InternLM/InternBootcamp
1
0
Fork 0
mirror of https://github.com/InternLM/InternBootcamp.git synced 2026-04-19 12:58:04 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions
InternBootcamp/examples/data/Intenbootcamp_eval/arc.jsonl
Yongkang Chen a8249acc18
update to tech report version (#10) 
* feat(run_eval): add checkpoint resume functionality and update example documentation;
- update new bootcamp benchmark dataset

* refactor(data_pipeline): optimize data generation pipeline; add multiple preset configurations for data generation

* docs: update bootcamp list and add new scripts

- Update Fulllist_InternBootcamp.md with new bootcamps and categories
- Add new scripts to .gitignore:
  - examples/pipelines/filter_autogen_configs.py
  - examples/pipelines/quickgen_data_configs_from_eval_meta.py
- Update dependencies in setup.py:
  - Add scipy and scikit-learn

* refactor(internbootcamp): update bootcamp modules and improve error handling

- Update import statements in __init__.py files
- Add timestamp to target directory name in verl_data_preprocess.py
- Improve error handling and scoring logic in bootcamp_judger.py
- Remove unnecessary comments and update puzzle descriptions in multiple files
2025-08-28 12:39:47 +08:00

100 lines
1.3 MiB
Raw Blame History

{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 3, 1, 5, 6, 6, 5, 6, 5, 1, 3, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[3, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[1, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 5, 6, 3, 6, 6, 6, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 3, 1, 5, 6, 6, 5, 6, 5, 1, 3, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 3, 1, 8, 6, 6, 8, 6, 8, 1, 3, 8, 6, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[3, 5, 5, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 5, 5, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[1, 5, 5, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 1, 8, 6, 3, 6, 6, 6, 3, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 5, 6, 3, 6, 6, 6, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 1, 1, 6, 4],\n[4, 6, 1, 1, 6, 4],\n[4, 6, 1, 1, 6, 4],\n[4, 6, 1, 1, 6, 5],\n[5, 6, 1, 1, 6, 6],\n[4, 6, 1, 1, 6, 5],\n[5, 6, 1, 1, 6, 4],\n[5, 6, 1, 1, 6, 4],\n[5, 6, 1, 1, 6, 5],\n[6, 6, 1, 1, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 5, 5, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 4, 4, 6, 4],\n[4, 6, 4, 4, 6, 4],\n[4, 6, 4, 4, 6, 4],\n[4, 6, 4, 5, 6, 5],\n[5, 6, 5, 1, 6, 6],\n[4, 6, 4, 5, 6, 5],\n[5, 6, 5, 4, 6, 4],\n[5, 6, 5, 4, 6, 4],\n[5, 6, 5, 5, 6, 5],\n[6, 6, 5, 5, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 5, 5, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 0, 0, 7, 6, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 8],\n[2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[7, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 0, 0, 7, 6, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 0, 0, 7, 6, 7, 8, 3, 3, 3, 3, 3, 3, 3, 8],\n[2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[7, 3, 3, 3, 3, 3, 3, 3, 3, 7, 5, 5, 5, 5, 5, 9, 3, 3, 3, 3, 3, 3, 3, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 9, 8, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6],\n[3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 3],\n[7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6],\n[0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 3],\n[1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6],\n[2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 0],\n[0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 3],\n[3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 3, 1, 5, 6, 6, 5, 6, 5, 1, 3, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3], [1, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 5, 6, 3, 6, 6, 6, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 3, 1, 5, 6, 6, 5, 6, 5, 1, 3, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 3, 1, 8, 6, 6, 8, 6, 8, 1, 3, 8, 6, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [3, 5, 5, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 5, 5, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [1, 5, 5, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 1, 8, 6, 3, 6, 6, 6, 3, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 5, 6, 3, 6, 6, 6, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {"input": [[6, 6, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 1, 1, 6, 4], [4, 6, 1, 1, 6, 4], [4, 6, 1, 1, 6, 4], [4, 6, 1, 1, 6, 5], [5, 6, 1, 1, 6, 6], [4, 6, 1, 1, 6, 5], [5, 6, 1, 1, 6, 4], [5, 6, 1, 1, 6, 4], [5, 6, 1, 1, 6, 5], [6, 6, 1, 1, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 5, 5, 6, 6]], "output": [[6, 6, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 4, 4, 6, 4], [4, 6, 4, 4, 6, 4], [4, 6, 4, 4, 6, 4], [4, 6, 4, 5, 6, 5], [5, 6, 5, 1, 6, 6], [4, 6, 4, 5, 6, 5], [5, 6, 5, 4, 6, 4], [5, 6, 5, 4, 6, 4], [5, 6, 5, 5, 6, 5], [6, 6, 5, 5, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 5, 5, 6, 6]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 0, 0, 7, 6, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 8], [2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [8, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [7, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 0, 0, 7, 6, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 0, 0, 7, 6, 7, 8, 3, 3, 3, 3, 3, 3, 3, 8], [2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [7, 3, 3, 3, 3, 3, 3, 3, 3, 7, 5, 5, 5, 5, 5, 9, 3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 9, 8, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6], [3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 3], [7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6], [0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 3], [1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6], [2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 0], [0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 3], [3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "1f642eb9"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 9],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 5, 5, 9, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 9, 8, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 9],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 9, 5],\n[5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 9, 5, 5, 5],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 9, 5, 5],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 9, 5, 5, 8, 5, 5, 5, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 9, 5, 5, 8, 9, 5, 5, 5],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5],\n[1, 1, 5, 5, 5],\n[5, 5, 5, 1, 1],\n[5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 5, 9, 2, 2, 2, 2, 5, 2, 2, 2, 2, 9, 5, 2, 2, 2, 9, 2],\n[2, 2, 9, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 9, 2, 2],\n[2, 2, 2, 2, 9, 5, 9, 2, 2, 2, 2, 5, 2, 2, 2, 9, 2, 5, 2, 2, 2, 2, 2],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[2, 2, 2, 2, 9, 5, 2, 2, 2, 2, 2, 5, 2, 9, 2, 2, 2, 5, 2, 2, 9, 2, 2],\n[2, 2, 2, 2, 2, 5, 2, 2, 2, 9, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[2, 2, 2, 2, 2, 5, 9, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2],\n[2, 2, 9, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 9, 9, 2, 2, 5, 9, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[2, 2, 1, 2]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 3, 9, 9, 0],\n[9, 9, 0, 3, 9, 9, 9],\n[9, 9, 9, 3, 9, 9, 9],\n[3, 3, 3, 3, 3, 3, 3],\n[9, 9, 9, 3, 9, 9, 9],\n[9, 9, 9, 3, 9, 0, 9],\n[9, 0, 9, 3, 9, 9, 9],\n[3, 3, 3, 3, 3, 3, 3],\n[9, 9, 0, 3, 0, 9, 9],\n[9, 0, 9, 3, 9, 9, 9],\n[9, 9, 9, 3, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9],\n[9, 9],\n[1, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 5, 3, 7, 5, 3, 7, 7, 3, 5, 7],\n[5, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7],\n[7, 7, 3, 7, 5, 3, 7, 7, 3, 5, 7],\n[7, 7, 3, 7, 7, 3, 7, 5, 3, 7, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[5, 5, 3, 7, 7, 3, 7, 7, 3, 7, 7],\n[7, 7, 3, 7, 5, 3, 5, 5, 3, 7, 5],\n[7, 7, 3, 5, 7, 3, 7, 7, 3, 7, 5],\n[7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 9], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5], [5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 5, 5, 9, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 9, 8, 5, 5, 5, 5], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 9], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 9, 5], [5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 9, 5, 5, 5], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 9, 5, 5], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 9, 5, 5, 8, 5, 5, 5, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 8, 5, 5, 9, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 9, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 9, 5, 5, 8, 9, 5, 5, 5], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 9, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5, 8, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5], [1, 1, 5, 5, 5], [5, 5, 5, 1, 1], [5, 5, 5, 5, 5], [5, 5, 5, 5, 5]]}, {"input": [[2, 2, 2, 2, 2, 5, 9, 2, 2, 2, 2, 5, 2, 2, 2, 2, 9, 5, 2, 2, 2, 9, 2], [2, 2, 9, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 9, 2, 2], [2, 2, 2, 2, 9, 5, 9, 2, 2, 2, 2, 5, 2, 2, 2, 9, 2, 5, 2, 2, 2, 2, 2], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 9, 5, 2, 2, 2, 2, 2, 5, 2, 9, 2, 2, 2, 5, 2, 2, 9, 2, 2], [2, 2, 2, 2, 2, 5, 2, 2, 2, 9, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 9, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2], [2, 2, 9, 2, 2, 5, 2, 2, 2, 2, 2, 5, 2, 9, 9, 2, 2, 5, 9, 2, 2, 2, 2]], "output": [[2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 1, 2]]}, {"input": [[9, 9, 9, 3, 9, 9, 0], [9, 9, 0, 3, 9, 9, 9], [9, 9, 9, 3, 9, 9, 9], [3, 3, 3, 3, 3, 3, 3], [9, 9, 9, 3, 9, 9, 9], [9, 9, 9, 3, 9, 0, 9], [9, 0, 9, 3, 9, 9, 9], [3, 3, 3, 3, 3, 3, 3], [9, 9, 0, 3, 0, 9, 9], [9, 0, 9, 3, 9, 9, 9], [9, 9, 9, 3, 9, 9, 9]], "output": [[9, 9], [9, 9], [1, 9]]}], "input_grid": [[7, 5, 3, 7, 5, 3, 7, 7, 3, 5, 7], [5, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7], [7, 7, 3, 7, 5, 3, 7, 7, 3, 5, 7], [7, 7, 3, 7, 7, 3, 7, 5, 3, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [5, 5, 3, 7, 7, 3, 7, 7, 3, 7, 7], [7, 7, 3, 7, 5, 3, 5, 5, 3, 7, 5], [7, 7, 3, 5, 7, 3, 7, 7, 3, 7, 5], [7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7]], "task_key": "6773b310"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1],\n[1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1],\n[1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2],\n[2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1],\n[1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2],\n[1, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[1, 2, 1, 5, 5, 5, 5, 1, 5, 5, 1, 2, 5, 2, 5, 1],\n[2, 5, 5, 5, 2, 1, 2, 5, 2, 5, 2, 5, 5, 2, 2, 5],\n[4, 5, 5, 1, 5, 4, 5, 2, 1, 2, 4, 1, 5, 4, 2, 2],\n[5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 1, 2, 2, 5, 1, 5],\n[5, 4, 1, 2, 5, 2, 1, 5, 5, 5, 5, 2, 5, 2, 2, 5],\n[5, 1, 5, 2, 1, 1, 5, 5, 5, 2, 5, 5, 5, 1, 5, 2],\n[5, 5, 1, 1, 5, 2, 5, 2, 2, 1, 5, 5, 1, 5, 2, 2],\n[2, 5, 1, 2, 1, 5, 2, 5, 5, 5, 5, 2, 5, 5, 5, 2],\n[5, 2, 5, 2, 2, 1, 5, 4, 5, 5, 2, 2, 5, 5, 2, 5],\n[2, 5, 2, 5, 5, 5, 2, 5, 1, 2, 2, 2, 5, 5, 5, 5],\n[5, 5, 1, 5, 5, 5, 2, 5, 2, 5, 1, 5, 5, 2, 5, 5],\n[1, 5, 5, 5, 2, 5, 1, 5, 2, 2, 5, 5, 1, 5, 5, 5],\n[2, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 1, 5, 5, 1, 5],\n[4, 5, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2],\n[2, 2, 2, 5, 4, 5, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2],\n[5, 5, 5, 4, 5, 5, 5, 4, 2, 2, 2, 5, 4, 2, 5, 1],\n[1, 1, 5, 1, 2, 5, 1, 5, 1, 2, 2, 5, 2, 1, 1, 4],\n[5, 5, 5, 2, 4, 5, 5, 1, 5, 2, 5, 2, 5, 2, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 2],\n[2, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 5, 5, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9],\n[9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 2, 8, 8, 2],\n[8, 8, 8, 8, 2, 8, 2, 8, 8, 8],\n[8, 2, 8, 8, 2, 2, 8, 8, 8, 2],\n[2, 8, 8, 8, 8, 8, 8, 2, 8, 8],\n[8, 2, 8, 8, 2, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 8, 8, 8, 8],\n[2, 8, 8, 8, 8, 2, 2, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 8, 8, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 2, 8, 8, 8, 2, 8, 8, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[2, 8, 8, 8, 8, 2, 8, 8, 8, 8],\n[2, 8, 8, 8, 2, 8, 8, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 2, 8, 8, 8, 8, 2, 8, 8],\n[2, 2, 8, 8, 2, 8, 8, 8, 8, 2],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2],\n[8, 8, 8, 2, 2, 8, 8, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1], [1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1], [1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2], [2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1], [1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2]], "output": [[2, 2], [1, 2]]}, {"input": [[1, 2, 1, 5, 5, 5, 5, 1, 5, 5, 1, 2, 5, 2, 5, 1], [2, 5, 5, 5, 2, 1, 2, 5, 2, 5, 2, 5, 5, 2, 2, 5], [4, 5, 5, 1, 5, 4, 5, 2, 1, 2, 4, 1, 5, 4, 2, 2], [5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 1, 2, 2, 5, 1, 5], [5, 4, 1, 2, 5, 2, 1, 5, 5, 5, 5, 2, 5, 2, 2, 5], [5, 1, 5, 2, 1, 1, 5, 5, 5, 2, 5, 5, 5, 1, 5, 2], [5, 5, 1, 1, 5, 2, 5, 2, 2, 1, 5, 5, 1, 5, 2, 2], [2, 5, 1, 2, 1, 5, 2, 5, 5, 5, 5, 2, 5, 5, 5, 2], [5, 2, 5, 2, 2, 1, 5, 4, 5, 5, 2, 2, 5, 5, 2, 5], [2, 5, 2, 5, 5, 5, 2, 5, 1, 2, 2, 2, 5, 5, 5, 5], [5, 5, 1, 5, 5, 5, 2, 5, 2, 5, 1, 5, 5, 2, 5, 5], [1, 5, 5, 5, 2, 5, 1, 5, 2, 2, 5, 5, 1, 5, 5, 5], [2, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 1, 5, 5, 1, 5], [4, 5, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2], [2, 2, 2, 5, 4, 5, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2], [5, 5, 5, 4, 5, 5, 5, 4, 2, 2, 2, 5, 4, 2, 5, 1], [1, 1, 5, 1, 2, 5, 1, 5, 1, 2, 2, 5, 2, 1, 1, 4], [5, 5, 5, 2, 4, 5, 5, 1, 5, 2, 5, 2, 5, 2, 5, 5]], "output": [[1, 2], [2, 5]]}, {"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 5, 5, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9], [9, 9]]}], "input_grid": [[8, 8, 8, 8, 8, 8, 2, 8, 8, 2], [8, 8, 8, 8, 2, 8, 2, 8, 8, 8], [8, 2, 8, 8, 2, 2, 8, 8, 8, 2], [2, 8, 8, 8, 8, 8, 8, 2, 8, 8], [8, 2, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [2, 8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 2, 8, 8, 8, 2, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 8, 8, 8, 8, 2, 8, 8, 8, 8], [2, 8, 8, 8, 2, 8, 8, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 8, 8, 8, 2, 8, 8], [2, 2, 8, 8, 2, 8, 8, 8, 8, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2], [8, 8, 8, 2, 2, 8, 8, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "task_key": "d10ecb37"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 0, 1, 1],\n[1, 1, 4, 4, 1, 4, 1, 1, 1, 1, 8, 8, 8, 8, 1, 1],\n[1, 1, 1, 1, 1, 4, 4, 1, 1, 1, 8, 8, 8, 8, 1, 1],\n[1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 8, 8, 8, 8, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1],\n[1, 5, 5, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 4, 4, 1],\n[1, 5, 5, 5, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 4, 1],\n[1, 5, 5, 5, 5, 5, 5, 1, 8, 8, 8, 8, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 8, 1, 1, 1, 1, 1],\n[1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 2, 2, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 2, 1, 9, 9, 1, 1, 1, 1, 1, 5, 5, 1],\n[1, 1, 1, 1, 2, 1, 9, 9, 9, 1, 7, 7, 1, 5, 5, 1],\n[1, 7, 7, 1, 1, 1, 9, 9, 9, 1, 7, 7, 1, 5, 5, 1],\n[1, 1, 7, 1, 7, 1, 9, 9, 9, 1, 7, 7, 1, 5, 5, 1],\n[1, 1, 1, 7, 1, 1, 1, 9, 9, 1, 7, 7, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 0, 0, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1],\n[1, 1, 0, 0, 1, 1, 1, 1, 5, 1, 5, 1, 1, 0, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 0],\n[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1],\n[0, 0, 0, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 0, 1],\n[1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 9, 9, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 1],\n[8, 8, 8, 8],\n[8, 8, 8, 8],\n[8, 8, 8, 8],\n[8, 8, 8, 1],\n[8, 8, 1, 1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 3, 3, 9, 9, 9, 7, 9, 9, 9, 9, 9],\n[9, 9, 9, 4, 9, 9, 9, 9, 3, 9, 9, 9, 7, 9, 9, 9, 9, 9],\n[9, 9, 9, 4, 4, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[5, 5, 5, 9, 9, 9, 9, 9, 3, 3, 9, 9, 0, 0, 0, 0, 0, 0],\n[5, 5, 5, 9, 9, 3, 3, 9, 9, 3, 9, 9, 0, 0, 0, 9, 0, 0],\n[5, 5, 5, 9, 9, 9, 9, 3, 3, 3, 3, 9, 9, 9, 9, 0, 0, 0],\n[5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9],\n[9, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 8, 8, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 8, 8, 9, 9],\n[7, 7, 9, 7, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 8, 8, 9, 9],\n[9, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 7, 7, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 7, 9, 9, 6, 2, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 3],\n[5, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 3, 3],\n[5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5],\n[5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 8],\n[5, 5, 6, 6, 6, 6, 5, 5, 8, 8, 8],\n[5, 5, 6, 6, 6, 5, 6, 5, 5, 8, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 5, 9, 9, 9, 5, 1, 5, 1],\n[5, 5, 5, 5, 5, 9, 5, 5, 1, 1, 1],\n[3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5],\n[5, 5, 5, 6, 6, 6, 5, 5, 0, 0, 0],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0],\n[5, 4, 4, 4, 5, 5, 5, 0, 0, 0, 0],\n[4, 3, 5, 4, 5, 5, 5, 5, 0, 0, 5],\n[4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 5, 5, 5, 8, 8, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 4, 4, 4],\n[4, 5, 5, 4],\n[4, 4, 4, 4],\n[4, 4, 4, 4],\n[4, 4, 4, 4],\n[4, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6],\n[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 0, 6, 6, 2, 2, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2],\n[6, 6, 6, 0, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 2, 6],\n[6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 5, 6, 5, 6, 6, 2, 2, 2],\n[6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 8, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6],\n[5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6],\n[6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6],\n[5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7],\n[6, 2, 2, 2, 2, 6, 2, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7],\n[6, 2, 6, 2, 2, 2, 2, 6, 6, 6, 7, 7, 7, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 2, 6, 2, 2, 2, 6, 6, 6, 7, 7, 7, 6, 6, 4, 4, 6, 6, 6, 2, 6, 6],\n[6, 2, 2, 2, 2, 2, 2, 6, 6, 6, 7, 7, 4, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 0, 1, 1], [1, 1, 4, 4, 1, 4, 1, 1, 1, 1, 8, 8, 8, 8, 1, 1], [1, 1, 1, 1, 1, 4, 4, 1, 1, 1, 8, 8, 8, 8, 1, 1], [1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 8, 8, 8, 8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1], [1, 5, 5, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 4, 4, 1], [1, 5, 5, 5, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 4, 1], [1, 5, 5, 5, 5, 5, 5, 1, 8, 8, 8, 8, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 8, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2, 1, 9, 9, 1, 1, 1, 1, 1, 5, 5, 1], [1, 1, 1, 1, 2, 1, 9, 9, 9, 1, 7, 7, 1, 5, 5, 1], [1, 7, 7, 1, 1, 1, 9, 9, 9, 1, 7, 7, 1, 5, 5, 1], [1, 1, 7, 1, 7, 1, 9, 9, 9, 1, 7, 7, 1, 5, 5, 1], [1, 1, 1, 7, 1, 1, 1, 9, 9, 1, 7, 7, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1], [1, 1, 0, 0, 1, 1, 1, 1, 5, 1, 5, 1, 1, 0, 1, 1], [1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1], [0, 0, 0, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 0, 1], [1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 9, 9, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1]], "output": [[8, 8, 8, 1], [8, 8, 8, 8], [8, 8, 8, 8], [8, 8, 8, 8], [8, 8, 8, 1], [8, 8, 1, 1]]}, {"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 3, 3, 9, 9, 9, 7, 9, 9, 9, 9, 9], [9, 9, 9, 4, 9, 9, 9, 9, 3, 9, 9, 9, 7, 9, 9, 9, 9, 9], [9, 9, 9, 4, 4, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [5, 5, 5, 9, 9, 9, 9, 9, 3, 3, 9, 9, 0, 0, 0, 0, 0, 0], [5, 5, 5, 9, 9, 3, 3, 9, 9, 3, 9, 9, 0, 0, 0, 9, 0, 0], [5, 5, 5, 9, 9, 9, 9, 3, 3, 3, 3, 9, 9, 9, 9, 0, 0, 0], [5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9], [9, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 8, 8, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 8, 8, 9, 9], [7, 7, 9, 7, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 8, 8, 9, 9], [9, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 7, 7, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9], [9, 9, 7, 9, 9, 6, 2, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 3], [5, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 3, 3], [5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9]], "output": [[6, 6, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6]]}, {"input": [[5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5], [5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 8], [5, 5, 6, 6, 6, 6, 5, 5, 8, 8, 8], [5, 5, 6, 6, 6, 5, 6, 5, 5, 8, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 5, 9, 9, 9, 5, 1, 5, 1], [5, 5, 5, 5, 5, 9, 5, 5, 1, 1, 1], [3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5], [5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5], [5, 5, 5, 6, 6, 6, 5, 5, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0], [5, 4, 4, 4, 5, 5, 5, 0, 0, 0, 0], [4, 3, 5, 4, 5, 5, 5, 5, 0, 0, 5], [4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5, 5, 8, 8, 5], [5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5]], "output": [[5, 4, 4, 4], [4, 5, 5, 4], [4, 4, 4, 4], [4, 4, 4, 4], [4, 4, 4, 4], [4, 4, 4, 4]]}], "input_grid": [[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6], [7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 0, 6, 6, 2, 2, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2], [6, 6, 6, 0, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 2, 6], [6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 5, 6, 5, 6, 6, 2, 2, 