9906+825=10731, C8:9847+825=10672$ | $C3:1, C9:1, C5:10731, C8:10672$ | | 223 | C5 | 10731 | 2 | 5365 | 1 | B5(5366), C6(5365) | $B5:+5366$ | $C6:+5365$ | $C3:1, C9:1, C8:10672, C6:5365$ | | 224 | C6 | 5365 | 2 | 2682 | 1 | B6(2683), C7(2682) | $B6:+2683$ | $C7:+2682$ | $C3:1, C9:1, C8:10672, C7:2682$ | | 225 | C7 | 2682 | 3 | 894 | 0 | B7(894), C5(894), C8(894) | $B7:+894$ | $C5:+894, C8:+894$ | $C3:1, C9:1, C5:10731+894=11625, C8:10672+894=11566$ | | 226 | C5 | 11625 | 2 | 5812 | 1 | B5(5813), C6(5812) | $B5:+5813$ | $C6:+5812$ | $C3:1, C9:1, C8:11566, C6:5812$ | | 227 | C6 | 5812 | 2 | 2906 | 0 | B6(2906), C7(2906) | $B6:+2906$ | $C7:+2906$ | $C3:1, C9:1, C8:11566, C7:2906$ | | 228 | C7 | 2906 | 3 | 968 | 2 | B7(969), C5(969), C8(968) | $B7:+969, C5:+969, C8:+968$ | $C5:11625+969=12594, C8:11566+968=12534$ | $C3:1, C9:1, C5:12594, C8:12534$ | | 229 | C5 | 12594 | 2 | 6297 | 0 | B5(6297), C6(6297) | $B5:+6297$ | $C6:+6297$ | $C3:1, C9:1, C8:12534, C6:6297$ | | 230 | C6 | 6297 | 2 | 3148 | 1 | B6(3149), C7(3148) | $B6:+3149$ | $C7:+3148$ | $C3:1, C9:1, C8:12534, C7:3148$ | | 231 | C7 | 3148 | 3 | 1049 | 1 | B7(1050), C5(1049), C8(1049) | $B7:+1050, C5:+1049, C8:+1049$ | $C5:12594+1049=13643, C8:12534+1049=13583$ | $C3:1, C9:1, C5:13643, C8:13583$ | | 232 | C5 | 13643 | 2 | 6821 | 1 | B5(6822), C6(6821) | $B5:+6822$ | $C6:+6821$ | $C3:1, C9:1, C8:13583, C6:6821$ | | 233 | C6 | 6821 | 2 | 3410 | 1 | B6(3411), C7(3410) | $B6:+3411$ | $C7:+3410$ | $C3:1, C9:1, C8:13583, C7:3410$ | | 234 | C7 | 3410 | 3 | 1136 | 2 | B7(1137), C5(1137), C8(1136) | $B7:+1137, C5:+1137, C8:+1136$ | $C5:13643+1137=14780, C8:13583+1136=14719$ | $C3:1, C9:1, C5:14780, C8:14719$ | | 235 | C5 | 14780 | 2 | 7390 | 0 | B5(7390), C6(7390) | $B5:+7390$ | $C6:+7390$ | $C3:1, C9:1, C8:14719, C6:7390$ | | 236 | C6 | 7390 | 2 | 3695 | 0 | B6(3695), C7(3695) | $B6:+3695$ | $C7:+3695$ | $C3:1, C9:1, C8:14719, C7:3695$ | | 237 | C7 | 3695 | 3 | 1231 | 2 | B7(1232), C5(1232), C8(1231) | $B7:+1232, C5:+1232, C8:+1231$ | $C5:14780+1232=16012, C8:14719+1231=15950$ | $C3:1, C9:1, C5:16012, C8:15950$ | | 238 | C5 | 16012 | 2 | 8006 | 0 | B5(8006), C6(8006) | $B5:+8006$ | $C6:+8006$ | $C3:1, C9:1, C8:15950, C6:8006$ | | 239 | C6 | 8006 | 2 | 4003 | 0 | B6(4003), C7(4003) | $B6:+4003$ | $C7:+4003$ | $C3:1, C9:1, C8:15950, C7:4003$ | | 240 | C7 | 4003 | 3 | 1334 | 1 | B7(1335), C5(1334), C8(1334) | $B7:+1335, C5:+1334, C8:+1334$ | $C5:16012+1334=1734  INFO 2026-02-15T15:33:59 +23ms service=bus type=message.part.updated publishing INFO 2026-02-15T15:33:59 +1ms service=bus type=message.updated publishing INFO 2026-02-15T15:33:59 +12ms service=bus type=message.updated publishing INFO 2026-02-15T15:33:59 +10ms service=bus type=session.status publishing INFO 2026-02-15T15:33:59 +1ms service=session.prompt step=1 sessionID=ses_39e1118b4ffereXCDS2xr1T17W loop INFO 2026-02-15T15:33:59 +13ms service=bus type=message.updated publishing INFO 2026-02-15T15:33:59 +2ms service=bus type=session.updated publishing INFO 2026-02-15T15:33:59 +2ms service=bus type=session.diff publishing INFO 2026-02-15T15:33:59 +9ms service=session.prompt sessionID=ses_39e1118b4ffereXCDS2xr1T17W exiting loop INFO 2026-02-15T15:33:59 +1ms service=session.compaction pruning INFO 2026-02-15T15:33:59 +7ms service=session.prompt sessionID=ses_39e1118b4ffereXCDS2xr1T17W cancel INFO 2026-02-15T15:33:59 +3ms service=bus type=session.status publishing INFO 2026-02-15T15:33:59 +0ms service=bus type=session.idle publishing INFO 2026-02-15T15:33:59 +2ms service=default directory=/app/input disposing instance INFO 2026-02-15T15:33:59 +2ms service=state key=/app/input waiting for state disposal to complete INFO 2026-02-15T15:33:59 +1ms 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.