2], [6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 8, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6], [5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6], [6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6], [5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7], [6, 2, 2, 2, 2, 6, 2, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7], [6, 2, 6, 2, 2, 2, 2, 6, 6, 6, 7, 7, 7, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6], [6, 6, 2, 6, 2, 2, 2, 6, 6, 6, 7, 7, 7, 6, 6, 4, 4, 6, 6, 6, 2, 6, 6], [6, 2, 2, 2, 2, 2, 2, 6, 6, 6, 7, 7, 4, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6]], "task_key": "48d8fb45"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 7, 7, 2, 7, 7, 7, 7, 7],\n[7, 8, 2, 7, 7, 7, 7, 7, 7],\n[7, 4, 0, 7, 7, 7, 7, 7, 7],\n[4, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 2, 7, 7, 7, 7],\n[8, 7, 7, 2, 7, 7, 7, 7, 7],\n[7, 8, 2, 7, 7, 7, 7, 7, 7],\n[7, 4, 0, 7, 7, 7, 7, 7, 7],\n[4, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 5, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 5, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 7, 7, 2, 7, 7, 7, 7, 7], [7, 8, 2, 7, 7, 7, 7, 7, 7], [7, 4, 0, 7, 7, 7, 7, 7, 7], [4, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 2, 7, 7, 7, 7], [8, 7, 7, 2, 7, 7, 7, 7, 7], [7, 8, 2, 7, 7, 7, 7, 7, 7], [7, 4, 0, 7, 7, 7, 7, 7, 7], [4, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 5, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 5, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "task_key": "7ddcd7ec"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 8, 2, 8, 9, 9, 9, 9, 9, 9, 4],\n[4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4],\n[9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4],\n[4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9],\n[4, 9, 4, 4, 4, 9, 4, 4, 4, 9, 4],\n[4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4],\n[4, 9, 4, 9, 4, 9, 4, 4, 4, 4, 4],\n[4, 9, 9, 9, 4, 9, 9, 9, 9, 9, 4],\n[4, 4, 4, 9, 4, 4, 4, 9, 4, 4, 4],\n[9, 9, 4, 9, 9, 9, 4, 9, 4, 9, 9],\n[4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4],\n[4, 9, 9, 9, 4, 9, 9, 9, 4, 9, 4],\n[4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4],\n[4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9],\n[4, 9, 4, 9, 4, 4, 4, 9, 4, 4, 4],\n[4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4],\n[4, 4, 4, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 9, 4, 9, 4, 9, 9, 9, 9, 9, 4],\n[4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4],\n[4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4],\n[4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4],\n[9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 4],\n[4, 4, 4, 9, 4, 9, 4, 9, 4, 9, 4],\n[4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4],\n[4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 8, 2, 8, 2, 8, 2, 8, 2, 8, 4],\n[4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4],\n[2, 8, 2, 8, 2, 8, 4, 9, 9, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4],\n[4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9],\n[4, 9, 4, 4, 4, 9, 4, 4, 4, 9, 4],\n[4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4],\n[4, 9, 4, 9, 4, 9, 4, 4, 4, 4, 4],\n[4, 9, 9, 9, 4, 9, 9, 9, 9, 9, 4],\n[4, 4, 4, 9, 4, 4, 4, 9, 4, 4, 4],\n[9, 9, 4, 9, 9, 9, 4, 9, 4, 9, 9],\n[4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4],\n[4, 9, 9, 9, 4, 9, 9, 9, 4, 9, 4],\n[4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4],\n[4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9],\n[4, 9, 4, 9, 4, 4, 4, 9, 4, 4, 4],\n[4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4],\n[4, 4, 4, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 9, 4, 9, 4, 9, 9, 9, 9, 9, 4],\n[4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4],\n[4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4],\n[4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4],\n[9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 4],\n[4, 4, 4, 9, 4, 9, 4, 9, 4, 9, 4],\n[4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4],\n[4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4],\n[4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4],\n[4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4],\n[3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4],\n[4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4],\n[4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4],\n[4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4],\n[4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4],\n[4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4],\n[4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4],\n[3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4],\n[4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4],\n[4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4],\n[4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3],\n[4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4],\n[4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4],\n[4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 0, 2, 4],\n[4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 0, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4],\n[4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4],\n[4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4],\n[3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4],\n[4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4],\n[4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4],\n[4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4],\n[4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4],\n[4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4],\n[4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4],\n[3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4],\n[4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4],\n[4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4],\n[4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4],\n[4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3],\n[4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4],\n[4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4],\n[4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 2, 0, 2, 0, 2, 4],\n[4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 0, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0],\n[7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 0],\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0],\n[7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 0],\n[0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0],\n[0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7],\n[0, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0],\n[0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 0],\n[0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7, 0],\n[7, 7, 0, 7, 0, 7, 0, 7, 0, 7, 0, 7, 0],\n[0, 0, 0, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0],\n[0, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0],\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0],\n[0, 4, 2, 7, 7, 7, 7, 7, 0, 7, 7, 7, 0],\n[0, 2, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0],\n[0, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7],\n[0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0],\n[7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 0],\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0],\n[7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 0],\n[0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0],\n[0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7],\n[0, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0],\n[0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 0],\n[0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7, 0],\n[7, 7, 0, 7, 0, 4, 0, 7, 0, 7, 0, 7, 0],\n[0, 0, 0, 7, 0, 2, 0, 7, 0, 7, 0, 0, 0],\n[0, 7, 7, 7, 0, 4, 0, 7, 7, 7, 7, 7, 0],\n[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 7, 0],\n[0, 4, 2, 4, 2, 4, 2, 4, 0, 7, 7, 7, 0],\n[0, 2, 0, 2, 0, 0, 0, 0, 0, 7, 0, 0, 0],\n[0, 4, 0, 4, 0, 7, 7, 7, 7, 7, 0, 7, 7],\n[0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8],\n[0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8],\n[8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8],\n[8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8],\n[8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8],\n[8, 0, 0, 0, 8, 0, 0, 3, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8],\n[8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 8, 2, 8, 9, 9, 9, 9, 9, 9, 4], [4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4], [9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 4], [4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4], [4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9], [4, 9, 4, 4, 4, 9, 4, 4, 4, 9, 4], [4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4], [4, 9, 4, 9, 4, 9, 4, 4, 4, 4, 4], [4, 9, 9, 9, 4, 9, 9, 9, 9, 9, 4], [4, 4, 4, 9, 4, 4, 4, 9, 4, 4, 4], [9, 9, 4, 9, 9, 9, 4, 9, 4, 9, 9], [4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4], [4, 9, 9, 9, 4, 9, 9, 9, 4, 9, 4], [4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4], [4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9], [4, 9, 4, 9, 4, 4, 4, 9, 4, 4, 4], [4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4], [4, 4, 4, 9, 4, 4, 4, 4, 4, 9, 4], [4, 9, 4, 9, 4, 9, 9, 9, 9, 9, 4], [4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4], [4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4], [4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4], [9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 4], [4, 4, 4, 9, 4, 9, 4, 9, 4, 9, 4], [4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4], [4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 8, 2, 8, 2, 8, 2, 8, 2, 8, 4], [4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4], [2, 8, 2, 8, 2, 8, 4, 9, 9, 9, 4], [4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4], [4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9], [4, 9, 4, 4, 4, 9, 4, 4, 4, 9, 4], [4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4], [4, 9, 4, 9, 4, 9, 4, 4, 4, 4, 4], [4, 9, 9, 9, 4, 9, 9, 9, 9, 9, 4], [4, 4, 4, 9, 4, 4, 4, 9, 4, 4, 4], [9, 9, 4, 9, 9, 9, 4, 9, 4, 9, 9], [4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4], [4, 9, 9, 9, 4, 9, 9, 9, 4, 9, 4], [4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4], [4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9], [4, 9, 4, 9, 4, 4, 4, 9, 4, 4, 4], [4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4], [4, 4, 4, 9, 4, 4, 4, 4, 4, 9, 4], [4, 9, 4, 9, 4, 9, 9, 9, 9, 9, 4], [4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4], [4, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4], [4, 4, 4, 9, 4, 4, 4, 9, 4, 9, 4], [9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 4], [4, 4, 4, 9, 4, 9, 4, 9, 4, 9, 4], [4, 9, 4, 9, 4, 9, 4, 9, 9, 9, 4], [4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 4]]}, {"input": [[4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4], [4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4], [4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4], [4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 3, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4], [3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4], [4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4], [4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3], [4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4], [4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4], [4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4], [3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4], [4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4], [4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4], [4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3], [4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4], [4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 0, 2, 4], [4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 0, 4]], "output": [[4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4], [4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4], [4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4], [4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 3, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4], [3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4], [4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4], [4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3], [4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4], [4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4], [4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4], [3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4], [4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4], [4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4], [4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4], [4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3], [4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4], [4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4], [4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 2, 0, 2, 0, 2, 4], [4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 0, 4]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 0], [0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0], [7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 0], [0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7], [0, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 0], [0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7, 0], [7, 7, 0, 7, 0, 7, 0, 7, 0, 7, 0, 7, 0], [0, 0, 0, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0], [0, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0], [0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0], [0, 4, 2, 7, 7, 7, 7, 7, 0, 7, 7, 7, 0], [0, 2, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 7], [0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 0], [0, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0], [7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 0, 7, 0], [0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 7], [0, 7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 0], [0, 7, 7, 7, 7, 7, 7, 7, 0, 7, 0, 7, 0], [0, 0, 0, 7, 0, 0, 0, 7, 0, 7, 0, 7, 0], [7, 7, 0, 7, 0, 4, 0, 7, 0, 7, 0, 7, 0], [0, 0, 0, 7, 0, 2, 0, 7, 0, 7, 0, 0, 0], [0, 7, 7, 7, 0, 4, 0, 7, 7, 7, 7, 7, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 7, 0], [0, 4, 2, 4, 2, 4, 2, 4, 0, 7, 7, 7, 0], [0, 2, 0, 2, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 4, 0, 4, 0, 7, 7, 7, 7, 7, 0, 7, 7], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8], [0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8], [8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8], [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8], [8, 0, 0, 0, 8, 0, 0, 3, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8], [8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8]], "task_key": "b782dc8a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0],\n[0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1],\n[1, 1, 1, 1],\n[1, 1, 1, 1],\n[1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 3, 6, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 5, 3, 4, 3, 3, 3, 1, 3, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 4, 3, 7, 3, 4, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7],\n[5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7],\n[5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7],\n[5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7],\n[3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 5, 5, 5],\n[5, 3, 5, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], "output": [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 3, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 3, 6, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 5, 3, 4, 3, 3, 3, 1, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 4, 3, 7, 3, 4, 3, 3]], "output": [[1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7], [5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7], [5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7], [5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 1, 1, 1, 1, 7, 7, 7, 7], [3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3], [3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3], [3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3], [3, 3, 3, 3, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 3, 3, 3, 3]]}], "input_grid": [[5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5], [5, 3, 5, 7]], "task_key": "46f33fce"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 9, 0, 5, 0, 7, 2, 9, 5, 7],\n[1, 5, 7, 0, 2, 0, 2, 5, 0, 1],\n[1, 9, 5, 1, 1, 1, 2, 3, 7, 6],\n[1, 0, 1, 3, 9, 7, 2, 0, 2, 2],\n[9, 2, 1, 2, 7, 2, 3, 1, 0, 2],\n[5, 5, 7, 0, 0, 7, 3, 6, 6, 3],\n[7, 2, 3, 0, 5, 1, 5, 5, 0, 0],\n[5, 6, 7, 5, 7, 9, 5, 2, 9, 0],\n[5, 2, 3, 1, 0, 0, 0, 2, 2, 3],\n[0, 5, 5, 5, 7, 5, 5, 2, 2, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 9, 0, 5, 0, 7, 2, 9, 5, 7, 0],\n[0, 0, 9, 0, 5, 0, 7, 2, 9, 5, 7, 7],\n[1, 1, 5, 7, 0, 2, 0, 2, 5, 0, 1, 1],\n[1, 1, 9, 5, 1, 1, 1, 2, 3, 7, 6, 6],\n[1, 1, 0, 1, 3, 9, 7, 2, 0, 2, 2, 2],\n[9, 9, 2, 1, 2, 7, 2, 3, 1, 0, 2, 2],\n[5, 5, 5, 7, 0, 0, 7, 3, 6, 6, 3, 3],\n[7, 7, 2, 3, 0, 5, 1, 5, 5, 0, 0, 0],\n[5, 5, 6, 7, 5, 7, 9, 5, 2, 9, 0, 0],\n[5, 5, 2, 3, 1, 0, 0, 0, 2, 2, 3, 3],\n[0, 0, 5, 5, 5, 7, 5, 5, 2, 2, 6, 6],\n[0, 0, 5, 5, 5, 7, 5, 5, 2, 2, 6, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 7, 0, 0, 2, 2, 2, 0, 2, 7, 7, 7],\n[7, 0, 2, 7, 7, 7, 0, 7, 7, 7, 2, 7],\n[2, 7, 0, 7, 2, 7, 7, 7, 0, 7, 0, 2],\n[0, 2, 0, 7, 2, 2, 0, 7, 7, 7, 7, 0],\n[2, 2, 0, 0, 2, 7, 7, 0, 2, 7, 0, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 2, 7, 0, 0, 2, 2, 2, 0, 2, 7, 7, 7, 0],\n[2, 2, 7, 0, 0, 2, 2, 2, 0, 2, 7, 7, 7, 7],\n[7, 7, 0, 2, 7, 7, 7, 0, 7, 7, 7, 2, 7, 7],\n[2, 2, 7, 0, 7, 2, 7, 7, 7, 0, 7, 0, 2, 2],\n[0, 0, 2, 0, 7, 2, 2, 0, 7, 7, 7, 7, 0, 0],\n[2, 2, 2, 0, 0, 2, 7, 7, 0, 2, 7, 0, 2, 2],\n[0, 2, 2, 0, 0, 2, 7, 7, 0, 2, 7, 0, 2, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 0, 0, 7],\n[7, 7, 0, 0],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 0, 0, 0],\n[7, 0, 7, 0],\n[7, 7, 0, 0],\n[7, 7, 0, 0],\n[0, 0, 0, 7],\n[0, 0, 0, 0],\n[7, 0, 0, 0],\n[7, 7, 7, 0],\n[7, 0, 0, 0],\n[0, 0, 7, 7],\n[0, 7, 7, 7],\n[0, 0, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 7, 0, 0, 7, 0],\n[7, 7, 0, 0, 7, 7],\n[7, 7, 7, 0, 0, 0],\n[7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7],\n[7, 7, 0, 0, 0, 0],\n[7, 7, 0, 7, 0, 0],\n[7, 7, 7, 0, 0, 0],\n[7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 7, 7],\n[0, 0, 0, 0, 0, 0],\n[7, 7, 0, 0, 0, 0],\n[7, 7, 7, 7, 0, 0],\n[7, 7, 0, 0, 0, 0],\n[0, 0, 0, 7, 7, 7],\n[0, 0, 7, 7, 7, 7],\n[0, 0, 0, 7, 7, 7],\n[0, 0, 0, 7, 7, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 2, 1, 1, 6, 1, 1, 6, 5, 6, 6, 6, 1, 1, 2, 6, 6],\n[1, 5, 5, 6, 5, 1, 1, 1, 2, 2, 2, 6, 1, 1, 5, 1, 2],\n[2, 6, 1, 1, 5, 2, 6, 1, 6, 6, 2, 2, 1, 2, 2, 2, 5],\n[1, 5, 1, 1, 2, 5, 6, 6, 2, 6, 1, 1, 5, 6, 6, 5, 1],\n[6, 2, 6, 2, 5, 2, 6, 6, 1, 6, 5, 1, 6, 1, 5, 6, 2],\n[6, 6, 2, 5, 2, 6, 2, 6, 5, 6, 2, 1, 2, 1, 2, 5, 1],\n[6, 2, 5, 1, 5, 2, 2, 1, 5, 5, 5, 5, 6, 5, 2, 1, 1],\n[6, 2, 2, 2, 2, 2, 5, 6, 1, 5, 1, 1, 2, 5, 2, 6, 5],\n[5, 2, 2, 5, 2, 1, 5, 1, 6, 2, 5, 5, 5, 5, 1, 2, 1],\n[2, 2, 2, 5, 6, 2, 2, 2, 2, 1, 5, 1, 2, 1, 1, 1, 5],\n[5, 2, 2, 2, 5, 1, 2, 6, 6, 6, 5, 2, 2, 1, 5, 1, 6],\n[1, 1, 1, 6, 1, 1, 5, 6, 6, 6, 5, 6, 6, 1, 6, 5, 1],\n[5, 6, 6, 2, 1, 1, 2, 5, 6, 1, 1, 2, 6, 2, 2, 2, 6],\n[1, 1, 5, 6, 6, 5, 5, 1, 1, 5, 6, 5, 1, 2, 1, 2, 6],\n[2, 1, 6, 2, 6, 5, 1, 2, 2, 5, 2, 6, 1, 6, 2, 2, 5],\n[5, 2, 5, 5, 1, 1, 6, 2, 2, 5, 2, 6, 2, 1, 6, 1, 1],\n[1, 5, 5, 6, 5, 1, 2, 6, 6, 6, 1, 1, 5, 5, 2, 2, 6],\n[6, 1, 6, 2, 5, 2, 1, 1, 1, 5, 5, 6, 2, 5, 2, 5, 5],\n[1, 2, 1, 6, 5, 2, 1, 5, 1, 6, 2, 6, 5, 1, 6, 5, 2],\n[2, 6, 6, 5, 1, 5, 2, 5, 6, 2, 2, 1, 5, 2, 1, 5, 5],\n[5, 1, 2, 1, 1, 5, 6, 2, 6, 2, 6, 5, 5, 1, 2, 1, 2],\n[1, 2, 5, 6, 6, 6, 1, 5, 1, 1, 5, 6, 1, 2, 1, 5, 1],\n[5, 2, 1, 5, 6, 5, 1, 5, 1, 1, 5, 6, 5, 2, 5, 6, 6],\n[5, 5, 5, 2, 5, 5, 5, 1, 2, 6, 6, 5, 1, 2, 1, 1, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 9, 0, 5, 0, 7, 2, 9, 5, 7], [1, 5, 7, 0, 2, 0, 2, 5, 0, 1], [1, 9, 5, 1, 1, 1, 2, 3, 7, 6], [1, 0, 1, 3, 9, 7, 2, 0, 2, 2], [9, 2, 1, 2, 7, 2, 3, 1, 0, 2], [5, 5, 7, 0, 0, 7, 3, 6, 6, 3], [7, 2, 3, 0, 5, 1, 5, 5, 0, 0], [5, 6, 7, 5, 7, 9, 5, 2, 9, 0], [5, 2, 3, 1, 0, 0, 0, 2, 2, 3], [0, 5, 5, 5, 7, 5, 5, 2, 2, 6]], "output": [[0, 0, 9, 0, 5, 0, 7, 2, 9, 5, 7, 0], [0, 0, 9, 0, 5, 0, 7, 2, 9, 5, 7, 7], [1, 1, 5, 7, 0, 2, 0, 2, 5, 0, 1, 1], [1, 1, 9, 5, 1, 1, 1, 2, 3, 7, 6, 6], [1, 1, 0, 1, 3, 9, 7, 2, 0, 2, 2, 2], [9, 9, 2, 1, 2, 7, 2, 3, 1, 0, 2, 2], [5, 5, 5, 7, 0, 0, 7, 3, 6, 6, 3, 3], [7, 7, 2, 3, 0, 5, 1, 5, 5, 0, 0, 0], [5, 5, 6, 7, 5, 7, 9, 5, 2, 9, 0, 0], [5, 5, 2, 3, 1, 0, 0, 0, 2, 2, 3, 3], [0, 0, 5, 5, 5, 7, 5, 5, 2, 2, 6, 6], [0, 0, 5, 5, 5, 7, 5, 5, 2, 2, 6, 0]]}, {"input": [[2, 7, 0, 0, 2, 2, 2, 0, 2, 7, 7, 7], [7, 0, 2, 7, 7, 7, 0, 7, 7, 7, 2, 7], [2, 7, 0, 7, 2, 7, 7, 7, 0, 7, 0, 2], [0, 2, 0, 7, 2, 2, 0, 7, 7, 7, 7, 0], [2, 2, 0, 0, 2, 7, 7, 0, 2, 7, 0, 2]], "output": [[0, 2, 7, 0, 0, 2, 2, 2, 0, 2, 7, 7, 7, 0], [2, 2, 7, 0, 0, 2, 2, 2, 0, 2, 7, 7, 7, 7], [7, 7, 0, 2, 7, 7, 7, 0, 7, 7, 7, 2, 7, 7], [2, 2, 7, 0, 7, 2, 7, 7, 7, 0, 7, 0, 2, 2], [0, 0, 2, 0, 7, 2, 2, 0, 7, 7, 7, 7, 0, 0], [2, 2, 2, 0, 0, 2, 7, 7, 0, 2, 7, 0, 2, 2], [0, 2, 2, 0, 0, 2, 7, 7, 0, 2, 7, 0, 2, 0]]}, {"input": [[7, 0, 0, 7], [7, 7, 0, 0], [7, 7, 7, 7], [7, 7, 7, 7], [7, 0, 0, 0], [7, 0, 7, 0], [7, 7, 0, 0], [7, 7, 0, 0], [0, 0, 0, 7], [0, 0, 0, 0], [7, 0, 0, 0], [7, 7, 7, 0], [7, 0, 0, 0], [0, 0, 7, 7], [0, 7, 7, 7], [0, 0, 7, 7]], "output": [[0, 7, 0, 0, 7, 0], [7, 7, 0, 0, 7, 7], [7, 7, 7, 0, 0, 0], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [7, 7, 0, 0, 0, 0], [7, 7, 0, 7, 0, 0], [7, 7, 7, 0, 0, 0], [7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 7, 7], [0, 0, 0, 0, 0, 0], [7, 7, 0, 0, 0, 0], [7, 7, 7, 7, 0, 0], [7, 7, 0, 0, 0, 0], [0, 0, 0, 7, 7, 7], [0, 0, 7, 7, 7, 7], [0, 0, 0, 7, 7, 7], [0, 0, 0, 7, 7, 0]]}], "input_grid": [[1, 2, 1, 1, 6, 1, 1, 6, 5, 6, 6, 6, 1, 1, 2, 6, 6], [1, 5, 5, 6, 5, 1, 1, 1, 2, 2, 2, 6, 1, 1, 5, 1, 2], [2, 6, 1, 1, 5, 2, 6, 1, 6, 6, 2, 2, 1, 2, 2, 2, 5], [1, 5, 1, 1, 2, 5, 6, 6, 2, 6, 1, 1, 5, 6, 6, 5, 1], [6, 2, 6, 2, 5, 2, 6, 6, 1, 6, 5, 1, 6, 1, 5, 6, 2], [6, 6, 2, 5, 2, 6, 2, 6, 5, 6, 2, 1, 2, 1, 2, 5, 1], [6, 2, 5, 1, 5, 2, 2, 1, 5, 5, 5, 5, 6, 5, 2, 1, 1], [6, 2, 2, 2, 2, 2, 5, 6, 1, 5, 1, 1, 2, 5, 2, 6, 5], [5, 2, 2, 5, 2, 1, 5, 1, 6, 2, 5, 5, 5, 5, 1, 2, 1], [2, 2, 2, 5, 6, 2, 2, 2, 2, 1, 5, 1, 2, 1, 1, 1, 5], [5, 2, 2, 2, 5, 1, 2, 6, 6, 6, 5, 2, 2, 1, 5, 1, 6], [1, 1, 1, 6, 1, 1, 5, 6, 6, 6, 5, 6, 6, 1, 6, 5, 1], [5, 6, 6, 2, 1, 1, 2, 5, 6, 1, 1, 2, 6, 2, 2, 2, 6], [1, 1, 5, 6, 6, 5, 5, 1, 1, 5, 6, 5, 1, 2, 1, 2, 6], [2, 1, 6, 2, 6, 5, 1, 2, 2, 5, 2, 6, 1, 6, 2, 2, 5], [5, 2, 5, 5, 1, 1, 6, 2, 2, 5, 2, 6, 2, 1, 6, 1, 1], [1, 5, 5, 6, 5, 1, 2, 6, 6, 6, 1, 1, 5, 5, 2, 2, 6], [6, 1, 6, 2, 5, 2, 1, 1, 1, 5, 5, 6, 2, 5, 2, 5, 5], [1, 2, 1, 6, 5, 2, 1, 5, 1, 6, 2, 6, 5, 1, 6, 5, 2], [2, 6, 6, 5, 1, 5, 2, 5, 6, 2, 2, 1, 5, 2, 1, 5, 5], [5, 1, 2, 1, 1, 5, 6, 2, 6, 2, 6, 5, 5, 1, 2, 1, 2], [1, 2, 5, 6, 6, 6, 1, 5, 1, 1, 5, 6, 1, 2, 1, 5, 1], [5, 2, 1, 5, 6, 5, 1, 5, 1, 1, 5, 6, 5, 2, 5, 6, 6], [5, 5, 5, 2, 5, 5, 5, 1, 2, 6, 6, 5, 1, 2, 1, 1, 2]], "task_key": "49d1d64f"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[7, 8, 8, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 8, 8, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 8, 8, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 8, 8, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[8, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[8, 8, 3, 1, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[3, 3, 3, 1, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7],\n[1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[1, 1, 1, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[1, 1, 1, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[1, 1, 1, 3, 3, 3, 3, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7],\n[1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8],\n[8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8],\n[8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 1, 8, 8, 8, 8],\n[8, 3, 7, 7, 3, 3, 3, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8],\n[8, 3, 7, 7, 3, 7, 7, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8],\n[8, 3, 3, 3, 3, 7, 7, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 3, 3, 3, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 3, 3, 3, 3, 3, 3, 3, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 3, 7, 7, 3, 7, 7, 3, 8, 8, 1, 1, 3, 3, 3, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 3, 7, 7, 3, 7, 7, 3, 8, 8, 1, 1, 3, 7, 7, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 3, 3, 3, 3, 3, 3, 3, 8, 8, 1, 1, 3, 7, 7, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 3, 3, 3, 3, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2],\n[8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2],\n[8, 8, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3],\n[8, 8, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3],\n[3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3],\n[3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 2, 3, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 2, 3, 3, 3, 3],\n[3, 3, 8, 8, 8, 8, 3, 3, 1, 2, 2, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 3, 3, 1, 2, 2, 2, 1, 1, 2],\n[3, 3, 8, 8, 8, 8, 3, 3, 1, 3, 3, 3, 3, 1, 2],\n[3, 3, 8, 8, 8, 8, 3, 3, 1, 3, 8, 8, 3, 1, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 8, 8, 3, 1, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 1, 2],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 9, 9, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 6],\n[6, 6, 9, 9, 6, 9, 9, 6, 9, 9, 6, 6, 6, 6, 6, 9, 9, 6, 6, 9, 9, 6, 9, 9, 6, 6, 6],\n[6, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 9, 9, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 9, 9, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 9, 9, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[7, 8, 8, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 8, 8, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[3, 8, 8, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 8, 8, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [8, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [8, 8, 3, 1, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [3, 3, 3, 1, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 7], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [1, 1, 1, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [1, 1, 1, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [1, 1, 1, 3, 3, 3, 3, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8], [8, 8, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8], [8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8], [8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 1, 8, 8, 8, 8], [8, 3, 7, 7, 3, 3, 3, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8], [8, 3, 7, 7, 3, 7, 7, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8], [8, 3, 3, 3, 3, 7, 7, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 3, 3, 3, 3, 1, 1, 8, 8, 8, 8, 3, 3, 7, 7, 7, 7, 3, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 3, 3, 3, 3, 3, 3, 3, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 3, 7, 7, 3, 7, 7, 3, 8, 8, 1, 1, 3, 3, 3, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 3, 7, 7, 3, 7, 7, 3, 8, 8, 1, 1, 3, 7, 7, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 3, 3, 3, 3, 3, 3, 3, 8, 8, 1, 1, 3, 7, 7, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 3, 3, 3, 3, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 8, 1, 1, 1, 1, 1, 8, 1, 1, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2], [8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2], [8, 8, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3], [8, 8, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3], [3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3], [3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3], [3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 2, 3, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 2, 3, 3, 3, 3], [3, 3, 8, 8, 8, 8, 3, 3, 1, 2, 2, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 3, 3, 1, 2, 2, 2, 1, 1, 2], [3, 3, 8, 8, 8, 8, 3, 3, 1, 3, 3, 3, 3, 1, 2], [3, 3, 8, 8, 8, 8, 3, 3, 1, 3, 8, 8, 3, 1, 2], [3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 8, 8, 3, 1, 2], [3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2]]}], "input_grid": [[6, 6, 6, 6, 6, 9, 9, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 6], [6, 6, 9, 9, 6, 9, 9, 6, 9, 9, 6, 6, 6, 6, 6, 9, 9, 6, 6, 9, 9, 6, 9, 9, 6, 6, 6], [6, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 9, 9, 6, 6, 6], [6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 9, 9, 6, 6, 6], [6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6], [6, 9, 9, 6, 6, 6, 9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "db93a21d"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 8, 3, 8, 3, 3, 8, 3, 3, 3],\n[3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 8, 3, 3, 3],\n[8, 3, 3, 3, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 4, 3, 3, 4, 4, 3, 4, 3],\n[3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3],\n[4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3],\n[4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3],\n[3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 8, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 8, 3, 8, 3, 3, 3, 8, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 2, 2, 2, 3, 8, 3, 3, 8, 3, 8, 3, 3, 8, 3, 3, 3],\n[3, 3, 8, 3, 3, 3, 8, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 8, 3, 3, 8, 3, 3, 3],\n[8, 3, 3, 3, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 4],\n[3, 2, 2, 2, 3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 2, 2, 3],\n[3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3],\n[8, 3, 3, 3, 8, 3, 3, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 2, 3],\n[3, 3, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 2, 2, 3, 4, 3, 3, 4],\n[3, 3, 3, 3, 3, 2, 3, 3, 8, 3, 8, 4, 3, 3, 4, 4, 3, 4, 3],\n[3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 8, 3, 3, 3, 8, 3, 2, 3, 3],\n[4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3],\n[3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 4, 3, 4, 3],\n[3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3],\n[4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3],\n[4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3],\n[3, 2, 2, 3, 4, 3, 4, 3, 2, 2, 2, 3, 3, 3, 8, 3, 8, 3, 3],\n[3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3],\n[3, 2, 2, 3, 4, 3, 4, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3],\n[4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3],\n[8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3],\n[3, 2, 2, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3],\n[8, 3, 3, 8, 3, 3, 2, 2, 2, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3],\n[3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3],\n[8, 3, 8, 3, 3, 2, 2, 2, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3],\n[3, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3],\n[8, 3, 8, 3, 8, 3, 3, 3, 8, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 0, 5, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 1, 0, 0, 1, 0],\n[7, 0, 7, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0],\n[7, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 8, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 6, 0, 0, 6, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0],\n[9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[9, 0, 0, 9, 0, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 0, 5, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 2, 2, 0, 5, 0, 0, 0, 5, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 1, 0, 0, 1, 0],\n[7, 0, 7, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0],\n[0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0],\n[7, 0, 7, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 8, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0],\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 6, 0, 0, 6, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0],\n[9, 0, 0, 9, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[9, 0, 0, 9, 0, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[3, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 3, 6, 6, 6, 3, 6, 3],\n[3, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 3],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 8, 3, 8, 3, 3, 8, 3, 3, 3], [3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 8, 3, 3, 3], [8, 3, 3, 3, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 4], [3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4], [3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 4, 3, 3, 4, 4, 3, 4, 3], [3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3], [4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3], [4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3], [8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3], [3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 3, 8, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 3, 8, 3, 8, 3, 3, 3, 8, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 2, 2, 2, 3, 8, 3, 3, 8, 3, 8, 3, 3, 8, 3, 3, 3], [3, 3, 8, 3, 3, 3, 8, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 8, 3, 3, 8, 3, 3, 3], [8, 3, 3, 3, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 4], [3, 2, 2, 2, 3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 2, 2, 3], [3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3], [8, 3, 3, 3, 8, 3, 3, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 2, 3], [3, 3, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 2, 2, 3, 4, 3, 3, 4], [3, 3, 3, 3, 3, 2, 3, 3, 8, 3, 8, 4, 3, 3, 4, 4, 3, 4, 3], [3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 8, 3, 3, 3, 8, 3, 2, 3, 3], [4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3], [3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 4, 3, 4, 3], [3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3], [4, 3, 3, 4, 8, 3, 3, 8, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3], [4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3], [3, 2, 2, 3, 4, 3, 4, 3, 2, 2, 2, 3, 3, 3, 8, 3, 8, 3, 3], [3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3], [3, 2, 2, 3, 4, 3, 4, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3], [4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3], [8, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3], [3, 2, 2, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 3, 3], [3, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3], [8, 3, 3, 8, 3, 3, 2, 2, 2, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3], [3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3], [8, 3, 8, 3, 3, 2, 2, 2, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3], [3, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3], [8, 3, 8, 3, 8, 3, 3, 3, 8, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 5, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 0, 5, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 1, 0, 0, 1, 0], [7, 0, 7, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [7, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 8, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 6, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0], [9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 9, 0, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 0, 5, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 5, 0, 0, 0, 5, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 1, 0, 0, 1, 0], [7, 0, 7, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0], [0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [7, 0, 7, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 8, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8], [0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 6, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0], [9, 0, 0, 9, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 9, 0, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [3, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 3, 6, 6, 6, 3, 6, 3], [3, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 3], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "af902bf9"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 4, 4, 4, 4, 4],\n[6, 6, 6, 6, 4, 4],\n[6, 6, 6, 4, 4, 6],\n[4, 6, 6, 6, 4, 6],\n[4, 6, 6, 4, 4, 6],\n[6, 4, 6, 6, 4, 6],\n[4, 4, 6, 6, 4, 6],\n[6, 6, 6, 6, 4, 4],\n[6, 6, 6, 6, 4, 6],\n[6, 6, 4, 6, 4, 6],\n[6, 6, 6, 4, 4, 6],\n[4, 6, 4, 6, 4, 6],\n[6, 6, 6, 6, 4, 6],\n[6, 6, 6, 6, 4, 6],\n[4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 4, 4, 4, 2, 4],\n[6, 6, 6, 6, 2, 4],\n[6, 6, 6, 4, 2, 6],\n[4, 6, 6, 6, 2, 6],\n[4, 6, 6, 4, 2, 6],\n[6, 4, 6, 6, 2, 6],\n[4, 4, 6, 6, 2, 6],\n[6, 6, 6, 6, 2, 4],\n[6, 6, 6, 6, 2, 6],\n[6, 6, 4, 6, 2, 6],\n[6, 6, 6, 4, 2, 6],\n[4, 6, 4, 6, 2, 6],\n[6, 6, 6, 6, 2, 6],\n[6, 6, 6, 6, 2, 6],\n[2, 2, 2, 2, 2, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 1, 4, 4, 4, 4, 1, 1, 4, 1, 1, 1, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[1, 1, 1, 4, 4, 1, 1, 1, 4, 1, 4, 1, 1, 1, 4],\n[4, 4, 1, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4],\n[4, 1, 4, 1, 4, 1, 1, 1, 4, 1, 4, 4, 1, 1, 4],\n[1, 1, 1, 1, 4, 1, 1, 1, 1, 4, 4, 1, 1, 1, 4],\n[1, 1, 1, 1, 4, 1, 1, 1, 4, 4, 1, 4, 1, 1, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 1, 4, 2, 4, 4, 1, 1, 4, 1, 1, 1, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[1, 1, 1, 4, 2, 1, 1, 1, 4, 1, 4, 1, 1, 1, 2],\n[4, 4, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2],\n[4, 1, 4, 1, 2, 1, 1, 1, 4, 1, 4, 4, 1, 1, 2],\n[1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 2],\n[1, 1, 1, 1, 2, 1, 1, 1, 4, 4, 1, 4, 1, 1, 2]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 4, 6, 4, 6, 6, 4, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 6, 4, 6, 4, 6, 4],\n[6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 6],\n[6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 6, 6, 4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4],\n[4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4],\n[6, 4, 6, 4, 4, 4, 6, 4, 6, 6, 6, 4, 4, 4, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 4, 4, 6, 4, 6, 6, 4, 4, 4, 4, 6, 4, 4, 4, 6, 6, 6, 6, 4, 4],\n[4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 6, 4, 6, 4, 4, 4],\n[4, 6, 6, 4, 4, 4, 6, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4],\n[6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 6, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4],\n[4, 6, 4, 6, 4, 6, 6, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 6, 4, 4, 4],\n[4, 4, 6, 4, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4, 4, 6, 4, 6, 4, 4, 4],\n[4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 2, 4, 6, 4, 4, 6, 4, 4, 2, 4, 4, 4, 6, 4, 2, 6, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 6, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 6, 4, 2, 4, 4, 4, 6, 4, 2, 4, 6, 4],\n[6, 4, 4, 4, 4, 4, 2, 6, 4, 4, 6, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 6, 6],\n[6, 4, 4, 4, 4, 6, 2, 4, 4, 4, 4, 4, 6, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 6, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 6, 4],\n[4, 4, 6, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 6, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4],\n[6, 4, 6, 4, 4, 4, 2, 4, 6, 6, 6, 4, 4, 4, 2, 4, 4, 4, 4, 6, 2, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 4, 2, 4, 6, 6, 4, 4, 4, 4, 2, 4, 4, 4, 6, 6, 2, 6, 4, 4],\n[4, 4, 4, 4, 4, 4, 2, 4, 6, 4, 4, 4, 4, 4, 2, 4, 4, 4, 6, 4, 2, 4, 4, 4],\n[4, 6, 6, 4, 4, 4, 2, 4, 4, 6, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 6, 4],\n[6, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 6, 4, 6, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4],\n[4, 6, 4, 6, 4, 6, 2, 4, 4, 6, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 4, 4, 2, 4, 4, 4],\n[4, 4, 6, 4, 4, 6, 2, 4, 4, 4, 4, 4, 4, 6, 2, 6, 4, 4, 6, 4, 2, 4, 4, 4],\n[4, 4, 4, 4, 6, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 9, 9, 1, 9],\n[1, 1, 1, 1, 1],\n[9, 1, 9, 1, 9],\n[9, 9, 9, 1, 9],\n[1, 9, 1, 1, 1],\n[1, 1, 1, 1, 1],\n[9, 9, 9, 1, 9],\n[9, 1, 9, 1, 9],\n[9, 9, 1, 1, 9],\n[9, 1, 9, 1, 9],\n[9, 9, 9, 1, 9],\n[9, 9, 9, 1, 9],\n[9, 9, 9, 1, 9],\n[9, 9, 9, 1, 9],\n[9, 1, 9, 1, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 4, 4, 4, 4, 4], [6, 6, 6, 6, 4, 4], [6, 6, 6, 4, 4, 6], [4, 6, 6, 6, 4, 6], [4, 6, 6, 4, 4, 6], [6, 4, 6, 6, 4, 6], [4, 4, 6, 6, 4, 6], [6, 6, 6, 6, 4, 4], [6, 6, 6, 6, 4, 6], [6, 6, 4, 6, 4, 6], [6, 6, 6, 4, 4, 6], [4, 6, 4, 6, 4, 6], [6, 6, 6, 6, 4, 6], [6, 6, 6, 6, 4, 6], [4, 4, 4, 4, 4, 4]], "output": [[6, 4, 4, 4, 2, 4], [6, 6, 6, 6, 2, 4], [6, 6, 6, 4, 2, 6], [4, 6, 6, 6, 2, 6], [4, 6, 6, 4, 2, 6], [6, 4, 6, 6, 2, 6], [4, 4, 6, 6, 2, 6], [6, 6, 6, 6, 2, 4], [6, 6, 6, 6, 2, 6], [6, 6, 4, 6, 2, 6], [6, 6, 6, 4, 2, 6], [4, 6, 4, 6, 2, 6], [6, 6, 6, 6, 2, 6], [6, 6, 6, 6, 2, 6], [2, 2, 2, 2, 2, 2]]}, {"input": [[4, 4, 1, 4, 4, 4, 4, 1, 1, 4, 1, 1, 1, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [1, 1, 1, 4, 4, 1, 1, 1, 4, 1, 4, 1, 1, 1, 4], [4, 4, 1, 1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4], [4, 1, 4, 1, 4, 1, 1, 1, 4, 1, 4, 4, 1, 1, 4], [1, 1, 1, 1, 4, 1, 1, 1, 1, 4, 4, 1, 1, 1, 4], [1, 1, 1, 1, 4, 1, 1, 1, 4, 4, 1, 4, 1, 1, 4]], "output": [[4, 4, 1, 4, 2, 4, 4, 1, 1, 4, 1, 1, 1, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 4, 2, 1, 1, 1, 4, 1, 4, 1, 1, 1, 2], [4, 4, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2], [4, 1, 4, 1, 2, 1, 1, 1, 4, 1, 4, 4, 1, 1, 2], [1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 4, 1, 1, 1, 2], [1, 1, 1, 1, 2, 1, 1, 1, 4, 4, 1, 4, 1, 1, 2]]}, {"input": [[4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 4, 6, 4, 6, 6, 4, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 6, 4, 6, 4, 6, 4], [6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 6], [6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4], [4, 4, 4, 4, 4, 4, 6, 6, 4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4], [4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4], [6, 4, 6, 4, 4, 4, 6, 4, 6, 6, 6, 4, 4, 4, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 4, 4, 6, 4, 6, 6, 4, 4, 4, 4, 6, 4, 4, 4, 6, 6, 6, 6, 4, 4], [4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 6, 4, 6, 4, 4, 4], [4, 6, 6, 4, 4, 4, 6, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 6, 4], [6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 6, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4], [4, 6, 4, 6, 4, 6, 6, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4], [4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 6, 4, 4, 4], [4, 4, 6, 4, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4, 4, 6, 4, 6, 4, 4, 4], [4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 2, 4, 6, 4, 4, 6, 4, 4, 2, 4, 4, 4, 6, 4, 2, 6, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 6, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 6, 4, 2, 4, 4, 4, 6, 4, 2, 4, 6, 4], [6, 4, 4, 4, 4, 4, 2, 6, 4, 4, 6, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 6, 6], [6, 4, 4, 4, 4, 6, 2, 4, 4, 4, 4, 4, 6, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 6, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 6, 4], [4, 4, 6, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 6, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4], [6, 4, 6, 4, 4, 4, 2, 4, 6, 6, 6, 4, 4, 4, 2, 4, 4, 4, 4, 6, 2, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 4, 2, 4, 6, 6, 4, 4, 4, 4, 2, 4, 4, 4, 6, 6, 2, 6, 4, 4], [4, 4, 4, 4, 4, 4, 2, 4, 6, 4, 4, 4, 4, 4, 2, 4, 4, 4, 6, 4, 2, 4, 4, 4], [4, 6, 6, 4, 4, 4, 2, 4, 4, 6, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 6, 4], [6, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 6, 4, 6, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4], [4, 6, 4, 6, 4, 6, 2, 4, 4, 6, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 6, 4, 4, 4, 4, 2, 4, 4, 4], [4, 4, 6, 4, 4, 6, 2, 4, 4, 4, 4, 4, 4, 6, 2, 6, 4, 4, 6, 4, 2, 4, 4, 4], [4, 4, 4, 4, 6, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4]]}], "input_grid": [[1, 9, 9, 1, 9], [1, 1, 1, 1, 1], [9, 1, 9, 1, 9], [9, 9, 9, 1, 9], [1, 9, 1, 1, 1], [1, 1, 1, 1, 1], [9, 9, 9, 1, 9], [9, 1, 9, 1, 9], [9, 9, 1, 1, 9], [9, 1, 9, 1, 9], [9, 9, 9, 1, 9], [9, 9, 9, 1, 9], [9, 9, 9, 1, 9], [9, 9, 9, 1, 9], [9, 1, 9, 1, 9]], "task_key": "c1d99e64"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 5, 6, 5, 6, 5, 6, 5, 6],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4, 5, 4, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 4, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[4, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 4, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 4, 5, 4],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[4, 5, 4, 5, 4, 5],\n[9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9],\n[9, 4, 5, 4, 5, 4],\n[9, 9, 9, 9, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 1, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 4, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 5, 6, 5, 6, 5, 6, 5, 6], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4, 5, 4, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 5, 4]]}, {"input": [[9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 4, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [4, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 4, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 9, 9, 4, 5, 4], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [4, 5, 4, 5, 4, 5], [9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9], [9, 4, 5, 4, 5, 4], [9, 9, 9, 9, 9, 9]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "97999447"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 5, 7, 7, 7, 5, 5, 5, 7, 7, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 5],\n[7, 5, 7, 5, 7, 7, 7, 5, 5, 7, 5, 7, 7, 5, 5, 7, 7, 7, 5, 5, 7, 7, 5],\n[5, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 5, 7, 7, 5, 7, 7, 7, 7, 5, 5, 7, 5],\n[5, 5, 5, 7, 7, 5, 7, 7, 5, 5, 5, 7, 7, 5, 5, 5, 7, 5, 7, 7, 7, 5, 5],\n[5, 7, 7, 5, 7, 7, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 5, 5, 7, 5, 5, 5, 7, 5, 5, 7, 5, 7, 7, 5, 5, 5, 5, 7, 7, 7],\n[5, 7, 7, 5, 7, 5, 7, 7, 5, 5, 7, 7, 7, 5, 7, 5, 5, 7, 7, 5, 5, 5, 7],\n[5, 7, 7, 7, 5, 7, 5, 5, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 5, 7, 5, 7, 5],\n[5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 5, 7, 7, 5, 7, 5, 5, 7, 7, 5, 5, 5, 7],\n[5, 7, 5, 5, 5, 7, 7, 5, 5, 7, 5, 7, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 5],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9],\n[7, 9, 9, 9, 7, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9],\n[7, 9, 7, 9, 9, 7, 7, 9, 7, 9, 9, 7, 9, 9, 7, 9, 7, 9, 9, 7, 9, 9, 9],\n[9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7],\n[9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 7, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 9, 9, 9, 9, 9, 7, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 7, 3, 3, 3, 7, 3, 7, 3, 3, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 3, 7, 7, 3, 3, 3, 7, 3, 7, 3, 3, 7, 7, 3, 3, 3, 7, 7, 7, 3, 7],\n[3, 7, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 7, 3, 7],\n[7, 7, 3, 3, 3, 7, 3, 3, 7, 7, 7, 3, 3, 7, 7, 7, 3, 7, 3, 3, 3, 7, 7],\n[7, 3, 3, 7, 3, 3, 7, 7, 7, 3, 7, 7, 7, 3, 3, 7, 7, 3, 3, 7, 3, 7, 7],\n[3, 7, 3, 7, 7, 3, 7, 7, 7, 3, 7, 3, 3, 7, 3, 3, 7, 7, 7, 7, 3, 3, 3],\n[7, 3, 3, 7, 3, 7, 3, 3, 7, 7, 3, 3, 3, 3, 3, 7, 7, 3, 3, 3, 7, 7, 3],\n[7, 3, 3, 3, 7, 3, 7, 7, 3, 3, 3, 7, 7, 7, 7, 3, 3, 3, 7, 3, 3, 3, 7],\n[7, 7, 7, 7, 7, 3, 3, 7, 7, 3, 7, 3, 3, 7, 3, 7, 7, 3, 3, 3, 7, 7, 3],\n[7, 3, 7, 7, 7, 3, 3, 7, 7, 7, 7, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 6, 6, 6, 6, 8, 6, 6, 8, 6, 8, 6, 8],\n[8, 8, 8, 6, 6, 6, 8, 8, 8, 8, 6, 8, 8, 8],\n[8, 8, 8, 6, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[9, 6, 9, 9, 6, 6, 6, 6, 9, 6, 6, 9, 6, 6],\n[6, 6, 6, 6, 6, 9, 6, 9, 9, 6, 9, 9, 9, 6],\n[6, 6, 6, 6, 6, 6, 6, 9, 6, 9, 6, 6, 9, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 3, 3, 3, 6, 6, 3, 6, 3, 3, 6, 6, 6, 3],\n[3, 3, 3, 6, 6, 3, 3, 6, 6, 3, 3, 6, 6, 3],\n[3, 3, 3, 6, 3, 3, 3, 6, 6, 6, 3, 3, 6, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 8, 7, 7, 7, 7, 8, 8, 8, 7, 8],\n[8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 8, 7, 8, 8, 7, 7, 8, 8, 7, 7, 8, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 8, 3],\n[8, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 8, 3, 3, 8, 8, 3, 3, 8, 8, 3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 4, 4, 4],\n[4, 4, 4, 4],\n[8, 4, 8, 4],\n[8, 4, 4, 4],\n[4, 8, 4, 8],\n[4, 8, 8, 4],\n[4, 4, 4, 4],\n[4, 8, 4, 4],\n[4, 8, 4, 4],\n[4, 4, 8, 8],\n[4, 8, 4, 8],\n[4, 4, 4, 4],\n[9, 9, 9, 9],\n[8, 8, 8, 8],\n[8, 8, 8, 0],\n[8, 8, 8, 8],\n[8, 8, 8, 0],\n[8, 8, 0, 8],\n[8, 8, 8, 0],\n[8, 8, 0, 0],\n[0, 0, 8, 0],\n[8, 0, 0, 8],\n[8, 0, 8, 8],\n[0, 8, 8, 8],\n[8, 8, 0, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[7, 7, 7, 5, 7, 7, 7, 5, 5, 5, 7, 7, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 5], [7, 5, 7, 5, 7, 7, 7, 5, 5, 7, 5, 7, 7, 5, 5, 7, 7, 7, 5, 5, 7, 7, 5], [5, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 5, 7, 7, 5, 7, 7, 7, 7, 5, 5, 7, 5], [5, 5, 5, 7, 7, 5, 7, 7, 5, 5, 5, 7, 7, 5, 5, 5, 7, 5, 7, 7, 7, 5, 5], [5, 7, 7, 5, 7, 7, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7, 5, 7, 7, 7], [7, 7, 7, 5, 5, 7, 5, 5, 5, 7, 5, 5, 7, 5, 7, 7, 5, 5, 5, 5, 7, 7, 7], [5, 7, 7, 5, 7, 5, 7, 7, 5, 5, 7, 7, 7, 5, 7, 5, 5, 7, 7, 5, 5, 5, 7], [5, 7, 7, 7, 5, 7, 5, 5, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 5, 7, 5, 7, 5], [5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 5, 7, 7, 5, 7, 5, 5, 7, 7, 5, 5, 5, 7], [5, 7, 5, 5, 5, 7, 7, 5, 5, 7, 5, 7, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 5], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9], [7, 9, 9, 9, 7, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9], [7, 9, 7, 9, 9, 7, 7, 9, 7, 9, 9, 7, 9, 9, 7, 9, 7, 9, 9, 7, 9, 9, 9], [9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7], [9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 7, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 9, 9, 9, 9, 9, 7, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9]], "output": [[3, 3, 3, 7, 3, 3, 3, 7, 3, 7, 3, 3, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 3, 7, 7, 3, 3, 3, 7, 3, 7, 3, 3, 7, 7, 3, 3, 3, 7, 7, 7, 3, 7], [3, 7, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 7, 3, 7], [7, 7, 3, 3, 3, 7, 3, 3, 7, 7, 7, 3, 3, 7, 7, 7, 3, 7, 3, 3, 3, 7, 7], [7, 3, 3, 7, 3, 3, 7, 7, 7, 3, 7, 7, 7, 3, 3, 7, 7, 3, 3, 7, 3, 7, 7], [3, 7, 3, 7, 7, 3, 7, 7, 7, 3, 7, 3, 3, 7, 3, 3, 7, 7, 7, 7, 3, 3, 3], [7, 3, 3, 7, 3, 7, 3, 3, 7, 7, 3, 3, 3, 3, 3, 7, 7, 3, 3, 3, 7, 7, 3], [7, 3, 3, 3, 7, 3, 7, 7, 3, 3, 3, 7, 7, 7, 7, 3, 3, 3, 7, 3, 3, 3, 7], [7, 7, 7, 7, 7, 3, 3, 7, 7, 3, 7, 3, 3, 7, 3, 7, 7, 3, 3, 3, 7, 7, 3], [7, 3, 7, 7, 7, 3, 3, 7, 7, 7, 7, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 7]]}, {"input": [[8, 8, 6, 6, 6, 6, 8, 6, 6, 8, 6, 8, 6, 8], [8, 8, 8, 6, 6, 6, 8, 8, 8, 8, 6, 8, 8, 8], [8, 8, 8, 6, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [9, 6, 9, 9, 6, 6, 6, 6, 9, 6, 6, 9, 6, 6], [6, 6, 6, 6, 6, 9, 6, 9, 9, 6, 9, 9, 9, 6], [6, 6, 6, 6, 6, 6, 6, 9, 6, 9, 6, 6, 9, 6]], "output": [[6, 3, 3, 3, 6, 6, 3, 6, 3, 3, 6, 6, 6, 3], [3, 3, 3, 6, 6, 3, 3, 6, 6, 3, 3, 6, 6, 3], [3, 3, 3, 6, 3, 3, 3, 6, 6, 6, 3, 3, 6, 3]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 8, 7, 7, 7, 7, 8, 8, 8, 7, 8], [8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 8, 7, 8, 8, 7, 7, 8, 8, 7, 7, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 8, 3], [8, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 8, 3, 3, 8, 8, 3, 3, 8, 8, 3, 3]]}], "input_grid": [[8, 4, 4, 4], [4, 4, 4, 4], [8, 4, 8, 4], [8, 4, 4, 4], [4, 8, 4, 8], [4, 8, 8, 4], [4, 4, 4, 4], [4, 8, 4, 4], [4, 8, 4, 4], [4, 4, 8, 8], [4, 8, 4, 8], [4, 4, 4, 4], [9, 9, 9, 9], [8, 8, 8, 8], [8, 8, 8, 0], [8, 8, 8, 8], [8, 8, 8, 0], [8, 8, 0, 8], [8, 8, 8, 0], [8, 8, 0, 0], [0, 0, 8, 0], [8, 0, 0, 8], [8, 0, 8, 8], [0, 8, 8, 8], [8, 8, 0, 8]], "task_key": "99b1bc43"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 5, 5],\n[5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 5, 5],\n[5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 3, 7, 7, 7, 7, 7, 7, 3, 5],\n[5, 5, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 1, 1, 3, 5, 5, 5, 3, 7, 4, 4, 4, 7, 7, 3, 5],\n[5, 5, 3, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 3, 1, 1, 3, 5, 5, 5, 3, 7, 4, 4, 4, 7, 7, 3, 5],\n[5, 5, 3, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 3, 7, 7, 7, 7, 7, 7, 3, 5],\n[5, 5, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5],\n[5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 3, 7, 7, 7, 7, 7, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 1, 1, 1, 1, 3, 5, 5, 3, 7, 7, 7, 7, 7, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 1, 1, 1, 1, 3, 5, 5, 3, 7, 7, 7, 7, 7, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 1, 1, 1, 1, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 2, 2, 0, 0],\n[0, 9, 9, 9, 9, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 2, 2, 0, 0],\n[0, 9, 9, 9, 9, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0],\n[0, 9, 9, 9, 9, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0],\n[0, 0, 0, 0, 6, 6, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0],\n[0, 0, 0, 0, 6, 6, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 6, 6, 0, 0, 6, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 8, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 8, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0],\n[0, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 0],\n[3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 3, 0, 0, 0, 3, 8, 8, 8, 8, 3, 3, 2, 2, 3, 0],\n[3, 9, 9, 9, 9, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 3, 8, 8, 8, 8, 3, 3, 2, 2, 3, 0],\n[3, 9, 9, 9, 9, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 0],\n[3, 9, 9, 9, 9, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 3, 0],\n[3, 3, 3, 3, 3, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 3, 7, 7, 7, 7, 7, 7, 3, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0],\n[0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 3, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 2, 4, 4, 4, 2, 2, 3, 0, 0, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 2, 4, 4, 4, 2, 2, 3, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 2, 2, 2, 2, 2, 2, 3, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 3, 1, 1, 1, 1, 3, 0],\n[0, 0, 0, 3, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 1, 1, 1, 1, 3, 0],\n[0, 0, 0, 3, 6, 6, 6, 4, 4, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 1, 1, 3, 0],\n[0, 0, 0, 3, 6, 6, 6, 4, 4, 6, 3, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 3, 6, 6, 6, 4, 4, 6, 3, 0, 0, 0, 3, 7, 7, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 3, 6, 6, 6, 6, 6, 6, 3, 0, 0, 0, 3, 7, 7, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 3, 6, 6, 6, 6, 6, 6, 3, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2],\n[2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2, 1, 1, 2, 2, 2],\n[2, 2, 2, 2, 9, 9, 9, 9, 2, 2, 2, 2, 9, 9, 2, 2, 1, 1, 2, 2, 2],\n[2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 9, 9, 2, 2, 1, 1, 2, 2, 2],\n[2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2],\n[2, 3, 1, 1, 1, 3, 3, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3, 9, 9, 3, 2],\n[2, 3, 1, 1, 1, 3, 3, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3, 9, 9, 3, 2],\n[2, 3, 3, 3, 3, 3, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2],\n[2, 2, 2, 2, 2, 2, 3, 1, 1, 3, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 9, 9, 3, 3, 3, 3, 3, 2, 2],\n[2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 9, 9, 3, 3, 1, 1, 3, 2, 2],\n[2, 2, 2, 3, 9, 9, 9, 9, 3, 2, 2, 3, 9, 9, 3, 3, 1, 1, 3, 2, 2],\n[2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 3, 9, 9, 3, 3, 1, 1, 3, 2, 2],\n[2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2],\n[2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2],\n[2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 2, 3, 9, 9, 9, 3, 2, 2, 2, 2],\n[2, 2, 2, 3, 9, 9, 9, 9, 3, 2, 2, 2, 3, 9, 9, 9, 3, 2, 2, 2, 2],\n[2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 9, 9, 9, 3, 2, 2, 2, 2],\n[2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2],\n[2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 2, 8, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 2, 8, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 7, 7, 8, 8, 9, 9, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 7, 7, 8, 8, 9, 9, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 7, 7, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 7, 7, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 5, 5], [5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 5, 5], [5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 3, 7, 7, 7, 7, 7, 7, 3, 5], [5, 5, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 1, 1, 3, 5, 5, 5, 3, 7, 4, 4, 4, 7, 7, 3, 5], [5, 5, 3, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 3, 1, 1, 3, 5, 5, 5, 3, 7, 4, 4, 4, 7, 7, 3, 5], [5, 5, 3, 8, 8, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 3, 7, 7, 7, 7, 7, 7, 3, 5], [5, 5, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 3, 7, 7, 7, 7, 7, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 1, 1, 1, 1, 3, 5, 5, 3, 7, 7, 7, 7, 7, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 1, 1, 1, 1, 3, 5, 5, 3, 7, 7, 7, 7, 7, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 1, 1, 1, 1, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 2, 2, 0, 0], [0, 9, 9, 9, 9, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 2, 2, 0, 0], [0, 9, 9, 9, 9, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0], [0, 9, 9, 9, 9, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 6, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 6, 6, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 6, 6, 0, 0, 6, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 8, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 8, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0], [0, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 0], [3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 3, 0, 0, 0, 3, 8, 8, 8, 8, 3, 3, 2, 2, 3, 0], [3, 9, 9, 9, 9, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 3, 8, 8, 8, 8, 3, 3, 2, 2, 3, 0], [3, 9, 9, 9, 9, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 0], [3, 9, 9, 9, 9, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 3, 0], [3, 3, 3, 3, 3, 3, 3, 7, 4, 4, 4, 4, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 3, 7, 7, 7, 7, 7, 7, 3, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0], [0, 3, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 2, 4, 4, 4, 2, 2, 3, 0, 0, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 2, 4, 4, 4, 2, 2, 3, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 2, 2, 2, 2, 2, 2, 3, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 0, 0, 0, 3, 1, 1, 1, 1, 3, 0], [0, 0, 0, 3, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 1, 1, 1, 1, 3, 0], [0, 0, 0, 3, 6, 6, 6, 4, 4, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 1, 1, 1, 3, 0], [0, 0, 0, 3, 6, 6, 6, 4, 4, 6, 3, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 3, 6, 6, 6, 4, 4, 6, 3, 0, 0, 0, 3, 7, 7, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 6, 6, 6, 6, 6, 6, 3, 0, 0, 0, 3, 7, 7, 7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 6, 6, 6, 6, 6, 6, 3, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2], [2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2], [2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2, 1, 1, 2, 2, 2], [2, 2, 2, 2, 9, 9, 9, 9, 2, 2, 2, 2, 9, 9, 2, 2, 1, 1, 2, 2, 2], [2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 9, 9, 2, 2, 1, 1, 2, 2, 2], [2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 9, 2, 2, 9, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2], [2, 3, 1, 1, 1, 3, 3, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3, 9, 9, 3, 2], [2, 3, 1, 1, 1, 3, 3, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3, 9, 9, 3, 2], [2, 3, 3, 3, 3, 3, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2], [2, 2, 2, 2, 2, 2, 3, 1, 1, 3, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 9, 9, 3, 3, 3, 3, 3, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 9, 9, 3, 3, 1, 1, 3, 2, 2], [2, 2, 2, 3, 9, 9, 9, 9, 3, 2, 2, 3, 9, 9, 3, 3, 1, 1, 3, 2, 2], [2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 3, 9, 9, 3, 3, 1, 1, 3, 2, 2], [2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2], [2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2], [2, 2, 2, 3, 9, 4, 4, 9, 3, 2, 2, 2, 3, 9, 9, 9, 3, 2, 2, 2, 2], [2, 2, 2, 3, 9, 9, 9, 9, 3, 2, 2, 2, 3, 9, 9, 9, 3, 2, 2, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 9, 9, 9, 3, 2, 2, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2], [2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 1, 1, 1, 3, 2, 2, 3, 9, 9, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}], "input_grid": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 8, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 8, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 5, 8, 8, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 5, 5, 5, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 7, 8, 8, 9, 9, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 7, 8, 8, 9, 9, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 7, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 7, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "task_key": "543a7ed5"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 7],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 0, 0, 7, 0, 0, 7, 0],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[5, 1, 1, 1, 1, 0, 0, 7, 0, 0, 0, 0],\n[1, 1, 1, 1, 5, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 5, 0, 0, 7, 0, 0, 0, 0],\n[5, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 0, 7, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 7, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 5, 1, 1, 5, 0, 7, 7, 0, 0, 7, 7],\n[1, 1, 5, 1, 1, 7, 0, 0, 7, 7, 7, 7],\n[5, 1, 1, 5, 5, 0, 7, 0, 7, 7, 7, 7],\n[5, 5, 1, 5, 5, 0, 0, 7, 7, 7, 7, 0],\n[1, 5, 5, 1, 1, 7, 7, 7, 7, 7, 0, 7],\n[5, 5, 5, 5, 1, 7, 7, 7, 7, 7, 0, 7],\n[5, 5, 1, 5, 5, 7, 7, 7, 0, 0, 7, 7],\n[1, 5, 5, 5, 5, 7, 7, 0, 7, 7, 7, 7],\n[5, 1, 5, 5, 5, 7, 7, 0, 7, 7, 7, 0],\n[1, 5, 5, 5, 5, 0, 7, 7, 7, 7, 7, 0],\n[5, 5, 5, 5, 5, 7, 7, 7, 7, 0, 0, 7],\n[5, 5, 5, 5, 1, 7, 7, 7, 7, 7, 0, 0],\n[5, 5, 5, 1, 5, 7, 7, 7, 0, 7, 7, 0],\n[5, 1, 1, 5, 5, 7, 0, 7, 7, 0, 7, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 4, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 4, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 4, 1, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 4, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 4, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 3, 3, 3, 2, 1, 2, 2, 4, 4, 3, 4, 1, 1, 2, 1, 2],\n[4, 4, 3, 3, 2, 2, 1, 1, 4, 3, 4, 4, 1, 2, 1, 2, 2],\n[4, 4, 4, 3, 2, 2, 1, 1, 3, 4, 4, 4, 2, 1, 2, 2, 1],\n[3, 4, 4, 4, 2, 1, 1, 2, 4, 4, 4, 3, 1, 2, 2, 1, 2],\n[3, 3, 4, 4, 1, 1, 2, 1, 4, 4, 3, 4, 2, 1, 1, 2, 2],\n[3, 3, 3, 4, 1, 1, 1, 1, 4, 3, 4, 3, 2, 1, 1, 2, 2],\n[4, 3, 4, 4, 1, 1, 1, 1, 3, 4, 3, 4, 1, 2, 2, 1, 2],\n[4, 4, 4, 3, 1, 1, 1, 1, 4, 3, 3, 4, 1, 2, 2, 2, 1],\n[4, 4, 4, 4, 1, 1, 1, 1, 4, 3, 4, 3, 2, 1, 2, 2, 2],\n[4, 4, 4, 4, 1, 2, 1, 1, 4, 4, 3, 3, 2, 2, 1, 2, 2],\n[3, 4, 4, 4, 1, 1, 2, 2, 4, 4, 4, 3, 2, 2, 2, 1, 2],\n[4, 4, 4, 4, 1, 1, 2, 1, 3, 4, 4, 4, 3, 3, 3, 3, 4],\n[4, 4, 3, 4, 1, 1, 1, 2, 3, 3, 4, 4, 4, 3, 3, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 6, 6, 6, 9, 3, 0, 3, 0, 0, 0],\n[0, 0, 3, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 6, 6, 9, 6, 0, 0, 6, 9, 6, 9],\n[0, 0, 0, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6],\n[0, 0, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[3, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 9, 6, 9],\n[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3],\n[0, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0],\n[3, 0, 3, 9, 9, 9, 9, 9, 3, 3, 3, 3, 3, 0],\n[0, 3, 0, 9, 9, 6, 9, 9, 3, 3, 3, 0, 0, 3],\n[3, 0, 3, 6, 9, 9, 9, 9, 3, 3, 0, 3, 0, 3],\n[0, 3, 0, 9, 6, 9, 9, 9, 3, 3, 3, 0, 3, 0],\n[3, 0, 0, 6, 9, 9, 9, 9, 0, 3, 9, 9, 6, 9],\n[0, 3, 0, 9, 9, 9, 9, 9, 3, 0, 9, 9, 9, 6],\n[0, 0, 3, 9, 9, 9, 9, 6, 9, 9, 6, 9, 9, 9],\n[0, 3, 3, 9, 9, 6, 6, 9, 9, 9, 9, 6, 9, 9],\n[3, 3, 3, 3, 3, 0, 0, 3, 9, 9, 9, 9, 6, 9],\n[3, 3, 3, 0, 0, 3, 3, 0, 9, 9, 9, 9, 9, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 5, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 9, 0, 0, 0, 8, 8, 0, 9, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 9, 0, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 9, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 9, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 5, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 9, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 7], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 7, 0, 0, 7, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [5, 1, 1, 1, 1, 0, 0, 7, 0, 0, 0, 0], [1, 1, 1, 1, 5, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 5, 0, 0, 7, 0, 0, 0, 0], [5, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 7, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 7, 0, 0, 0, 0, 0, 0]], "output": [[1, 5, 1, 1, 5, 0, 7, 7, 0, 0, 7, 7], [1, 1, 5, 1, 1, 7, 0, 0, 7, 7, 7, 7], [5, 1, 1, 5, 5, 0, 7, 0, 7, 7, 7, 7], [5, 5, 1, 5, 5, 0, 0, 7, 7, 7, 7, 0], [1, 5, 5, 1, 1, 7, 7, 7, 7, 7, 0, 7], [5, 5, 5, 5, 1, 7, 7, 7, 7, 7, 0, 7], [5, 5, 1, 5, 5, 7, 7, 7, 0, 0, 7, 7], [1, 5, 5, 5, 5, 7, 7, 0, 7, 7, 7, 7], [5, 1, 5, 5, 5, 7, 7, 0, 7, 7, 7, 0], [1, 5, 5, 5, 5, 0, 7, 7, 7, 7, 7, 0], [5, 5, 5, 5, 5, 7, 7, 7, 7, 0, 0, 7], [5, 5, 5, 5, 1, 7, 7, 7, 7, 7, 0, 0], [5, 5, 5, 1, 5, 7, 7, 7, 0, 7, 7, 0], [5, 1, 1, 5, 5, 7, 0, 7, 7, 0, 7, 7]]}, {"input": [[4, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 4, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 4, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 4, 1, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 4, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2], [3, 3, 3, 3, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 4, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[4, 3, 3, 3, 2, 1, 2, 2, 4, 4, 3, 4, 1, 1, 2, 1, 2], [4, 4, 3, 3, 2, 2, 1, 1, 4, 3, 4, 4, 1, 2, 1, 2, 2], [4, 4, 4, 3, 2, 2, 1, 1, 3, 4, 4, 4, 2, 1, 2, 2, 1], [3, 4, 4, 4, 2, 1, 1, 2, 4, 4, 4, 3, 1, 2, 2, 1, 2], [3, 3, 4, 4, 1, 1, 2, 1, 4, 4, 3, 4, 2, 1, 1, 2, 2], [3, 3, 3, 4, 1, 1, 1, 1, 4, 3, 4, 3, 2, 1, 1, 2, 2], [4, 3, 4, 4, 1, 1, 1, 1, 3, 4, 3, 4, 1, 2, 2, 1, 2], [4, 4, 4, 3, 1, 1, 1, 1, 4, 3, 3, 4, 1, 2, 2, 2, 1], [4, 4, 4, 4, 1, 1, 1, 1, 4, 3, 4, 3, 2, 1, 2, 2, 2], [4, 4, 4, 4, 1, 2, 1, 1, 4, 4, 3, 3, 2, 2, 1, 2, 2], [3, 4, 4, 4, 1, 1, 2, 2, 4, 4, 4, 3, 2, 2, 2, 1, 2], [4, 4, 4, 4, 1, 1, 2, 1, 3, 4, 4, 4, 3, 3, 3, 3, 4], [4, 4, 3, 4, 1, 1, 1, 2, 3, 3, 4, 4, 4, 3, 3, 3, 3]]}, {"input": [[0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 9, 3, 0, 3, 0, 0, 0], [0, 0, 3, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 6, 6, 9, 6, 0, 0, 6, 9, 6, 9], [0, 0, 0, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6], [0, 0, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [3, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 9, 6, 9], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6]], "output": [[3, 3, 0, 3, 3, 3, 3, 3, 0, 0, 3, 3, 3, 3], [0, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0], [3, 0, 3, 9, 9, 9, 9, 9, 3, 3, 3, 3, 3, 0], [0, 3, 0, 9, 9, 6, 9, 9, 3, 3, 3, 0, 0, 3], [3, 0, 3, 6, 9, 9, 9, 9, 3, 3, 0, 3, 0, 3], [0, 3, 0, 9, 6, 9, 9, 9, 3, 3, 3, 0, 3, 0], [3, 0, 0, 6, 9, 9, 9, 9, 0, 3, 9, 9, 6, 9], [0, 3, 0, 9, 9, 9, 9, 9, 3, 0, 9, 9, 9, 6], [0, 0, 3, 9, 9, 9, 9, 6, 9, 9, 6, 9, 9, 9], [0, 3, 3, 9, 9, 6, 6, 9, 9, 9, 9, 6, 9, 9], [3, 3, 3, 3, 3, 0, 0, 3, 9, 9, 9, 9, 6, 9], [3, 3, 3, 0, 0, 3, 3, 0, 9, 9, 9, 9, 9, 6]]}], "input_grid": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 5, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 9, 0, 0, 0, 8, 8, 0, 9, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 9, 0, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 9, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 9, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 5, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 9, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8]], "task_key": "d07ae81c"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 7, 7, 7, 5, 7, 1, 4, 7, 7, 7],\n[7, 2, 7, 4, 1, 2, 7, 2, 5, 9, 6],\n[7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 9],\n[7, 7, 7, 0, 5, 6, 5, 7, 7, 0, 6],\n[7, 7, 7, 6, 4, 2, 1, 7, 9, 2, 7],\n[7, 1, 7, 7, 1, 5, 2, 7, 1, 7, 7],\n[7, 1, 1, 1, 6, 7, 1, 6, 7, 5, 1],\n[9, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7],\n[2, 7, 7, 7, 0, 7, 9, 5, 2, 7, 7],\n[7, 1, 4, 0, 7, 2, 4, 1, 7, 7, 7],\n[7, 7, 1, 7, 5, 6, 7, 7, 7, 7, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 7, 7, 7, 5, 7, 1, 4, 7, 7, 7, 7, 7, 2, 9, 7, 7, 7, 7, 7, 7, 4],\n[7, 2, 7, 4, 1, 2, 7, 2, 5, 9, 6, 7, 1, 7, 7, 1, 1, 7, 7, 7, 2, 7],\n[7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 9, 1, 4, 7, 7, 1, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 0, 5, 6, 5, 7, 7, 0, 6, 7, 0, 7, 7, 1, 7, 6, 0, 2, 4, 7],\n[7, 7, 7, 6, 4, 2, 1, 7, 9, 2, 7, 5, 7, 0, 7, 6, 1, 4, 5, 7, 1, 5],\n[7, 1, 7, 7, 1, 5, 2, 7, 1, 7, 7, 6, 2, 7, 7, 7, 5, 2, 6, 7, 2, 7],\n[7, 1, 1, 1, 6, 7, 1, 6, 7, 5, 1, 7, 4, 9, 7, 1, 2, 1, 5, 7, 7, 1],\n[9, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 1, 5, 6, 6, 7, 7, 7, 7, 2, 4],\n[2, 7, 7, 7, 0, 7, 9, 5, 2, 7, 7, 7, 7, 2, 7, 7, 1, 9, 7, 7, 5, 7],\n[7, 1, 4, 0, 7, 2, 4, 1, 7, 7, 7, 7, 7, 7, 7, 5, 7, 2, 0, 7, 9, 7],\n[7, 7, 1, 7, 5, 6, 7, 7, 7, 7, 5, 5, 7, 7, 7, 1, 7, 7, 6, 9, 6, 7],\n[7, 6, 9, 6, 7, 7, 1, 7, 7, 7, 5, 5, 7, 7, 7, 7, 6, 5, 7, 1, 7, 7],\n[7, 9, 7, 0, 2, 7, 5, 7, 7, 7, 7, 7, 7, 7, 1, 4, 2, 7, 0, 4, 1, 7],\n[7, 5, 7, 7, 9, 1, 7, 7, 2, 7, 7, 7, 7, 2, 5, 9, 7, 0, 7, 7, 7, 2],\n[4, 2, 7, 7, 7, 7, 6, 6, 5, 1, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 9],\n[1, 7, 7, 5, 1, 2, 1, 7, 9, 4, 7, 1, 5, 7, 6, 1, 7, 6, 1, 1, 1, 7],\n[7, 2, 7, 6, 2, 5, 7, 7, 7, 2, 6, 7, 7, 1, 7, 2, 5, 1, 7, 7, 1, 7],\n[5, 1, 7, 5, 4, 1, 6, 7, 0, 7, 5, 7, 2, 9, 7, 1, 2, 4, 6, 7, 7, 7],\n[7, 4, 2, 0, 6, 7, 1, 7, 7, 0, 7, 6, 0, 7, 7, 5, 6, 5, 0, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 1, 7, 7, 4, 1, 9, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7],\n[7, 2, 7, 7, 7, 1, 1, 7, 7, 1, 7, 6, 9, 5, 2, 7, 2, 1, 4, 7, 2, 7],\n[4, 7, 7, 7, 7, 7, 7, 9, 2, 7, 7, 7, 7, 7, 4, 1, 7, 5, 7, 7, 7, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[7, 9, 2, 7, 9, 7, 2],\n[2, 7, 2, 7, 2, 7, 7],\n[9, 7, 2, 7, 2, 2, 9],\n[2, 7, 9, 7, 7, 7, 2],\n[7, 7, 2, 2, 2, 9, 7],\n[2, 9, 7, 9, 2, 9, 9],\n[9, 7, 7, 9, 7, 7, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 9, 2, 7, 9, 7, 2, 9, 2, 7, 2, 9, 2, 7],\n[2, 7, 2, 7, 2, 7, 7, 7, 9, 7, 7, 7, 7, 9],\n[9, 7, 2, 7, 2, 2, 9, 7, 7, 2, 9, 2, 2, 2],\n[2, 7, 9, 7, 7, 7, 2, 9, 9, 2, 7, 7, 7, 7],\n[7, 7, 2, 2, 2, 9, 7, 7, 2, 2, 7, 2, 2, 9],\n[2, 9, 7, 9, 2, 9, 9, 7, 9, 9, 7, 2, 7, 7],\n[9, 7, 7, 9, 7, 7, 9, 9, 9, 7, 2, 9, 7, 2],\n[2, 7, 9, 2, 7, 9, 9, 9, 7, 7, 9, 7, 7, 9],\n[7, 7, 2, 7, 9, 9, 7, 9, 9, 2, 9, 7, 9, 2],\n[9, 2, 2, 7, 2, 2, 7, 7, 9, 2, 2, 2, 7, 7],\n[7, 7, 7, 7, 2, 9, 9, 2, 7, 7, 7, 9, 7, 2],\n[2, 2, 2, 9, 2, 7, 7, 9, 2, 2, 7, 2, 7, 9],\n[9, 7, 7, 7, 7, 9, 7, 7, 7, 2, 7, 2, 7, 2],\n[7, 2, 9, 2, 7, 2, 9, 2, 7, 9, 7, 2, 9, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 3, 3, 7, 3, 7, 3, 3, 3, 3],\n[3, 3, 1, 0, 3, 6, 3, 6, 3, 3],\n[5, 3, 8, 6, 0, 3, 1, 5, 3, 6],\n[3, 6, 3, 0, 8, 3, 3, 5, 1, 1],\n[3, 3, 3, 3, 8, 5, 3, 6, 3, 3],\n[3, 3, 6, 3, 3, 4, 3, 3, 7, 3],\n[5, 3, 3, 3, 5, 3, 3, 7, 3, 1],\n[3, 3, 3, 5, 3, 3, 3, 6, 5, 3],\n[3, 3, 5, 3, 3, 3, 7, 3, 3, 4],\n[5, 5, 5, 3, 3, 5, 6, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 3, 3, 7, 3, 7, 3, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 5, 3, 1],\n[3, 3, 1, 0, 3, 6, 3, 6, 3, 3, 5, 3, 3, 3, 3, 3, 6, 3, 3, 3],\n[5, 3, 8, 6, 0, 3, 1, 5, 3, 6, 5, 5, 3, 3, 6, 3, 3, 8, 1, 3],\n[3, 6, 3, 0, 8, 3, 3, 5, 1, 1, 3, 3, 5, 3, 3, 3, 0, 6, 0, 7],\n[3, 3, 3, 3, 8, 5, 3, 6, 3, 3, 3, 3, 3, 5, 3, 8, 8, 0, 3, 3],\n[3, 3, 6, 3, 3, 4, 3, 3, 7, 3, 5, 3, 3, 3, 4, 5, 3, 3, 6, 7],\n[5, 3, 3, 3, 5, 3, 3, 7, 3, 1, 6, 7, 3, 3, 3, 3, 3, 1, 3, 3],\n[3, 3, 3, 5, 3, 3, 3, 6, 5, 3, 3, 3, 6, 7, 3, 6, 5, 5, 6, 3],\n[3, 3, 5, 3, 3, 3, 7, 3, 3, 4, 3, 3, 5, 3, 7, 3, 1, 3, 3, 3],\n[5, 5, 5, 3, 3, 5, 6, 3, 3, 3, 3, 4, 3, 1, 3, 3, 1, 6, 3, 3],\n[3, 3, 6, 1, 3, 3, 1, 3, 4, 3, 3, 3, 3, 6, 5, 3, 3, 5, 5, 5],\n[3, 3, 3, 1, 3, 7, 3, 5, 3, 3, 4, 3, 3, 7, 3, 3, 3, 5, 3, 3],\n[3, 6, 5, 5, 6, 3, 7, 6, 3, 3, 3, 5, 6, 3, 3, 3, 5, 3, 3, 3],\n[3, 3, 1, 3, 3, 3, 3, 3, 7, 6, 1, 3, 7, 3, 3, 5, 3, 3, 3, 5],\n[7, 6, 3, 3, 5, 4, 3, 3, 3, 5, 3, 7, 3, 3, 4, 3, 3, 6, 3, 3],\n[3, 3, 0, 8, 8, 3, 5, 3, 3, 3, 3, 3, 6, 3, 5, 8, 3, 3, 3, 3],\n[7, 0, 6, 0, 3, 3, 3, 5, 3, 3, 1, 1, 5, 3, 3, 8, 0, 3, 6, 3],\n[3, 1, 8, 3, 3, 6, 3, 3, 5, 5, 6, 3, 5, 1, 3, 0, 6, 8, 3, 5],\n[3, 3, 3, 6, 3, 3, 3, 3, 3, 5, 3, 3, 6, 3, 6, 3, 0, 1, 3, 3],\n[1, 3, 5, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 3, 7, 3, 7, 3, 3, 1]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 1, 4, 7, 4, 4, 4, 8, 6, 6, 4, 4, 4, 0],\n[4, 2, 8, 4, 4, 4, 3, 4, 8, 7, 4, 4, 4, 1],\n[4, 4, 4, 4, 6, 4, 4, 4, 0, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 2, 2, 4, 4, 8, 4, 4, 6, 6],\n[1, 6, 0, 4, 4, 3, 4, 4, 4, 4, 4, 6, 4, 3],\n[4, 4, 1, 0, 4, 4, 3, 6, 4, 4, 4, 4, 4, 4],\n[1, 9, 4, 4, 3, 4, 4, 4, 3, 2, 4, 8, 6, 4],\n[4, 4, 4, 0, 4, 4, 6, 4, 7, 3, 4, 4, 4, 4],\n[6, 4, 1, 4, 4, 6, 7, 6, 0, 4, 6, 1, 4, 4],\n[4, 1, 3, 4, 4, 3, 4, 4, 1, 3, 7, 2, 4, 4],\n[8, 1, 1, 9, 4, 1, 4, 4, 4, 4, 4, 4, 4, 6],\n[8, 4, 4, 9, 4, 4, 4, 4, 6, 1, 4, 4, 4, 1],\n[0, 4, 9, 4, 6, 2, 4, 4, 2, 4, 4, 1, 1, 4],\n[4, 0, 4, 4, 7, 4, 6, 3, 4, 2, 7, 0, 8, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 7, 7, 7, 5, 7, 1, 4, 7, 7, 7], [7, 2, 7, 4, 1, 2, 7, 2, 5, 9, 6], [7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 9], [7, 7, 7, 0, 5, 6, 5, 7, 7, 0, 6], [7, 7, 7, 6, 4, 2, 1, 7, 9, 2, 7], [7, 1, 7, 7, 1, 5, 2, 7, 1, 7, 7], [7, 1, 1, 1, 6, 7, 1, 6, 7, 5, 1], [9, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7], [2, 7, 7, 7, 0, 7, 9, 5, 2, 7, 7], [7, 1, 4, 0, 7, 2, 4, 1, 7, 7, 7], [7, 7, 1, 7, 5, 6, 7, 7, 7, 7, 5]], "output": [[4, 7, 7, 7, 5, 7, 1, 4, 7, 7, 7, 7, 7, 2, 9, 7, 7, 7, 7, 7, 7, 4], [7, 2, 7, 4, 1, 2, 7, 2, 5, 9, 6, 7, 1, 7, 7, 1, 1, 7, 7, 7, 2, 7], [7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 9, 1, 4, 7, 7, 1, 7, 7, 7, 7, 7, 7], [7, 7, 7, 0, 5, 6, 5, 7, 7, 0, 6, 7, 0, 7, 7, 1, 7, 6, 0, 2, 4, 7], [7, 7, 7, 6, 4, 2, 1, 7, 9, 2, 7, 5, 7, 0, 7, 6, 1, 4, 5, 7, 1, 5], [7, 1, 7, 7, 1, 5, 2, 7, 1, 7, 7, 6, 2, 7, 7, 7, 5, 2, 6, 7, 2, 7], [7, 1, 1, 1, 6, 7, 1, 6, 7, 5, 1, 7, 4, 9, 7, 1, 2, 1, 5, 7, 7, 1], [9, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 1, 5, 6, 6, 7, 7, 7, 7, 2, 4], [2, 7, 7, 7, 0, 7, 9, 5, 2, 7, 7, 7, 7, 2, 7, 7, 1, 9, 7, 7, 5, 7], [7, 1, 4, 0, 7, 2, 4, 1, 7, 7, 7, 7, 7, 7, 7, 5, 7, 2, 0, 7, 9, 7], [7, 7, 1, 7, 5, 6, 7, 7, 7, 7, 5, 5, 7, 7, 7, 1, 7, 7, 6, 9, 6, 7], [7, 6, 9, 6, 7, 7, 1, 7, 7, 7, 5, 5, 7, 7, 7, 7, 6, 5, 7, 1, 7, 7], [7, 9, 7, 0, 2, 7, 5, 7, 7, 7, 7, 7, 7, 7, 1, 4, 2, 7, 0, 4, 1, 7], [7, 5, 7, 7, 9, 1, 7, 7, 2, 7, 7, 7, 7, 2, 5, 9, 7, 0, 7, 7, 7, 2], [4, 2, 7, 7, 7, 7, 6, 6, 5, 1, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 9], [1, 7, 7, 5, 1, 2, 1, 7, 9, 4, 7, 1, 5, 7, 6, 1, 7, 6, 1, 1, 1, 7], [7, 2, 7, 6, 2, 5, 7, 7, 7, 2, 6, 7, 7, 1, 7, 2, 5, 1, 7, 7, 1, 7], [5, 1, 7, 5, 4, 1, 6, 7, 0, 7, 5, 7, 2, 9, 7, 1, 2, 4, 6, 7, 7, 7], [7, 4, 2, 0, 6, 7, 1, 7, 7, 0, 7, 6, 0, 7, 7, 5, 6, 5, 0, 7, 7, 7], [7, 7, 7, 7, 7, 7, 1, 7, 7, 4, 1, 9, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7], [7, 2, 7, 7, 7, 1, 1, 7, 7, 1, 7, 6, 9, 5, 2, 7, 2, 1, 4, 7, 2, 7], [4, 7, 7, 7, 7, 7, 7, 9, 2, 7, 7, 7, 7, 7, 4, 1, 7, 5, 7, 7, 7, 4]]}, {"input": [[7, 9, 2, 7, 9, 7, 2], [2, 7, 2, 7, 2, 7, 7], [9, 7, 2, 7, 2, 2, 9], [2, 7, 9, 7, 7, 7, 2], [7, 7, 2, 2, 2, 9, 7], [2, 9, 7, 9, 2, 9, 9], [9, 7, 7, 9, 7, 7, 9]], "output": [[7, 9, 2, 7, 9, 7, 2, 9, 2, 7, 2, 9, 2, 7], [2, 7, 2, 7, 2, 7, 7, 7, 9, 7, 7, 7, 7, 9], [9, 7, 2, 7, 2, 2, 9, 7, 7, 2, 9, 2, 2, 2], [2, 7, 9, 7, 7, 7, 2, 9, 9, 2, 7, 7, 7, 7], [7, 7, 2, 2, 2, 9, 7, 7, 2, 2, 7, 2, 2, 9], [2, 9, 7, 9, 2, 9, 9, 7, 9, 9, 7, 2, 7, 7], [9, 7, 7, 9, 7, 7, 9, 9, 9, 7, 2, 9, 7, 2], [2, 7, 9, 2, 7, 9, 9, 9, 7, 7, 9, 7, 7, 9], [7, 7, 2, 7, 9, 9, 7, 9, 9, 2, 9, 7, 9, 2], [9, 2, 2, 7, 2, 2, 7, 7, 9, 2, 2, 2, 7, 7], [7, 7, 7, 7, 2, 9, 9, 2, 7, 7, 7, 9, 7, 2], [2, 2, 2, 9, 2, 7, 7, 9, 2, 2, 7, 2, 7, 9], [9, 7, 7, 7, 7, 9, 7, 7, 7, 2, 7, 2, 7, 2], [7, 2, 9, 2, 7, 2, 9, 2, 7, 9, 7, 2, 9, 7]]}, {"input": [[1, 3, 3, 7, 3, 7, 3, 3, 3, 3], [3, 3, 1, 0, 3, 6, 3, 6, 3, 3], [5, 3, 8, 6, 0, 3, 1, 5, 3, 6], [3, 6, 3, 0, 8, 3, 3, 5, 1, 1], [3, 3, 3, 3, 8, 5, 3, 6, 3, 3], [3, 3, 6, 3, 3, 4, 3, 3, 7, 3], [5, 3, 3, 3, 5, 3, 3, 7, 3, 1], [3, 3, 3, 5, 3, 3, 3, 6, 5, 3], [3, 3, 5, 3, 3, 3, 7, 3, 3, 4], [5, 5, 5, 3, 3, 5, 6, 3, 3, 3]], "output": [[1, 3, 3, 7, 3, 7, 3, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 5, 3, 1], [3, 3, 1, 0, 3, 6, 3, 6, 3, 3, 5, 3, 3, 3, 3, 3, 6, 3, 3, 3], [5, 3, 8, 6, 0, 3, 1, 5, 3, 6, 5, 5, 3, 3, 6, 3, 3, 8, 1, 3], [3, 6, 3, 0, 8, 3, 3, 5, 1, 1, 3, 3, 5, 3, 3, 3, 0, 6, 0, 7], [3, 3, 3, 3, 8, 5, 3, 6, 3, 3, 3, 3, 3, 5, 3, 8, 8, 0, 3, 3], [3, 3, 6, 3, 3, 4, 3, 3, 7, 3, 5, 3, 3, 3, 4, 5, 3, 3, 6, 7], [5, 3, 3, 3, 5, 3, 3, 7, 3, 1, 6, 7, 3, 3, 3, 3, 3, 1, 3, 3], [3, 3, 3, 5, 3, 3, 3, 6, 5, 3, 3, 3, 6, 7, 3, 6, 5, 5, 6, 3], [3, 3, 5, 3, 3, 3, 7, 3, 3, 4, 3, 3, 5, 3, 7, 3, 1, 3, 3, 3], [5, 5, 5, 3, 3, 5, 6, 3, 3, 3, 3, 4, 3, 1, 3, 3, 1, 6, 3, 3], [3, 3, 6, 1, 3, 3, 1, 3, 4, 3, 3, 3, 3, 6, 5, 3, 3, 5, 5, 5], [3, 3, 3, 1, 3, 7, 3, 5, 3, 3, 4, 3, 3, 7, 3, 3, 3, 5, 3, 3], [3, 6, 5, 5, 6, 3, 7, 6, 3, 3, 3, 5, 6, 3, 3, 3, 5, 3, 3, 3], [3, 3, 1, 3, 3, 3, 3, 3, 7, 6, 1, 3, 7, 3, 3, 5, 3, 3, 3, 5], [7, 6, 3, 3, 5, 4, 3, 3, 3, 5, 3, 7, 3, 3, 4, 3, 3, 6, 3, 3], [3, 3, 0, 8, 8, 3, 5, 3, 3, 3, 3, 3, 6, 3, 5, 8, 3, 3, 3, 3], [7, 0, 6, 0, 3, 3, 3, 5, 3, 3, 1, 1, 5, 3, 3, 8, 0, 3, 6, 3], [3, 1, 8, 3, 3, 6, 3, 3, 5, 5, 6, 3, 5, 1, 3, 0, 6, 8, 3, 5], [3, 3, 3, 6, 3, 3, 3, 3, 3, 5, 3, 3, 6, 3, 6, 3, 0, 1, 3, 3], [1, 3, 5, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 3, 7, 3, 7, 3, 3, 1]]}], "input_grid": [[4, 1, 4, 7, 4, 4, 4, 8, 6, 6, 4, 4, 4, 0], [4, 2, 8, 4, 4, 4, 3, 4, 8, 7, 4, 4, 4, 1], [4, 4, 4, 4, 6, 4, 4, 4, 0, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 2, 2, 4, 4, 8, 4, 4, 6, 6], [1, 6, 0, 4, 4, 3, 4, 4, 4, 4, 4, 6, 4, 3], [4, 4, 1, 0, 4, 4, 3, 6, 4, 4, 4, 4, 4, 4], [1, 9, 4, 4, 3, 4, 4, 4, 3, 2, 4, 8, 6, 4], [4, 4, 4, 0, 4, 4, 6, 4, 7, 3, 4, 4, 4, 4], [6, 4, 1, 4, 4, 6, 7, 6, 0, 4, 6, 1, 4, 4], [4, 1, 3, 4, 4, 3, 4, 4, 1, 3, 7, 2, 4, 4], [8, 1, 1, 9, 4, 1, 4, 4, 4, 4, 4, 4, 4, 6], [8, 4, 4, 9, 4, 4, 4, 4, 6, 1, 4, 4, 4, 1], [0, 4, 9, 4, 6, 2, 4, 4, 2, 4, 4, 1, 1, 4], [4, 0, 4, 4, 7, 4, 6, 3, 4, 2, 7, 0, 8, 4]], "task_key": "7fe24cdd"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 2, 9, 2, 0, 0, 0, 0, 5, 5, 2, 9, 2, 9, 5, 2],\n[9, 9, 5, 2, 9, 5, 0, 0, 0, 0, 9, 5, 2, 9, 5, 5, 2, 9],\n[2, 9, 9, 9, 2, 5, 0, 0, 0, 0, 9, 9, 9, 2, 5, 2, 2, 9],\n[2, 5, 9, 2, 9, 5, 0, 0, 0, 0, 5, 9, 2, 9, 5, 2, 9, 5],\n[5, 9, 5, 2, 2, 5, 5, 5, 2, 5, 9, 5, 2, 2, 5, 5, 5, 2],\n[9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5],\n[9, 2, 5, 5, 2, 2, 2, 5, 2, 9, 2, 5, 5, 2, 2, 2, 5, 2],\n[2, 9, 2, 2, 5, 9, 2, 9, 2, 2, 9, 2, 2, 5, 9, 2, 9, 2],\n[9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5],\n[2, 2, 9, 5, 5, 2, 5, 5, 5, 2, 2, 9, 5, 5, 2, 5, 5, 5],\n[5, 5, 5, 2, 9, 2, 9, 5, 2, 5, 5, 5, 2, 9, 2, 9, 5, 2],\n[9, 9, 5, 2, 9, 5, 5, 2, 9, 9, 9, 5, 2, 9, 5, 5, 2, 9],\n[2, 9, 9, 9, 2, 5, 2, 2, 9, 2, 9, 9, 9, 2, 5, 2, 2, 9],\n[2, 5, 9, 2, 9, 5, 2, 9, 5, 2, 5, 9, 2, 9, 5, 2, 9, 5],\n[5, 9, 5, 2, 2, 5, 5, 5, 2, 5, 9, 5, 2, 2, 5, 5, 5, 2],\n[9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5],\n[9, 2, 5, 5, 2, 2, 2, 5, 2, 9, 2, 5, 5, 2, 2, 2, 5, 2],\n[2, 9, 2, 2, 5, 9, 2, 9, 2, 2, 9, 2, 2, 5, 9, 2, 9, 2],\n[9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5],\n[2, 2, 9, 5, 5, 2, 5, 5, 5, 2, 2, 9, 5, 5, 2, 5, 5, 5],\n[5, 5, 5, 2, 9, 2, 9, 5, 2, 5, 5, 5, 2, 9, 2, 9, 5, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 5, 2, 5],\n[5, 2, 9, 9],\n[2, 2, 9, 2],\n[2, 9, 5, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4],\n[1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3],\n[4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4],\n[4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3],\n[3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1],\n[4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4],\n[3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4],\n[3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1],\n[1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3],\n[1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1],\n[4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4],\n[1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3],\n[4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4],\n[4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3],\n[0, 0, 0, 0, 0, 1, 4, 4, 3, 3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1],\n[0, 0, 0, 0, 0, 1, 4, 4, 3, 4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4],\n[0, 0, 0, 0, 0, 1, 4, 1, 1, 3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1],\n[0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3],\n[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1],\n[0, 0, 0, 0, 0, 1, 3, 3, 3, 4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3],\n[0, 0, 0, 0, 0, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4],\n[0, 0, 0, 0, 0, 1, 3, 3, 1, 4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3],\n[0, 0, 0, 0, 0, 1, 4, 4, 3, 3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1],\n[0, 0, 0, 0, 0, 1, 4, 4, 3, 4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4],\n[0, 0, 0, 0, 0, 1, 4, 1, 1, 3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1],\n[0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 1, 3, 4, 3],\n[4, 4, 3, 3, 4],\n[3, 4, 4, 3, 1],\n[3, 1, 3, 4, 4],\n[1, 3, 4, 4, 3],\n[1, 1, 3, 3, 1],\n[4, 4, 3, 1, 4],\n[1, 3, 1, 3, 3],\n[4, 4, 4, 3, 4],\n[4, 3, 1, 3, 3],\n[3, 1, 3, 4, 3],\n[4, 4, 3, 3, 4],\n[3, 4, 4, 3, 1],\n[3, 1, 3, 4, 4],\n[1, 3, 4, 4, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6],\n[2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7],\n[8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1],\n[7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1],\n[7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4],\n[5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8],\n[2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8],\n[2, 8, 2, 8, 2, 8, 2, 8, 0, 0, 0, 0, 0, 8, 2, 8, 2, 8],\n[6, 4, 6, 4, 6, 4, 6, 4, 0, 0, 0, 0, 0, 4, 6, 4, 6, 4],\n[1, 6, 1, 6, 1, 6, 1, 6, 0, 0, 0, 0, 0, 6, 1, 6, 1, 6],\n[2, 7, 2, 7, 2, 7, 2, 7, 0, 0, 0, 0, 0, 7, 2, 7, 2, 7],\n[8, 1, 8, 1, 8, 1, 8, 1, 0, 0, 0, 0, 0, 1, 8, 1, 8, 1],\n[7, 1, 7, 1, 7, 1, 7, 1, 0, 0, 0, 0, 0, 1, 7, 1, 7, 1],\n[7, 4, 7, 4, 7, 4, 7, 4, 0, 0, 0, 0, 0, 4, 7, 4, 7, 4],\n[5, 8, 5, 8, 5, 8, 5, 8, 0, 0, 0, 0, 0, 8, 5, 8, 5, 8],\n[2, 8, 2, 8, 2, 8, 2, 8, 0, 0, 0, 0, 0, 8, 2, 8, 2, 8],\n[2, 8, 2, 8, 2, 8, 2, 8, 0, 0, 0, 0, 0, 8, 2, 8, 2, 8],\n[6, 4, 6, 4, 6, 4, 6, 4, 0, 0, 0, 0, 0, 4, 6, 4, 6, 4],\n[1, 6, 1, 6, 1, 6, 1, 6, 0, 0, 0, 0, 0, 6, 1, 6, 1, 6],\n[2, 7, 2, 7, 2, 7, 2, 7, 0, 0, 0, 0, 0, 7, 2, 7, 2, 7],\n[8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1],\n[7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1],\n[7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4],\n[5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8],\n[2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 8, 2, 8, 2],\n[6, 4, 6, 4, 6],\n[1, 6, 1, 6, 1],\n[2, 7, 2, 7, 2],\n[8, 1, 8, 1, 8],\n[7, 1, 7, 1, 7],\n[7, 4, 7, 4, 7],\n[5, 8, 5, 8, 5],\n[2, 8, 2, 8, 2],\n[2, 8, 2, 8, 2],\n[6, 4, 6, 4, 6],\n[1, 6, 1, 6, 1],\n[2, 7, 2, 7, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9],\n[9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9],\n[9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9],\n[9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9],\n[9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9],\n[9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9],\n[9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1],\n[1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9],\n[9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 2, 9, 2, 0, 0, 0, 0, 5, 5, 2, 9, 2, 9, 5, 2], [9, 9, 5, 2, 9, 5, 0, 0, 0, 0, 9, 5, 2, 9, 5, 5, 2, 9], [2, 9, 9, 9, 2, 5, 0, 0, 0, 0, 9, 9, 9, 2, 5, 2, 2, 9], [2, 5, 9, 2, 9, 5, 0, 0, 0, 0, 5, 9, 2, 9, 5, 2, 9, 5], [5, 9, 5, 2, 2, 5, 5, 5, 2, 5, 9, 5, 2, 2, 5, 5, 5, 2], [9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5], [9, 2, 5, 5, 2, 2, 2, 5, 2, 9, 2, 5, 5, 2, 2, 2, 5, 2], [2, 9, 2, 2, 5, 9, 2, 9, 2, 2, 9, 2, 2, 5, 9, 2, 9, 2], [9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5], [2, 2, 9, 5, 5, 2, 5, 5, 5, 2, 2, 9, 5, 5, 2, 5, 5, 5], [5, 5, 5, 2, 9, 2, 9, 5, 2, 5, 5, 5, 2, 9, 2, 9, 5, 2], [9, 9, 5, 2, 9, 5, 5, 2, 9, 9, 9, 5, 2, 9, 5, 5, 2, 9], [2, 9, 9, 9, 2, 5, 2, 2, 9, 2, 9, 9, 9, 2, 5, 2, 2, 9], [2, 5, 9, 2, 9, 5, 2, 9, 5, 2, 5, 9, 2, 9, 5, 2, 9, 5], [5, 9, 5, 2, 2, 5, 5, 5, 2, 5, 9, 5, 2, 2, 5, 5, 5, 2], [9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5], [9, 2, 5, 5, 2, 2, 2, 5, 2, 9, 2, 5, 5, 2, 2, 2, 5, 2], [2, 9, 2, 2, 5, 9, 2, 9, 2, 2, 9, 2, 2, 5, 9, 2, 9, 2], [9, 5, 5, 5, 9, 9, 9, 9, 5, 9, 5, 5, 5, 9, 9, 9, 9, 5], [2, 2, 9, 5, 5, 2, 5, 5, 5, 2, 2, 9, 5, 5, 2, 5, 5, 5], [5, 5, 5, 2, 9, 2, 9, 5, 2, 5, 5, 5, 2, 9, 2, 9, 5, 2]], "output": [[9, 5, 2, 5], [5, 2, 9, 9], [2, 2, 9, 2], [2, 9, 5, 2]]}, {"input": [[4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4], [1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3], [4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4], [4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3], [3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1], [4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4], [3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4], [3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1], [1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3], [1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1], [4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4], [1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3], [4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4], [4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3], [0, 0, 0, 0, 0, 1, 4, 4, 3, 3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1], [0, 0, 0, 0, 0, 1, 4, 4, 3, 4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4], [0, 0, 0, 0, 0, 1, 4, 1, 1, 3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4], [0, 0, 0, 0, 0, 4, 4, 4, 4, 3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1], [0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 3, 3, 3, 4, 4, 3, 1, 4, 1, 3, 3, 3, 4, 4], [0, 0, 0, 0, 0, 4, 4, 4, 4, 1, 3, 1, 3, 3, 4, 4, 4, 4, 1, 3], [0, 0, 0, 0, 0, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3, 4, 4], [0, 0, 0, 0, 0, 1, 3, 3, 1, 4, 3, 1, 3, 3, 1, 3, 3, 1, 4, 3], [0, 0, 0, 0, 0, 1, 4, 4, 3, 3, 1, 3, 4, 3, 1, 4, 4, 3, 3, 1], [0, 0, 0, 0, 0, 1, 4, 4, 3, 4, 4, 3, 3, 4, 1, 4, 4, 3, 4, 4], [0, 0, 0, 0, 0, 1, 4, 1, 1, 3, 4, 4, 3, 1, 1, 4, 1, 1, 3, 4], [0, 0, 0, 0, 0, 4, 4, 4, 4, 3, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1], [0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 3, 4, 4, 3, 4, 4, 4, 1, 1, 3]], "output": [[3, 1, 3, 4, 3], [4, 4, 3, 3, 4], [3, 4, 4, 3, 1], [3, 1, 3, 4, 4], [1, 3, 4, 4, 3], [1, 1, 3, 3, 1], [4, 4, 3, 1, 4], [1, 3, 1, 3, 3], [4, 4, 4, 3, 4], [4, 3, 1, 3, 3], [3, 1, 3, 4, 3], [4, 4, 3, 3, 4], [3, 4, 4, 3, 1], [3, 1, 3, 4, 4], [1, 3, 4, 4, 3]]}, {"input": [[1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6], [2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], [8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1], [7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1], [7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4], [5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8], [2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8], [2, 8, 2, 8, 2, 8, 2, 8, 0, 0, 0, 0, 0, 8, 2, 8, 2, 8], [6, 4, 6, 4, 6, 4, 6, 4, 0, 0, 0, 0, 0, 4, 6, 4, 6, 4], [1, 6, 1, 6, 1, 6, 1, 6, 0, 0, 0, 0, 0, 6, 1, 6, 1, 6], [2, 7, 2, 7, 2, 7, 2, 7, 0, 0, 0, 0, 0, 7, 2, 7, 2, 7], [8, 1, 8, 1, 8, 1, 8, 1, 0, 0, 0, 0, 0, 1, 8, 1, 8, 1], [7, 1, 7, 1, 7, 1, 7, 1, 0, 0, 0, 0, 0, 1, 7, 1, 7, 1], [7, 4, 7, 4, 7, 4, 7, 4, 0, 0, 0, 0, 0, 4, 7, 4, 7, 4], [5, 8, 5, 8, 5, 8, 5, 8, 0, 0, 0, 0, 0, 8, 5, 8, 5, 8], [2, 8, 2, 8, 2, 8, 2, 8, 0, 0, 0, 0, 0, 8, 2, 8, 2, 8], [2, 8, 2, 8, 2, 8, 2, 8, 0, 0, 0, 0, 0, 8, 2, 8, 2, 8], [6, 4, 6, 4, 6, 4, 6, 4, 0, 0, 0, 0, 0, 4, 6, 4, 6, 4], [1, 6, 1, 6, 1, 6, 1, 6, 0, 0, 0, 0, 0, 6, 1, 6, 1, 6], [2, 7, 2, 7, 2, 7, 2, 7, 0, 0, 0, 0, 0, 7, 2, 7, 2, 7], [8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1], [7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1], [7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4, 7, 4], [5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8], [2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8]], "output": [[2, 8, 2, 8, 2], [6, 4, 6, 4, 6], [1, 6, 1, 6, 1], [2, 7, 2, 7, 2], [8, 1, 8, 1, 8], [7, 1, 7, 1, 7], [7, 4, 7, 4, 7], [5, 8, 5, 8, 5], [2, 8, 2, 8, 2], [2, 8, 2, 8, 2], [6, 4, 6, 4, 6], [1, 6, 1, 6, 1], [2, 7, 2, 7, 2]]}], "input_grid": [[9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9], [9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9], [9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9], [9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9], [9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 4, 1, 1, 1, 9], [9, 1, 9, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9], [9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1, 1, 4, 9, 1, 9, 4, 4, 4, 1], [1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9, 9, 9, 1, 4, 1, 4, 1, 9, 9], [9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9, 1, 4, 9, 9, 4, 1, 1, 1, 9]], "task_key": "f9012d9b"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 5, 4, 4, 4, 3, 4, 3, 1, 5, 4, 5, 4, 2, 2, 2, 4, 7, 6, 4, 4],\n[7, 4, 5, 8, 9, 4, 4, 4, 4, 4, 0, 4, 2, 3, 4, 8, 4, 4, 4, 4, 6],\n[3, 8, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 2, 0, 4, 7, 0, 4, 1, 4, 4],\n[4, 4, 7, 4, 4, 1, 2, 4, 4, 4, 4, 4, 4, 4, 7, 9, 4, 4, 6, 4, 4],\n[7, 8, 0, 4, 3, 4, 4, 4, 4, 4, 2, 4, 9, 4, 4, 2, 7, 4, 4, 3, 7],\n[4, 4, 4, 4, 8, 4, 4, 4, 4, 3, 4, 9, 2, 4, 4, 4, 9, 2, 4, 4, 4],\n[5, 4, 0, 8, 4, 4, 7, 4, 8, 7, 2, 4, 4, 6, 1, 4, 4, 4, 2, 6, 4],\n[4, 9, 4, 4, 4, 4, 4, 0, 0, 4, 0, 6, 6, 9, 8, 4, 4, 4, 1, 6, 4],\n[4, 4, 4, 4, 8, 5, 4, 4, 2, 4, 4, 4, 8, 6, 4, 5, 4, 4, 4, 1, 4],\n[6, 5, 1, 4, 4, 1, 0, 4, 4, 4, 6, 4, 1, 4, 4, 0, 4, 4, 4, 1, 4],\n[8, 4, 3, 1, 3, 4, 1, 4, 7, 7, 4, 7, 4, 1, 4, 4, 7, 4, 0, 4, 4],\n[4, 4, 4, 4, 4, 0, 4, 7, 7, 8, 6, 6, 6, 4, 4, 1, 3, 8, 4, 4, 0],\n[4, 4, 4, 4, 4, 0, 4, 7, 7, 8, 6, 6, 6, 4, 4, 1, 3, 8, 4, 4, 0],\n[8, 4, 3, 1, 3, 4, 1, 4, 7, 7, 4, 7, 4, 1, 4, 4, 7, 4, 0, 4, 4],\n[6, 5, 1, 4, 4, 1, 0, 4, 4, 4, 6, 4, 1, 4, 4, 0, 4, 4, 4, 1, 4],\n[4, 4, 4, 4, 8, 5, 4, 4, 2, 4, 4, 4, 8, 6, 4, 5, 4, 4, 4, 1, 4],\n[4, 9, 4, 4, 4, 4, 4, 0, 0, 4, 0, 6, 6, 9, 8, 4, 4, 4, 1, 6, 4],\n[5, 4, 0, 8, 4, 4, 7, 4, 8, 7, 2, 4, 4, 6, 1, 4, 4, 4, 2, 6, 4],\n[4, 4, 4, 4, 8, 4, 4, 4, 4, 3, 4, 9, 2, 4, 4, 4, 9, 2, 4, 4, 4],\n[7, 8, 0, 4, 3, 4, 4, 4, 4, 4, 2, 4, 9, 4, 4, 2, 7, 4, 4, 3, 7],\n[4, 4, 7, 4, 4, 1, 2, 4, 4, 4, 4, 4, 4, 4, 7, 9, 4, 4, 6, 4, 4],\n[3, 8, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 2, 0, 4, 7, 0, 4, 1, 4, 4],\n[7, 4, 5, 8, 9, 4, 4, 4, 4, 4, 0, 4, 2, 3, 4, 8, 4, 4, 4, 4, 6],\n[4, 5, 4, 4, 4, 3, 4, 3, 1, 5, 4, 5, 4, 2, 2, 2, 4, 7, 6, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 6, 8, 8, 2, 8, 6, 7, 0, 4, 4, 0, 5, 0, 7, 7, 8, 8, 6, 5],\n[4, 7, 2, 2, 5, 7, 9, 9, 0, 9, 9, 0, 9, 9, 7, 5, 7, 2, 5, 5],\n[4, 0, 2, 8, 9, 0, 0, 4, 5, 4, 8, 8, 4, 5, 0, 0, 8, 2, 4, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 3, 0, 3, 8, 0, 3, 8, 3, 0, 2, 4],\n[3, 0, 7, 2, 3, 4, 0, 3, 4, 3, 8, 9],\n[4, 0, 8, 0, 5, 2, 8, 5, 8, 5, 0, 4],\n[8, 8, 8, 0, 9, 0, 0, 9, 0, 7, 4, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 6, 8, 1, 6, 3, 1, 8, 6, 1, 1, 1, 3, 1, 3, 3, 8, 1, 1, 1, 6, 3, 8, 8, 6, 3, 1, 8, 8],\n[6, 1, 3, 8, 8, 1, 8, 1, 3, 1, 8, 3, 1, 8, 1, 8, 3, 8, 3, 3, 1, 1, 1, 1, 8, 1, 3, 8, 6],\n[6, 8, 8, 1, 1, 6, 3, 3, 1, 1, 8, 3, 8, 3, 3, 8, 3, 3, 8, 3, 1, 1, 1, 1, 1, 8, 1, 6, 8],\n[1, 3, 3, 3, 3, 6, 1, 1, 8, 8, 3, 8, 3, 8, 1, 3, 8, 1, 1, 3, 1, 3, 3, 3, 3, 1, 1, 3, 3],\n[8, 3, 1, 1, 8, 8, 3, 8, 8, 1, 3, 1, 8, 8, 1, 8, 1, 3, 6, 1, 1, 3, 1, 8, 3, 3, 6, 3, 3],\n[8, 3, 3, 3, 1, 6, 6, 1, 3, 1, 6, 3, 3, 8, 6, 8, 3, 1, 8, 8, 3, 3, 6, 1, 6, 6, 8, 8, 8],\n[3, 8, 3, 3, 8, 8, 8, 3, 6, 8, 3, 8, 1, 1, 3, 1, 1, 8, 3, 8, 1, 3, 3, 1, 3, 8, 1, 3, 8],\n[1, 3, 1, 8, 3, 8, 1, 8, 1, 1, 8, 3, 3, 8, 1, 8, 1, 8, 8, 8, 8, 1, 8, 8, 6, 3, 1, 3, 3],\n[6, 1, 1, 3, 8, 8, 6, 3, 3, 1, 3, 3, 6, 1, 8, 8, 8, 8, 1, 1, 1, 3, 3, 1, 8, 1, 8, 1, 8],\n[3, 3, 1, 1, 1, 6, 3, 3, 3, 1, 3, 1, 8, 1, 8, 8, 8, 8, 6, 1, 6, 3, 8, 1, 1, 8, 1, 8, 1],\n[1, 1, 8, 1, 1, 3, 1, 8, 3, 8, 8, 1, 3, 1, 8, 3, 8, 6, 8, 1, 3, 8, 6, 8, 3, 8, 3, 6, 1],\n[1, 8, 1, 3, 8, 1, 3, 3, 8, 1, 1, 1, 8, 1, 8, 8, 3, 8, 1, 3, 8, 8, 1, 8, 6, 6, 1, 1, 3],\n[3, 1, 6, 1, 1, 3, 6, 6, 1, 3, 3, 1, 1, 6, 3, 1, 1, 1, 1, 3, 6, 8, 8, 6, 1, 1, 8, 1, 3],\n[1, 8, 1, 3, 8, 1, 3, 3, 8, 1, 1, 1, 8, 1, 8, 8, 3, 8, 1, 3, 8, 8, 1, 8, 6, 6, 1, 1, 3],\n[1, 1, 8, 1, 1, 3, 1, 8, 3, 8, 8, 1, 3, 1, 8, 3, 8, 6, 8, 1, 3, 8, 6, 8, 3, 8, 3, 6, 1],\n[3, 3, 1, 1, 1, 6, 3, 3, 3, 1, 3, 1, 8, 1, 8, 8, 8, 8, 6, 1, 6, 3, 8, 1, 1, 8, 1, 8, 1],\n[6, 1, 1, 3, 8, 8, 6, 3, 3, 1, 3, 3, 6, 1, 8, 8, 8, 8, 1, 1, 1, 3, 3, 1, 8, 1, 8, 1, 8],\n[1, 3, 1, 8, 3, 8, 1, 8, 1, 1, 8, 3, 3, 8, 1, 8, 1, 8, 8, 8, 8, 1, 8, 8, 6, 3, 1, 3, 3],\n[3, 8, 3, 3, 8, 8, 8, 3, 6, 8, 3, 8, 1, 1, 3, 1, 1, 8, 3, 8, 1, 3, 3, 1, 3, 8, 1, 3, 8],\n[8, 3, 3, 3, 1, 6, 6, 1, 3, 1, 6, 3, 3, 8, 6, 8, 3, 1, 8, 8, 3, 3, 6, 1, 6, 6, 8, 8, 8],\n[8, 3, 1, 1, 8, 8, 3, 8, 8, 1, 3, 1, 8, 8, 1, 8, 1, 3, 6, 1, 1, 3, 1, 8, 3, 3, 6, 3, 3],\n[1, 3, 3, 3, 3, 6, 1, 1, 8, 8, 3, 8, 3, 8, 1, 3, 8, 1, 1, 3, 1, 3, 3, 3, 3, 1, 1, 3, 3],\n[6, 8, 8, 1, 1, 6, 3, 3, 1, 1, 8, 3, 8, 3, 3, 8, 3, 3, 8, 3, 1, 1, 1, 1, 1, 8, 1, 6, 8],\n[6, 1, 3, 8, 8, 1, 8, 1, 3, 1, 8, 3, 1, 8, 1, 8, 3, 8, 3, 3, 1, 1, 1, 1, 8, 1, 3, 8, 6],\n[8, 6, 8, 1, 6, 3, 1, 8, 6, 1, 1, 1, 3, 1, 3, 3, 8, 1, 1, 1, 6, 3, 8, 8, 6, 3, 1, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 5, 4, 4, 4, 3, 4, 3, 1, 5, 4, 5, 4, 2, 2, 2, 4, 7, 6, 4, 4], [7, 4, 5, 8, 9, 4, 4, 4, 4, 4, 0, 4, 2, 3, 4, 8, 4, 4, 4, 4, 6], [3, 8, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 2, 0, 4, 7, 0, 4, 1, 4, 4], [4, 4, 7, 4, 4, 1, 2, 4, 4, 4, 4, 4, 4, 4, 7, 9, 4, 4, 6, 4, 4], [7, 8, 0, 4, 3, 4, 4, 4, 4, 4, 2, 4, 9, 4, 4, 2, 7, 4, 4, 3, 7], [4, 4, 4, 4, 8, 4, 4, 4, 4, 3, 4, 9, 2, 4, 4, 4, 9, 2, 4, 4, 4], [5, 4, 0, 8, 4, 4, 7, 4, 8, 7, 2, 4, 4, 6, 1, 4, 4, 4, 2, 6, 4], [4, 9, 4, 4, 4, 4, 4, 0, 0, 4, 0, 6, 6, 9, 8, 4, 4, 4, 1, 6, 4], [4, 4, 4, 4, 8, 5, 4, 4, 2, 4, 4, 4, 8, 6, 4, 5, 4, 4, 4, 1, 4], [6, 5, 1, 4, 4, 1, 0, 4, 4, 4, 6, 4, 1, 4, 4, 0, 4, 4, 4, 1, 4], [8, 4, 3, 1, 3, 4, 1, 4, 7, 7, 4, 7, 4, 1, 4, 4, 7, 4, 0, 4, 4], [4, 4, 4, 4, 4, 0, 4, 7, 7, 8, 6, 6, 6, 4, 4, 1, 3, 8, 4, 4, 0], [4, 4, 4, 4, 4, 0, 4, 7, 7, 8, 6, 6, 6, 4, 4, 1, 3, 8, 4, 4, 0], [8, 4, 3, 1, 3, 4, 1, 4, 7, 7, 4, 7, 4, 1, 4, 4, 7, 4, 0, 4, 4], [6, 5, 1, 4, 4, 1, 0, 4, 4, 4, 6, 4, 1, 4, 4, 0, 4, 4, 4, 1, 4], [4, 4, 4, 4, 8, 5, 4, 4, 2, 4, 4, 4, 8, 6, 4, 5, 4, 4, 4, 1, 4], [4, 9, 4, 4, 4, 4, 4, 0, 0, 4, 0, 6, 6, 9, 8, 4, 4, 4, 1, 6, 4], [5, 4, 0, 8, 4, 4, 7, 4, 8, 7, 2, 4, 4, 6, 1, 4, 4, 4, 2, 6, 4], [4, 4, 4, 4, 8, 4, 4, 4, 4, 3, 4, 9, 2, 4, 4, 4, 9, 2, 4, 4, 4], [7, 8, 0, 4, 3, 4, 4, 4, 4, 4, 2, 4, 9, 4, 4, 2, 7, 4, 4, 3, 7], [4, 4, 7, 4, 4, 1, 2, 4, 4, 4, 4, 4, 4, 4, 7, 9, 4, 4, 6, 4, 4], [3, 8, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 2, 0, 4, 7, 0, 4, 1, 4, 4], [7, 4, 5, 8, 9, 4, 4, 4, 4, 4, 0, 4, 2, 3, 4, 8, 4, 4, 4, 4, 6], [4, 5, 4, 4, 4, 3, 4, 3, 1, 5, 4, 5, 4, 2, 2, 2, 4, 7, 6, 4, 4]], "output": [[1]]}, {"input": [[5, 6, 8, 8, 2, 8, 6, 7, 0, 4, 4, 0, 5, 0, 7, 7, 8, 8, 6, 5], [4, 7, 2, 2, 5, 7, 9, 9, 0, 9, 9, 0, 9, 9, 7, 5, 7, 2, 5, 5], [4, 0, 2, 8, 9, 0, 0, 4, 5, 4, 8, 8, 4, 5, 0, 0, 8, 2, 4, 5]], "output": [[7]]}, {"input": [[4, 3, 0, 3, 8, 0, 3, 8, 3, 0, 2, 4], [3, 0, 7, 2, 3, 4, 0, 3, 4, 3, 8, 9], [4, 0, 8, 0, 5, 2, 8, 5, 8, 5, 0, 4], [8, 8, 8, 0, 9, 0, 0, 9, 0, 7, 4, 0]], "output": [[7]]}], "input_grid": [[8, 6, 8, 1, 6, 3, 1, 8, 6, 1, 1, 1, 3, 1, 3, 3, 8, 1, 1, 1, 6, 3, 8, 8, 6, 3, 1, 8, 8], [6, 1, 3, 8, 8, 1, 8, 1, 3, 1, 8, 3, 1, 8, 1, 8, 3, 8, 3, 3, 1, 1, 1, 1, 8, 1, 3, 8, 6], [6, 8, 8, 1, 1, 6, 3, 3, 1, 1, 8, 3, 8, 3, 3, 8, 3, 3, 8, 3, 1, 1, 1, 1, 1, 8, 1, 6, 8], [1, 3, 3, 3, 3, 6, 1, 1, 8, 8, 3, 8, 3, 8, 1, 3, 8, 1, 1, 3, 1, 3, 3, 3, 3, 1, 1, 3, 3], [8, 3, 1, 1, 8, 8, 3, 8, 8, 1, 3, 1, 8, 8, 1, 8, 1, 3, 6, 1, 1, 3, 1, 8, 3, 3, 6, 3, 3], [8, 3, 3, 3, 1, 6, 6, 1, 3, 1, 6, 3, 3, 8, 6, 8, 3, 1, 8, 8, 3, 3, 6, 1, 6, 6, 8, 8, 8], [3, 8, 3, 3, 8, 8, 8, 3, 6, 8, 3, 8, 1, 1, 3, 1, 1, 8, 3, 8, 1, 3, 3, 1, 3, 8, 1, 3, 8], [1, 3, 1, 8, 3, 8, 1, 8, 1, 1, 8, 3, 3, 8, 1, 8, 1, 8, 8, 8, 8, 1, 8, 8, 6, 3, 1, 3, 3], [6, 1, 1, 3, 8, 8, 6, 3, 3, 1, 3, 3, 6, 1, 8, 8, 8, 8, 1, 1, 1, 3, 3, 1, 8, 1, 8, 1, 8], [3, 3, 1, 1, 1, 6, 3, 3, 3, 1, 3, 1, 8, 1, 8, 8, 8, 8, 6, 1, 6, 3, 8, 1, 1, 8, 1, 8, 1], [1, 1, 8, 1, 1, 3, 1, 8, 3, 8, 8, 1, 3, 1, 8, 3, 8, 6, 8, 1, 3, 8, 6, 8, 3, 8, 3, 6, 1], [1, 8, 1, 3, 8, 1, 3, 3, 8, 1, 1, 1, 8, 1, 8, 8, 3, 8, 1, 3, 8, 8, 1, 8, 6, 6, 1, 1, 3], [3, 1, 6, 1, 1, 3, 6, 6, 1, 3, 3, 1, 1, 6, 3, 1, 1, 1, 1, 3, 6, 8, 8, 6, 1, 1, 8, 1, 3], [1, 8, 1, 3, 8, 1, 3, 3, 8, 1, 1, 1, 8, 1, 8, 8, 3, 8, 1, 3, 8, 8, 1, 8, 6, 6, 1, 1, 3], [1, 1, 8, 1, 1, 3, 1, 8, 3, 8, 8, 1, 3, 1, 8, 3, 8, 6, 8, 1, 3, 8, 6, 8, 3, 8, 3, 6, 1], [3, 3, 1, 1, 1, 6, 3, 3, 3, 1, 3, 1, 8, 1, 8, 8, 8, 8, 6, 1, 6, 3, 8, 1, 1, 8, 1, 8, 1], [6, 1, 1, 3, 8, 8, 6, 3, 3, 1, 3, 3, 6, 1, 8, 8, 8, 8, 1, 1, 1, 3, 3, 1, 8, 1, 8, 1, 8], [1, 3, 1, 8, 3, 8, 1, 8, 1, 1, 8, 3, 3, 8, 1, 8, 1, 8, 8, 8, 8, 1, 8, 8, 6, 3, 1, 3, 3], [3, 8, 3, 3, 8, 8, 8, 3, 6, 8, 3, 8, 1, 1, 3, 1, 1, 8, 3, 8, 1, 3, 3, 1, 3, 8, 1, 3, 8], [8, 3, 3, 3, 1, 6, 6, 1, 3, 1, 6, 3, 3, 8, 6, 8, 3, 1, 8, 8, 3, 3, 6, 1, 6, 6, 8, 8, 8], [8, 3, 1, 1, 8, 8, 3, 8, 8, 1, 3, 1, 8, 8, 1, 8, 1, 3, 6, 1, 1, 3, 1, 8, 3, 3, 6, 3, 3], [1, 3, 3, 3, 3, 6, 1, 1, 8, 8, 3, 8, 3, 8, 1, 3, 8, 1, 1, 3, 1, 3, 3, 3, 3, 1, 1, 3, 3], [6, 8, 8, 1, 1, 6, 3, 3, 1, 1, 8, 3, 8, 3, 3, 8, 3, 3, 8, 3, 1, 1, 1, 1, 1, 8, 1, 6, 8], [6, 1, 3, 8, 8, 1, 8, 1, 3, 1, 8, 3, 1, 8, 1, 8, 3, 8, 3, 3, 1, 1, 1, 1, 8, 1, 3, 8, 6], [8, 6, 8, 1, 6, 3, 1, 8, 6, 1, 1, 1, 3, 1, 3, 3, 8, 1, 1, 1, 6, 3, 8, 8, 6, 3, 1, 8, 8]], "task_key": "44f52bb0"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 3, 3, 0, 7, 3, 7, 4, 4, 7, 0],\n[0, 3, 0, 5, 4, 4, 5, 7, 7, 5, 5],\n[0, 4, 7, 5, 5, 5, 5, 7, 3, 4, 7],\n[3, 5, 7, 3, 3, 7, 7, 3, 4, 4, 5],\n[7, 4, 5, 3, 4, 4, 3, 5, 3, 4, 3],\n[7, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5],\n[5, 5, 7, 3, 4, 5, 7, 4, 7, 5, 4],\n[5, 4, 4, 3, 5, 4, 7, 4, 7, 7, 7],\n[4, 4, 7, 3, 7, 7, 3, 7, 4, 4, 5],\n[5, 3, 4, 7, 5, 5, 7, 7, 4, 5, 3],\n[3, 5, 7, 3, 7, 5, 5, 7, 5, 4, 5],\n[7, 5, 4, 5, 3, 4, 5, 3, 7, 7, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 3, 3, 0, 7, 3, 7, 4, 4, 7, 0, 0, 7, 4, 4, 7, 3, 7, 0, 3, 3, 4],\n[0, 3, 0, 5, 4, 4, 5, 7, 7, 5, 5, 5, 5, 7, 7, 5, 4, 4, 5, 0, 3, 0],\n[0, 4, 7, 5, 5, 5, 5, 7, 3, 4, 7, 7, 4, 3, 7, 5, 5, 5, 5, 7, 4, 0],\n[3, 5, 7, 3, 3, 7, 7, 3, 4, 4, 5, 5, 4, 4, 3, 7, 7, 3, 3, 7, 5, 3],\n[7, 4, 5, 3, 4, 4, 3, 5, 3, 4, 3, 3, 4, 3, 5, 3, 4, 4, 3, 5, 4, 7],\n[7, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5, 5, 5, 4, 3, 4, 4, 4, 3, 3, 5, 7],\n[5, 5, 7, 3, 4, 5, 7, 4, 7, 5, 4, 4, 5, 7, 4, 7, 5, 4, 3, 7, 5, 5],\n[5, 4, 4, 3, 5, 4, 7, 4, 7, 7, 7, 7, 7, 7, 4, 7, 4, 5, 3, 4, 4, 5],\n[4, 4, 7, 3, 7, 7, 3, 7, 4, 4, 5, 5, 4, 4, 7, 3, 7, 7, 3, 7, 4, 4],\n[5, 3, 4, 7, 5, 5, 7, 7, 4, 5, 3, 3, 5, 4, 7, 7, 5, 5, 7, 4, 3, 5],\n[3, 5, 7, 3, 7, 5, 5, 7, 5, 4, 5, 5, 4, 5, 7, 5, 5, 7, 3, 7, 5, 3],\n[7, 5, 4, 5, 3, 4, 5, 3, 7, 7, 4, 4, 7, 7, 3, 5, 4, 3, 5, 4, 5, 7],\n[7, 5, 4, 5, 3, 4, 5, 3, 7, 7, 4, 4, 7, 7, 3, 5, 4, 3, 5, 4, 5, 7],\n[3, 5, 7, 3, 7, 5, 5, 7, 5, 4, 5, 5, 4, 5, 7, 5, 5, 7, 3, 7, 5, 3],\n[5, 3, 4, 7, 5, 5, 7, 7, 4, 5, 3, 3, 5, 4, 7, 7, 5, 5, 7, 4, 3, 5],\n[4, 4, 7, 3, 7, 7, 3, 7, 4, 4, 5, 5, 4, 4, 7, 3, 7, 7, 3, 7, 4, 4],\n[5, 4, 4, 3, 5, 4, 7, 4, 7, 7, 7, 7, 7, 7, 4, 7, 4, 5, 3, 4, 4, 5],\n[5, 5, 7, 3, 4, 5, 7, 4, 7, 5, 4, 4, 5, 7, 4, 7, 5, 4, 3, 7, 5, 5],\n[7, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5, 5, 5, 4, 3, 4, 4, 4, 3, 3, 5, 7],\n[7, 4, 5, 3, 4, 4, 3, 5, 3, 4, 3, 3, 4, 3, 5, 3, 4, 4, 3, 5, 4, 7],\n[3, 5, 7, 3, 3, 7, 7, 3, 4, 4, 5, 5, 4, 4, 3, 7, 7, 3, 3, 7, 5, 3],\n[0, 4, 7, 5, 5, 5, 5, 7, 3, 4, 7, 7, 4, 3, 7, 5, 5, 5, 5, 7, 4, 0],\n[0, 3, 0, 5, 4, 4, 5, 7, 7, 5, 5, 5, 5, 7, 7, 5, 4, 4, 5, 0, 3, 0],\n[4, 3, 3, 0, 7, 3, 7, 4, 4, 7, 0, 0, 7, 4, 4, 7, 3, 7, 0, 3, 3, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[7, 7, 3, 8, 4, 7, 8, 7],\n[3, 7, 3, 7, 7, 4, 3, 4],\n[7, 7, 8, 7, 7, 8, 7, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 3, 8, 4, 7, 8, 7, 7, 8, 7, 4, 8, 3, 7, 7],\n[3, 7, 3, 7, 7, 4, 3, 4, 4, 3, 4, 7, 7, 3, 7, 3],\n[7, 7, 8, 7, 7, 8, 7, 4, 4, 7, 8, 7, 7, 8, 7, 7],\n[7, 7, 8, 7, 7, 8, 7, 4, 4, 7, 8, 7, 7, 8, 7, 7],\n[3, 7, 3, 7, 7, 4, 3, 4, 4, 3, 4, 7, 7, 3, 7, 3],\n[7, 7, 3, 8, 4, 7, 8, 7, 7, 8, 7, 4, 8, 3, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 2],\n[0, 7],\n[2, 0],\n[7, 2],\n[2, 2],\n[2, 2],\n[2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 2, 2, 7],\n[0, 7, 7, 0],\n[2, 0, 0, 2],\n[7, 2, 2, 7],\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[2, 2, 2, 2],\n[7, 2, 2, 7],\n[2, 0, 0, 2],\n[0, 7, 7, 0],\n[7, 2, 2, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 0, 4, 2, 6, 5, 2, 5],\n[8, 6, 5, 4, 3, 2, 4, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 3, 3, 0, 7, 3, 7, 4, 4, 7, 0], [0, 3, 0, 5, 4, 4, 5, 7, 7, 5, 5], [0, 4, 7, 5, 5, 5, 5, 7, 3, 4, 7], [3, 5, 7, 3, 3, 7, 7, 3, 4, 4, 5], [7, 4, 5, 3, 4, 4, 3, 5, 3, 4, 3], [7, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5], [5, 5, 7, 3, 4, 5, 7, 4, 7, 5, 4], [5, 4, 4, 3, 5, 4, 7, 4, 7, 7, 7], [4, 4, 7, 3, 7, 7, 3, 7, 4, 4, 5], [5, 3, 4, 7, 5, 5, 7, 7, 4, 5, 3], [3, 5, 7, 3, 7, 5, 5, 7, 5, 4, 5], [7, 5, 4, 5, 3, 4, 5, 3, 7, 7, 4]], "output": [[4, 3, 3, 0, 7, 3, 7, 4, 4, 7, 0, 0, 7, 4, 4, 7, 3, 7, 0, 3, 3, 4], [0, 3, 0, 5, 4, 4, 5, 7, 7, 5, 5, 5, 5, 7, 7, 5, 4, 4, 5, 0, 3, 0], [0, 4, 7, 5, 5, 5, 5, 7, 3, 4, 7, 7, 4, 3, 7, 5, 5, 5, 5, 7, 4, 0], [3, 5, 7, 3, 3, 7, 7, 3, 4, 4, 5, 5, 4, 4, 3, 7, 7, 3, 3, 7, 5, 3], [7, 4, 5, 3, 4, 4, 3, 5, 3, 4, 3, 3, 4, 3, 5, 3, 4, 4, 3, 5, 4, 7], [7, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5, 5, 5, 4, 3, 4, 4, 4, 3, 3, 5, 7], [5, 5, 7, 3, 4, 5, 7, 4, 7, 5, 4, 4, 5, 7, 4, 7, 5, 4, 3, 7, 5, 5], [5, 4, 4, 3, 5, 4, 7, 4, 7, 7, 7, 7, 7, 7, 4, 7, 4, 5, 3, 4, 4, 5], [4, 4, 7, 3, 7, 7, 3, 7, 4, 4, 5, 5, 4, 4, 7, 3, 7, 7, 3, 7, 4, 4], [5, 3, 4, 7, 5, 5, 7, 7, 4, 5, 3, 3, 5, 4, 7, 7, 5, 5, 7, 4, 3, 5], [3, 5, 7, 3, 7, 5, 5, 7, 5, 4, 5, 5, 4, 5, 7, 5, 5, 7, 3, 7, 5, 3], [7, 5, 4, 5, 3, 4, 5, 3, 7, 7, 4, 4, 7, 7, 3, 5, 4, 3, 5, 4, 5, 7], [7, 5, 4, 5, 3, 4, 5, 3, 7, 7, 4, 4, 7, 7, 3, 5, 4, 3, 5, 4, 5, 7], [3, 5, 7, 3, 7, 5, 5, 7, 5, 4, 5, 5, 4, 5, 7, 5, 5, 7, 3, 7, 5, 3], [5, 3, 4, 7, 5, 5, 7, 7, 4, 5, 3, 3, 5, 4, 7, 7, 5, 5, 7, 4, 3, 5], [4, 4, 7, 3, 7, 7, 3, 7, 4, 4, 5, 5, 4, 4, 7, 3, 7, 7, 3, 7, 4, 4], [5, 4, 4, 3, 5, 4, 7, 4, 7, 7, 7, 7, 7, 7, 4, 7, 4, 5, 3, 4, 4, 5], [5, 5, 7, 3, 4, 5, 7, 4, 7, 5, 4, 4, 5, 7, 4, 7, 5, 4, 3, 7, 5, 5], [7, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5, 5, 5, 4, 3, 4, 4, 4, 3, 3, 5, 7], [7, 4, 5, 3, 4, 4, 3, 5, 3, 4, 3, 3, 4, 3, 5, 3, 4, 4, 3, 5, 4, 7], [3, 5, 7, 3, 3, 7, 7, 3, 4, 4, 5, 5, 4, 4, 3, 7, 7, 3, 3, 7, 5, 3], [0, 4, 7, 5, 5, 5, 5, 7, 3, 4, 7, 7, 4, 3, 7, 5, 5, 5, 5, 7, 4, 0], [0, 3, 0, 5, 4, 4, 5, 7, 7, 5, 5, 5, 5, 7, 7, 5, 4, 4, 5, 0, 3, 0], [4, 3, 3, 0, 7, 3, 7, 4, 4, 7, 0, 0, 7, 4, 4, 7, 3, 7, 0, 3, 3, 4]]}, {"input": [[7, 7, 3, 8, 4, 7, 8, 7], [3, 7, 3, 7, 7, 4, 3, 4], [7, 7, 8, 7, 7, 8, 7, 4]], "output": [[7, 7, 3, 8, 4, 7, 8, 7, 7, 8, 7, 4, 8, 3, 7, 7], [3, 7, 3, 7, 7, 4, 3, 4, 4, 3, 4, 7, 7, 3, 7, 3], [7, 7, 8, 7, 7, 8, 7, 4, 4, 7, 8, 7, 7, 8, 7, 7], [7, 7, 8, 7, 7, 8, 7, 4, 4, 7, 8, 7, 7, 8, 7, 7], [3, 7, 3, 7, 7, 4, 3, 4, 4, 3, 4, 7, 7, 3, 7, 3], [7, 7, 3, 8, 4, 7, 8, 7, 7, 8, 7, 4, 8, 3, 7, 7]]}, {"input": [[7, 2], [0, 7], [2, 0], [7, 2], [2, 2], [2, 2], [2, 2]], "output": [[7, 2, 2, 7], [0, 7, 7, 0], [2, 0, 0, 2], [7, 2, 2, 7], [2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2], [7, 2, 2, 7], [2, 0, 0, 2], [0, 7, 7, 0], [7, 2, 2, 7]]}], "input_grid": [[6, 0, 4, 2, 6, 5, 2, 5], [8, 6, 5, 4, 3, 2, 4, 2]], "task_key": "67e8384a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[7, 6, 1, 7, 6, 1, 5, 5, 5, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6],\n[6, 6, 8, 6, 6, 8, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 1, 7, 6, 1, 7, 6, 1, 7],\n[5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 1, 7, 6, 1],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 8, 6, 6, 8],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 8, 6, 6, 8, 6, 6, 8],\n[7, 6, 1, 5, 5, 5, 5, 5, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6],\n[6, 6, 8, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[6, 6, 8, 6, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[1, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 7, 6, 1, 7, 6, 1, 7],\n[8, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6],\n[8, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 8, 6],\n[6, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 6, 1, 5, 5, 1, 7, 6, 1],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 5, 5, 5, 8, 5, 5, 8, 6, 6, 8],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6],\n[6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7],\n[8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6],\n[8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6],\n[6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6],\n[6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6],\n[1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7],\n[8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6],\n[8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6],\n[6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8],\n[6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 9, 8, 1, 8, 0, 2, 2, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 2, 2, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 2, 2, 0, 8, 9],\n[1, 8, 0, 8, 9, 2, 2, 2, 1, 1, 0],\n[9, 0, 1, 1, 0, 2, 2, 2, 8, 1, 8],\n[8, 9, 8, 1, 8, 0, 2, 2, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9],\n[2, 2, 2, 2, 2, 8, 1, 8, 0, 8, 9],\n[2, 2, 2, 2, 2, 9, 9, 0, 1, 1, 0],\n[2, 2, 2, 2, 2, 9, 8, 9, 8, 1, 8],\n[2, 2, 2, 2, 2, 0, 8, 9, 9, 9, 0],\n[2, 2, 2, 2, 2, 1, 1, 0, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9],\n[1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0],\n[9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8],\n[8, 2, 2, 1, 8, 0, 8, 9, 9, 9, 0],\n[8, 2, 2, 9, 0, 2, 2, 2, 2, 8, 9],\n[1, 2, 2, 2, 2, 2, 2, 2, 2, 8, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0],\n[2, 2, 2, 2, 2, 9, 8, 9, 8, 1, 8],\n[2, 2, 2, 2, 2, 0, 8, 9, 9, 9, 0],\n[8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 9],\n[1, 2, 2, 2, 2, 2, 2, 2, 2, 8, 9],\n[1, 8, 0, 2, 2, 2, 2, 2, 2, 1, 0],\n[9, 0, 1, 1, 0, 2, 2, 2, 2, 1, 8],\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9],\n[1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0],\n[9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8],\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9],\n[1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0],\n[9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8],\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9],\n[1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0],\n[9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8],\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9],\n[1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0],\n[9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8],\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0],\n[8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9],\n[1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9],\n[1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0],\n[9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8],\n[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 9, 2, 4, 0, 2, 9, 3, 4, 9, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 4, 5, 5, 9, 5, 5, 0, 9, 2, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 0, 4, 6, 4, 0, 4, 5, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 4, 0, 2, 9, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 6, 4, 0, 4, 5, 5, 9, 5, 5, 7, 7, 7, 7, 7, 7, 9],\n[7, 7, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5],\n[5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4],\n[0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 7, 7, 7, 7, 7, 2, 9],\n[4, 0, 2, 9, 3, 7, 7, 0, 4, 6, 4, 7, 7, 7, 7, 7, 5, 5],\n[5, 9, 5, 5, 0, 7, 7, 4, 0, 2, 9, 7, 7, 7, 0, 4, 6, 4],\n[0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5],\n[5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4],\n[0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9],\n[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5],\n[5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4],\n[0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9],\n[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5],\n[5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4],\n[0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9],\n[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5],\n[5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4],\n[0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3],\n[5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4],\n[3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5],\n[4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3],\n[7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4],\n[5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 5, 3, 7],\n[8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 7, 0, 5],\n[2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8],\n[7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 8, 5, 2],\n[3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7],\n[4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3],\n[5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4],\n[3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5],\n[4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3],\n[7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4],\n[5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 5, 3, 7],\n[8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 7, 0, 5],\n[2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8],\n[7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 1, 1, 1, 0, 3, 3, 8, 5, 2],\n[3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1],\n[4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1],\n[5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1],\n[3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7, 8, 1, 1, 1, 1, 1],\n[4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3, 2, 1, 1, 1, 1, 1],\n[7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [7, 6, 1, 7, 6, 1, 5, 5, 5, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6], [6, 6, 8, 6, 6, 8, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6], [6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 1, 7, 6, 1, 7, 6, 1, 7], [5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 1, 7, 6, 1], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 8, 6, 6, 8], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 8, 6, 6, 8, 6, 6, 8], [7, 6, 1, 5, 5, 5, 5, 5, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6], [6, 6, 8, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6], [6, 6, 8, 6, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8, 6, 6], [1, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 7, 6, 1, 7, 6, 1, 7], [8, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8, 6], [8, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 8, 6], [6, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 6, 1, 5, 5, 1, 7, 6, 1], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 5, 5, 5, 8, 5, 5, 8, 6, 6, 8], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 5, 5, 5, 8, 6, 6, 8, 6, 6, 8]], "output": [[6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6], [6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6], [6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6], [1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7], [8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6], [8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6], [6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6], [6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6], [6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6], [1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7], [8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6], [8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6], [6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1, 7, 6, 1], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8], [6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8, 6, 6, 8]]}, {"input": [[8, 9, 8, 1, 8, 0, 2, 2, 9, 9, 0], [8, 9, 9, 9, 0, 1, 2, 2, 9, 8, 9], [1, 0, 9, 8, 9, 8, 2, 2, 0, 8, 9], [1, 8, 0, 8, 9, 2, 2, 2, 1, 1, 0], [9, 0, 1, 1, 0, 2, 2, 2, 8, 1, 8], [8, 9, 8, 1, 8, 0, 2, 2, 9, 9, 0], [8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9], [2, 2, 2, 2, 2, 8, 1, 8, 0, 8, 9], [2, 2, 2, 2, 2, 9, 9, 0, 1, 1, 0], [2, 2, 2, 2, 2, 9, 8, 9, 8, 1, 8], [2, 2, 2, 2, 2, 0, 8, 9, 9, 9, 0], [2, 2, 2, 2, 2, 1, 1, 0, 9, 8, 9], [1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9], [1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0], [9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8], [8, 2, 2, 1, 8, 0, 8, 9, 9, 9, 0], [8, 2, 2, 9, 0, 2, 2, 2, 2, 8, 9], [1, 2, 2, 2, 2, 2, 2, 2, 2, 8, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0], [2, 2, 2, 2, 2, 9, 8, 9, 8, 1, 8], [2, 2, 2, 2, 2, 0, 8, 9, 9, 9, 0], [8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 9], [1, 2, 2, 2, 2, 2, 2, 2, 2, 8, 9], [1, 8, 0, 2, 2, 2, 2, 2, 2, 1, 0], [9, 0, 1, 1, 0, 2, 2, 2, 2, 1, 8], [8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0]], "output": [[8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0], [8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9], [1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9], [1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0], [9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8], [8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0], [8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9], [1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9], [1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0], [9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8], [8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0], [8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9], [1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9], [1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0], [9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8], [8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0], [8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9], [1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9], [1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0], [9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8], [8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0], [8, 9, 9, 9, 0, 1, 1, 0, 9, 8, 9], [1, 0, 9, 8, 9, 8, 1, 8, 0, 8, 9], [1, 8, 0, 8, 9, 9, 9, 0, 1, 1, 0], [9, 0, 1, 1, 0, 9, 8, 9, 8, 1, 8], [8, 9, 8, 1, 8, 0, 8, 9, 9, 9, 0]]}, {"input": [[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 7, 7, 7, 7], [7, 7, 7, 7, 7, 9, 2, 4, 0, 2, 9, 3, 4, 9, 7, 7, 7, 7], [7, 7, 7, 7, 7, 4, 5, 5, 9, 5, 5, 0, 9, 2, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 0, 4, 6, 4, 0, 4, 5, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 4, 0, 2, 9, 7, 7, 7, 7, 7, 7, 7], [7, 7, 6, 4, 0, 4, 5, 5, 9, 5, 5, 7, 7, 7, 7, 7, 7, 9], [7, 7, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5], [5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4], [0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 7, 7, 7, 7, 7, 2, 9], [4, 0, 2, 9, 3, 7, 7, 0, 4, 6, 4, 7, 7, 7, 7, 7, 5, 5], [5, 9, 5, 5, 0, 7, 7, 4, 0, 2, 9, 7, 7, 7, 0, 4, 6, 4], [0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9]], "output": [[4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5], [5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4], [0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9], [4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5], [5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4], [0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9], [4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5], [5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4], [0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9], [4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5], [5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9, 3, 4, 9, 0, 4, 6, 4], [0, 4, 6, 4, 0, 4, 5, 5, 9, 5, 5, 0, 9, 2, 4, 0, 2, 9]]}], "input_grid": [[4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3], [5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4], [3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5], [4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3], [7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4], [5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 5, 3, 7], [8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 7, 0, 5], [2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8], [7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 8, 5, 2], [3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7], [4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3], [5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4], [3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5], [4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3], [7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4], [5, 2, 4, 3, 7, 8, 7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 5, 3, 7], [8, 0, 3, 2, 4, 7, 3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 7, 0, 5], [2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 2, 3, 8], [7, 8, 2, 0, 2, 5, 5, 4, 4, 7, 1, 1, 1, 0, 3, 3, 8, 5, 2], [3, 2, 0, 8, 7, 0, 3, 4, 7, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1], [4, 3, 3, 4, 4, 8, 4, 0, 2, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1], [5, 4, 4, 7, 5, 3, 7, 0, 3, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1], [3, 4, 7, 3, 7, 0, 5, 2, 4, 3, 7, 8, 7, 8, 1, 1, 1, 1, 1], [4, 0, 2, 3, 2, 3, 8, 0, 3, 2, 4, 7, 3, 2, 1, 1, 1, 1, 1], [7, 0, 3, 3, 8, 5, 2, 7, 8, 8, 5, 3, 4, 3, 3, 4, 4, 8, 4]], "task_key": "484b58aa"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 6, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 5, 5, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 5, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 6, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6],\n[4, 4, 4, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 6, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 5, 5, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 5, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5]]}], "input_grid": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 6, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6], [4, 4, 4, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "3618c87e"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[2, 2, 2, 2, 2, 5],\n[2, 2, 2, 2, 2, 3],\n[2, 2, 2, 2, 2, 1],\n[2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 1],\n[2, 2, 2, 2, 2, 4],\n[2, 2, 2, 2, 2, 5],\n[2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 5],\n[2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 1],\n[0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[5, 5, 5, 5, 5, 5],\n[3, 3, 3, 3, 3, 3],\n[1, 1, 1, 1, 1, 1],\n[8, 8, 8, 8, 8, 8],\n[1, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 4],\n[5, 5, 5, 5, 5, 5],\n[9, 9, 9, 9, 9, 9],\n[5, 5, 5, 5, 5, 5],\n[8, 8, 8, 8, 8, 8],\n[1, 1, 1, 1, 1, 1],\n[0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 9, 3, 4, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 9, 3, 4, 0],\n[0, 0, 0, 7, 3, 7, 0, 0, 9, 7, 9, 3, 4, 0],\n[0, 0, 0, 7, 3, 7, 0, 0, 9, 7, 9, 3, 4, 0],\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0],\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0],\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 0, 0, 0, 0, 0],\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 0, 0, 0, 0, 0],\n[8, 6, 6, 7, 3, 7, 2, 6, 9, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0],\n[0, 0, 6, 7, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0],\n[0, 0, 6, 7, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[1, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[8, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0],\n[9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 4], [2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 1], [0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5], [3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4], [5, 5, 5, 5, 5, 5], [9, 9, 9, 9, 9, 9], [5, 5, 5, 5, 5, 5], [8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]]}, {"input": [[8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]], "output": [[8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 9, 3, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 9, 3, 4, 0], [0, 0, 0, 7, 3, 7, 0, 0, 9, 7, 9, 3, 4, 0], [0, 0, 0, 7, 3, 7, 0, 0, 9, 7, 9, 3, 4, 0], [8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0], [8, 6, 6, 7, 3, 7, 2, 6, 9, 7, 9, 3, 4, 0], [8, 6, 6, 7, 3, 7, 2, 6, 9, 0, 0, 0, 0, 0], [8, 6, 6, 7, 3, 7, 2, 6, 9, 0, 0, 0, 0, 0], [8, 6, 6, 7, 3, 7, 2, 6, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0], [0, 0, 6, 7, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0], [0, 0, 6, 7, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3], [6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [1, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [8, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0]], "task_key": "c9f8e694"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[6, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 0, 0, 4],\n[0, 0, 0, 0, 0],\n[0, 0, 2, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5],\n[5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 6, 6, 6],\n[6, 9, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9],\n[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 6, 6],\n[0, 6, 6],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7],\n[5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [6, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[6, 6, 0, 0, 4], [0, 0, 0, 0, 0], [0, 0, 2, 0, 0]]}, {"input": [[5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5], [5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5, 9, 9, 9, 9, 5]], "output": [[9, 6, 6, 6], [6, 9, 9, 9]]}, {"input": [[0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9], [0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 0], [9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9]], "output": [[0, 6, 6], [0, 6, 6], [0, 0, 0], [0, 0, 0], [0, 0, 0]]}], "input_grid": [[7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7], [5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5]], "task_key": "7837ac64"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 9, 5, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 0, 5, 0, 5, 5, 5, 5, 5, 5, 0, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 5, 5, 5, 0, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5],\n[5, 0, 5, 0, 0, 0, 5, 5, 5, 5, 5, 9, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 5, 5, 0, 0, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 5, 5, 5, 0, 5, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 0, 5, 5, 5, 0, 0, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5],\n[5, 5, 0, 5, 5, 5, 0, 0, 5, 5, 0, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 9, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5],\n[0, 5, 0, 5, 5, 5, 5, 0, 0, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 9, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0],\n[5, 0, 5, 5, 5, 5, 5, 5, 0, 5, 0, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 0, 5, 5, 0, 0, 0, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 5, 5, 5, 0, 0, 0, 5, 5, 9, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 0, 0, 0, 5, 0, 0, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0],\n[3, 3, 0, 3, 0, 0, 0, 0, 0, 0, 3],\n[0, 3, 0, 0, 0, 0, 3, 0, 3, 3, 0],\n[0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0],\n[0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0],\n[0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0],\n[0, 0, 3, 0, 0, 0, 3, 3, 0, 0, 3],\n[3, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0],\n[0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 3],\n[0, 0, 3, 0, 0, 3, 3, 3, 0, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0],\n[3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0],\n[0, 0, 3, 3, 3, 0, 3, 3, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 0, 6, 0, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[6, 0, 6, 0, 6, 0, 6, 0, 0, 0, 6, 6, 6, 0, 0],\n[6, 6, 0, 0, 0, 6, 6, 0, 6, 0, 0, 6, 0, 0, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0],\n[4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0],\n[0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 0, 3, 0, 3, 0, 0, 3, 3, 3, 3, 3, 0, 3],\n[0, 0, 3, 0, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 0],\n[3, 3, 0, 0, 3, 0, 3, 0, 3, 0, 3, 3, 0, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 0, 6, 6, 0, 6, 0, 6, 6, 6, 6, 0],\n[0, 0, 6, 6, 6, 6, 6, 6, 0, 6, 0, 0],\n[0, 6, 0, 6, 6, 6, 6, 0, 0, 6, 6, 0],\n[0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6],\n[0, 6, 6, 0, 0, 0, 6, 0, 0, 6, 0, 6],\n[6, 6, 6, 6, 0, 0, 0, 6, 6, 0, 6, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0, 5],\n[5, 5, 5, 5, 0, 5, 5, 0, 5, 0, 5, 5],\n[5, 0, 5, 0, 5, 0, 5, 5, 5, 0, 5, 5],\n[0, 5, 5, 0, 5, 5, 5, 5, 0, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 3, 0, 3, 3, 3, 3, 0, 0, 0, 0, 3],\n[3, 0, 0, 3, 0, 3, 0, 0, 3, 0, 3, 3],\n[3, 3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3],\n[3, 0, 0, 0, 3, 0, 3, 3, 0, 3, 0, 0],\n[3, 3, 0, 0, 3, 0, 0, 3, 3, 3, 3, 0],\n[3, 0, 0, 3, 3, 3, 3, 0, 3, 3, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 5, 0, 5],\n[5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 0, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 5, 5, 5],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 9, 5, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 5, 0, 5, 5, 5, 5, 5, 5, 0, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 0, 5, 5, 5, 5, 0, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5], [5, 0, 5, 0, 0, 0, 5, 5, 5, 5, 5, 9, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 0, 5, 5, 5, 0, 0, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 0, 5, 5, 5, 5, 0, 5, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 0, 5, 5, 5, 0, 0, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5], [5, 5, 0, 5, 5, 5, 0, 0, 5, 5, 0, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 9, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5], [0, 5, 0, 5, 5, 5, 5, 0, 0, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 9, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0], [5, 0, 5, 5, 5, 5, 5, 5, 0, 5, 0, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 0, 5, 5, 0, 0, 0, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 0, 5, 5, 5, 5, 0, 0, 0, 5, 5, 9, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 0, 0, 0, 5, 0, 0, 5, 0, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5]], "output": [[0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0], [3, 3, 0, 3, 0, 0, 0, 0, 0, 0, 3], [0, 3, 0, 0, 0, 0, 3, 0, 3, 3, 0], [0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0, 3, 3, 0, 0, 3], [3, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 3], [0, 0, 3, 0, 0, 3, 3, 3, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [0, 0, 3, 3, 3, 0, 3, 3, 0, 0, 0]]}, {"input": [[6, 6, 0, 6, 0, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6], [6, 0, 6, 0, 6, 0, 6, 0, 0, 0, 6, 6, 6, 0, 0], [6, 6, 0, 0, 0, 6, 6, 0, 6, 0, 0, 6, 0, 0, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0], [4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0]], "output": [[3, 3, 0, 3, 0, 3, 0, 0, 3, 3, 3, 3, 3, 0, 3], [0, 0, 3, 0, 0, 0, 3, 0, 0, 3, 3, 3, 0, 0, 0], [3, 3, 0, 0, 3, 0, 3, 0, 3, 0, 3, 3, 0, 3, 3]]}, {"input": [[6, 0, 6, 6, 0, 6, 0, 6, 6, 6, 6, 0], [0, 0, 6, 6, 6, 6, 6, 6, 0, 6, 0, 0], [0, 6, 0, 6, 6, 6, 6, 0, 0, 6, 6, 0], [0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 6, 6, 0, 0, 0, 6, 0, 0, 6, 0, 6], [6, 6, 6, 6, 0, 0, 0, 6, 6, 0, 6, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5], [5, 0, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5], [5, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0, 5], [5, 5, 5, 5, 0, 5, 5, 0, 5, 0, 5, 5], [5, 0, 5, 0, 5, 0, 5, 5, 5, 0, 5, 5], [0, 5, 5, 0, 5, 5, 5, 5, 0, 5, 5, 5]], "output": [[0, 3, 0, 3, 3, 3, 3, 0, 0, 0, 0, 3], [3, 0, 0, 3, 0, 3, 0, 0, 3, 0, 3, 3], [3, 3, 3, 0, 3, 0, 0, 3, 0, 0, 3, 3], [3, 0, 0, 0, 3, 0, 3, 3, 0, 3, 0, 0], [3, 3, 0, 0, 3, 0, 0, 3, 3, 3, 3, 0], [3, 0, 0, 3, 3, 3, 3, 0, 3, 3, 0, 0]]}], "input_grid": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 5, 0, 5], [5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5], [5, 0, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 5, 5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 0, 8, 8, 8, 8, 8]], "task_key": "3428a4f5"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 2, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 2, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 2, 2, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 1, 2, 2, 1, 6, 2, 2, 2, 2, 2, 6, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 6, 2, 2, 2, 2, 2, 6, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 2, 2, 6, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 8, 8, 0],\n[3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0],\n[3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 2, 2, 2, 2, 9, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 6, 2, 2, 2, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 4, 2, 2, 2, 2, 2, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 2, 2, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 2, 2, 2, 2, 2, 3, 7, 2, 2, 2, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 2, 2, 2, 2, 2, 3, 7, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 8, 8, 0],\n[3, 2, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, 2, 2, 8, 0],\n[3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7],\n[7, 6, 2, 2, 2, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7],\n[7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7],\n[7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7],\n[7, 7, 7, 0, 2, 2, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7],\n[7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 1],\n[1, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 1],\n[1, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 1],\n[1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1],\n[1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1],\n[1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1],\n[1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 2, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 2, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 2, 2, 1, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 1, 2, 2, 1, 6, 2, 2, 2, 2, 2, 6, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 6, 2, 2, 2, 2, 2, 6, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 6, 2, 2, 2, 2, 2, 6, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 8, 8, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 2, 2, 2, 2, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 2, 2, 2, 6, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 4, 2, 2, 2, 2, 2, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 2, 2, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 2, 2, 2, 2, 2, 3, 7, 2, 2, 2, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 2, 2, 2, 2, 2, 3, 7, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 8, 8, 0], [3, 2, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, 2, 2, 8, 0], [3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7], [7, 6, 2, 2, 2, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7], [7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7], [7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 2, 2, 2, 2, 4, 7, 7, 7, 7], [7, 7, 7, 0, 2, 2, 0, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [7, 7, 7, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}], "input_grid": [[1, 1, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 1], [1, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 1], [1, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 1], [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1], [1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1], [1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1], [1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1], [1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1], [1, 1, 1, 4, 4, 4, 4, 4, 8, 8, 8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "task_key": "bb43febb"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 7, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 4, 7, 4, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 7, 7, 4, 7, 7, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 4, 7, 4, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 7, 3, 3, 3, 3, 0, 0, 4, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 4, 7, 4, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 4, 7, 7, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 4, 7, 4, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 2, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 5, 6, 5, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 5, 2, 6, 6, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 6, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 5, 6, 5, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 5, 2, 6, 6, 6, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 5, 5, 5, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 4, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 4, 5, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 7, 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[8, 8, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 8, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 8, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 7, 8, 7, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 8, 8, 8, 8, 4, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 7, 8, 7, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 5, 5, 5, 8, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 8, 5, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 7, 8, 7, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 4, 8, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 7, 8, 7, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 8, 5, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 7, 8, 7, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 7, 8, 7, 5, 5, 5, 5, 5, 5, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 2, 2, 2, 1, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 1, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 7, 1, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 7, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 4, 7, 4, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 7, 7, 4, 7, 7, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 4, 7, 4, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 7, 3, 3, 3, 3, 0, 0, 4, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 4, 7, 4, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 4, 7, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 4, 7, 4, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 7, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 2, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 5, 6, 5, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 5, 2, 6, 6, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 6, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 5, 6, 5, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 5, 2, 6, 6, 6, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 5, 5, 5, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 4, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 4, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5], [0, 7, 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 8, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 8, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 7, 8, 7, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 8, 8, 8, 4, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 7, 8, 7, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 5, 5, 5, 8, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 8, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 7, 8, 7, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 4, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 7, 8, 7, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 8, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 7, 8, 7, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 7, 8, 7, 5, 5, 5, 5, 5, 5, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 2, 2, 2, 1, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 1, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 7, 1, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "264363fd"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 1, 1, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 1, 1, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 6]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9],\n[6, 6, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 1, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 6, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 6, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 1, 1, 9, 9, 9, 9],\n[9, 9, 9, 6, 6, 6, 1, 1, 9, 9, 9, 9],\n[9, 9, 9, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[1, 9, 9, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6],\n[1, 1, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6],\n[3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6],\n[3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 1, 1, 6, 6, 6, 6, 3, 3, 6, 6, 3, 3],\n[6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 3, 3, 6, 6, 3, 3],\n[6, 1, 1, 3, 6, 6, 6, 1, 1, 3, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 3, 1, 6, 6, 1, 1, 3, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 1, 6, 6, 6],\n[6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 3, 3, 3, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6],\n[1, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 1, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 1, 6, 6, 6, 6, 6],\n[6, 6, 6, 3, 3, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 1],\n[6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 3, 6, 1],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 1, 1, 6, 6, 6, 3, 3, 6, 6, 6, 1],\n[6, 3, 1, 6, 6, 6, 6, 6, 1, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 1, 6, 6, 6, 6, 6, 1, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6],\n[6, 6, 1, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 3, 1],\n[6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 1, 1, 6, 6, 6, 3, 1, 1, 1, 6, 6, 6, 6, 6, 3, 1],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 3, 1, 1, 1, 6, 6, 6, 6, 6, 3, 1],\n[3, 3, 3, 6, 6, 6, 3, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 1, 6, 3, 3, 3, 1, 6, 6, 3, 3, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 1, 6, 3, 3, 3, 1, 6, 6, 1, 1, 1, 6],\n[6, 1, 1, 6, 6, 6, 1, 1, 1, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 6, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0, 0, 8, 8, 8, 0, 0, 0, 8, 8, 1, 1, 1],\n[0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 8, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 1, 1, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6], [6, 1, 1, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[1, 1, 1, 1, 6]]}, {"input": [[6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9], [6, 6, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 1, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 6, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 6, 9, 9, 9], [9, 9, 9, 1, 9, 9, 1, 1, 9, 9, 9, 9], [9, 9, 9, 6, 6, 6, 1, 1, 9, 9, 9, 9], [9, 9, 9, 6, 6, 6, 9, 9, 9, 9, 9, 9], [1, 9, 9, 6, 6, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6], [1, 1, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[1, 1, 1, 9, 9]]}, {"input": [[3, 3, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6], [3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6], [3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 1, 1, 6, 6, 6, 6, 3, 3, 6, 6, 3, 3], [6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 3, 3, 6, 6, 3, 3], [6, 1, 1, 3, 6, 6, 6, 1, 1, 3, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 3, 1, 6, 6, 1, 1, 3, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 1, 6, 6, 6], [6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 3, 3, 3, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6], [1, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 1, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 1, 6, 6, 6, 6, 6], [6, 6, 6, 3, 3, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 1], [6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 3, 6, 1], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 1, 1, 6, 6, 6, 3, 3, 6, 6, 6, 1], [6, 3, 1, 6, 6, 6, 6, 6, 1, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 1, 6, 6, 6, 6, 6, 1, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6], [6, 6, 1, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 3, 1], [6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 1, 1, 6, 6, 6, 3, 1, 1, 1, 6, 6, 6, 6, 6, 3, 1], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 3, 1, 1, 1, 6, 6, 6, 6, 6, 3, 1], [3, 3, 3, 6, 6, 6, 3, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 6, 6], [6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 1, 6, 3, 3, 3, 1, 6, 6, 3, 3, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 1, 6, 3, 3, 3, 1, 6, 6, 1, 1, 1, 6], [6, 1, 1, 6, 6, 6, 1, 1, 1, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6]], "output": [[1, 1, 1, 6, 6]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 1, 1, 1, 0, 0, 8, 8, 8, 0, 0, 0, 8, 8, 1, 1, 1], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "1fad071e"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0],\n[0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0],\n[0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0],\n[0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9],\n[0, 0, 0],\n[0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4],\n[4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4],\n[4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4],\n[4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4],\n[4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4],\n[4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4],\n[4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 4],\n[4, 4, 4],\n[4, 4, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5],\n[3, 3, 5],\n[3, 3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6],\n[6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 6, 6, 6],\n[6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 6, 6, 6],\n[6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6],\n[6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6],\n[6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 9, 9, 9, 9, 9, 9, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[9, 9, 9], [0, 0, 0], [0, 0, 0]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4], [4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4], [4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4], [4, 4, 4, 4, 4, 4, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 4], [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[7, 7, 4], [4, 4, 4], [4, 4, 4]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3]], "output": [[5, 5, 5], [3, 3, 5], [3, 3, 3]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6], [6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 6, 6, 6], [6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 6, 6, 6], [6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6], [6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6], [6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "b0c4d837"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 2, 2],\n[2, 7, 6, 6, 6, 6, 6, 6, 7, 7, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 7, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 7, 2, 7, 7],\n[2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 7, 2, 7, 2, 7],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 7, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 7, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 7, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 7, 6, 6, 6, 6, 6, 6, 2, 7, 7, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2],\n[2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3],\n[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[3, 3, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 3, 3],\n[2, 3, 3, 9, 9, 2, 2, 2],\n[3, 2, 2, 9, 9, 2, 2, 2],\n[2, 3, 2, 9, 9, 2, 3, 3],\n[3, 2, 3, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 3, 3, 2],\n[2, 2, 2, 9, 9, 2, 3, 2],\n[2, 2, 2, 9, 9, 3, 2, 3],\n[2, 2, 2, 9, 9, 2, 3, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 3, 2, 3],\n[2, 2, 2, 9, 9, 2, 3, 3],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[3, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 3, 3, 2],\n[2, 3, 3, 9, 9, 2, 2, 2],\n[3, 2, 3, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 3, 2, 3],\n[2, 3, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[3, 3, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 9, 9, 9, 2, 2, 2],\n[2, 2, 9, 9, 9, 9, 9, 2],\n[2, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 2, 2, 9, 9, 9, 2, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 2, 2, 9, 9, 9, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 2, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 9, 9, 9, 9, 2, 2, 2],\n[2, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 9, 9, 2],\n[2, 2, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2],\n[2, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 9, 9, 2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 2, 2, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 2, 2, 8, 8, 8, 2, 4, 4, 4, 2],\n[2, 4, 2, 2, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 2, 2], [2, 7, 6, 6, 6, 6, 6, 6, 7, 7, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 7, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 7, 2, 7, 7], [2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 7, 2, 7, 2, 7], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 7, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 7, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 7, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 7, 6, 6, 6, 6, 6, 6, 2, 7, 7, 2, 2]], "output": [[2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2], [2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2]]}, {"input": [[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3]], "output": [[3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3], [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3]]}, {"input": [[3, 2, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [3, 3, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 3, 3], [2, 3, 3, 9, 9, 2, 2, 2], [3, 2, 2, 9, 9, 2, 2, 2], [2, 3, 2, 9, 9, 2, 3, 3], [3, 2, 3, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 3, 3, 2], [2, 2, 2, 9, 9, 2, 3, 2], [2, 2, 2, 9, 9, 3, 2, 3], [2, 2, 2, 9, 9, 2, 3, 2], [2, 2, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 3, 2, 3], [2, 2, 2, 9, 9, 2, 3, 3], [2, 2, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [3, 2, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 3, 3, 2], [2, 3, 3, 9, 9, 2, 2, 2], [3, 2, 3, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 3, 2, 3], [2, 3, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [3, 3, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2]], "output": [[2, 2, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [2, 9, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 9, 9, 9, 9, 2, 2, 2], [2, 2, 9, 9, 9, 2, 2, 2], [2, 2, 9, 9, 9, 9, 9, 2], [2, 9, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 2, 2, 9, 9, 9, 2, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 2, 2, 9, 9, 9, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 2, 2, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [2, 2, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 9, 9, 9, 9, 2, 2, 2], [2, 9, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 9, 9, 2], [2, 2, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2], [2, 9, 9, 9, 9, 2, 2, 2], [2, 2, 2, 9, 9, 2, 2, 2]]}], "input_grid": [[4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 2, 2, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 2, 2, 8, 8, 8, 2, 4, 4, 4, 2], [2, 4, 2, 2, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 8, 8, 4, 4, 4, 4, 4]], "task_key": "4093f84a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 8, 9, 9, 9, 4, 4, 9, 8, 8, 8, 8, 9, 7, 9, 9, 9, 9, 5, 5, 5],\n[7, 7, 7, 9, 9, 9, 9, 4, 4, 4, 9, 8, 8, 9, 8, 9, 7, 9, 9, 9, 9, 5, 5, 9],\n[7, 7, 9, 9, 8, 9, 9, 4, 4, 4, 9, 8, 8, 8, 8, 9, 7, 7, 9, 9, 5, 5, 5, 9],\n[7, 9, 9, 9, 8, 8, 9, 4, 4, 9, 9, 8, 8, 8, 8, 9, 7, 7, 9, 9, 5, 5, 5, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[0, 9, 9, 9, 9, 8, 9, 9, 1, 1, 9, 0, 9, 0, 0, 9, 1, 1, 9, 9, 9, 8, 8, 8],\n[0, 0, 0, 9, 8, 8, 9, 1, 1, 1, 9, 9, 0, 9, 0, 9, 1, 1, 1, 9, 9, 8, 8, 8],\n[0, 0, 0, 9, 8, 8, 9, 1, 1, 1, 9, 0, 0, 0, 9, 9, 1, 1, 9, 9, 9, 8, 8, 8],\n[0, 0, 0, 9, 9, 9, 9, 1, 1, 1, 9, 0, 9, 0, 0, 9, 1, 1, 1, 9, 8, 8, 8, 8],\n[0, 0, 9, 9, 8, 8, 9, 1, 1, 1, 9, 0, 9, 9, 0, 9, 1, 1, 9, 9, 8, 8, 9, 8],\n[0, 0, 9, 9, 9, 8, 9, 1, 1, 1, 9, 0, 9, 9, 0, 9, 1, 1, 9, 9, 9, 8, 8, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[7, 9, 7, 9, 5, 5, 9, 9, 9, 0, 9, 9, 9, 5, 9, 9, 4, 4, 9, 9, 9, 8, 8, 8],\n[9, 7, 7, 9, 9, 5, 9, 0, 0, 0, 9, 5, 5, 5, 5, 9, 4, 9, 4, 9, 9, 8, 8, 8],\n[9, 9, 7, 9, 9, 9, 9, 0, 0, 0, 9, 5, 5, 9, 5, 9, 4, 9, 4, 9, 8, 9, 8, 8],\n[7, 7, 7, 9, 5, 9, 9, 0, 0, 0, 9, 5, 5, 5, 5, 9, 9, 9, 4, 9, 8, 8, 9, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 5, 5, 9, 7, 7, 9, 4, 9, 4, 9, 1, 1, 1, 1, 9, 1, 1, 1, 9, 6, 9, 6, 6],\n[5, 9, 5, 9, 9, 7, 9, 4, 4, 9, 9, 1, 1, 9, 1, 9, 1, 9, 9, 9, 9, 6, 6, 6],\n[5, 5, 9, 9, 9, 7, 9, 9, 4, 4, 9, 1, 1, 1, 1, 9, 1, 1, 9, 9, 6, 6, 9, 6],\n[5, 9, 9, 9, 7, 7, 9, 4, 4, 4, 9, 1, 1, 1, 9, 9, 1, 9, 1, 9, 6, 9, 6, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 7, 9, 0, 0, 9, 1, 1, 1, 9, 9, 4, 9, 9, 9, 5, 5, 5, 9, 0, 0, 0, 0],\n[7, 7, 9, 9, 0, 0, 9, 1, 9, 1, 9, 4, 4, 9, 9, 9, 9, 9, 5, 9, 9, 0, 0, 0],\n[9, 7, 7, 9, 9, 9, 9, 1, 1, 1, 9, 4, 4, 4, 4, 9, 9, 5, 5, 9, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 8, 4, 8, 7, 5],\n[0, 8, 1, 0, 1, 8],\n[7, 5, 0, 5, 4, 8],\n[5, 7, 4, 1, 1, 6],\n[7, 0, 1, 4, 5, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[1, 6, 1, 6, 6, 8, 8, 8, 8, 8, 6, 8, 6, 6, 6, 0, 0, 0, 0, 0, 6, 6, 1, 1, 1, 6],\n[1, 1, 1, 6, 6, 8, 8, 6, 6, 8, 8, 8, 6, 8, 6, 6, 6, 0, 0, 0, 6, 6, 1, 6, 6, 6],\n[1, 1, 1, 6, 6, 6, 8, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 1, 6, 1],\n[1, 1, 6, 6, 6, 8, 6, 8, 8, 8, 8, 8, 8, 6, 6, 0, 0, 0, 0, 0, 6, 6, 1, 6, 1, 1],\n[1, 1, 1, 6, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 6, 0, 6, 0, 0, 0, 0, 6, 1, 1, 6, 1],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 0, 0, 6, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 6, 5, 6, 6, 6, 6, 5, 6, 8, 8, 8, 6],\n[0, 0, 6, 6, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 5, 5, 5, 6, 6, 8, 8, 8, 8],\n[0, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 5, 6, 5, 6, 5, 6, 8, 8, 8, 6],\n[0, 0, 0, 6, 6, 8, 8, 6, 8, 8, 8, 8, 8, 8, 6, 5, 5, 5, 5, 5, 6, 6, 8, 8, 8, 8],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 0, 6, 6, 6, 5, 5, 6, 5, 5, 5, 5, 5, 6, 6, 6, 5, 6, 5, 5, 5, 6, 6, 6, 8, 8],\n[0, 0, 0, 6, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 8, 8, 6],\n[0, 0, 0, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 8, 6],\n[0, 0, 6, 6, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 6, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 8, 0, 1],\n[0, 8, 5, 8],\n[0, 5, 5, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 1, 8, 8, 8, 1, 9, 9, 9, 1, 5, 5, 5, 1, 5, 5, 1, 1, 1, 8, 1, 9, 9, 1, 1, 1, 0, 1, 0],\n[8, 8, 8, 1, 8, 1, 9, 9, 9, 1, 5, 5, 1, 5, 5, 5, 1, 8, 8, 1, 1, 9, 9, 1, 0, 0, 1, 0, 0],\n[8, 8, 8, 8, 8, 1, 9, 9, 1, 1, 5, 5, 5, 5, 1, 5, 1, 8, 8, 8, 1, 9, 9, 1, 0, 0, 0, 0, 1],\n[8, 8, 8, 8, 8, 1, 9, 1, 9, 1, 5, 1, 5, 5, 5, 5, 1, 8, 8, 8, 1, 9, 9, 1, 1, 0, 0, 0, 1],\n[8, 1, 8, 8, 8, 1, 9, 9, 9, 1, 1, 5, 5, 1, 5, 5, 1, 8, 8, 8, 1, 9, 1, 1, 1, 0, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 1, 9, 9, 1, 9, 9, 1, 5, 1, 1, 1, 5, 5, 1, 9, 1, 9, 9, 1],\n[0, 0, 0, 0, 0, 1, 5, 1, 1, 1, 9, 9, 1, 9, 9, 1, 1, 5, 1, 5, 1, 5, 5, 1, 1, 1, 9, 9, 9],\n[0, 1, 1, 0, 1, 1, 1, 5, 1, 1, 9, 9, 1, 9, 9, 9, 1, 1, 5, 5, 1, 1, 1, 1, 1, 9, 9, 1, 9],\n[1, 0, 0, 0, 1, 1, 1, 5, 5, 1, 9, 9, 9, 1, 1, 9, 1, 5, 1, 5, 1, 5, 5, 1, 9, 9, 9, 1, 9],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[8, 8, 1, 1, 8, 1, 4, 4, 4, 1, 9, 9, 9, 9, 9, 1, 1, 1, 0, 0, 1, 1, 7, 1, 8, 8, 8, 8, 1],\n[8, 1, 8, 1, 8, 1, 4, 4, 4, 1, 9, 9, 9, 9, 9, 9, 1, 0, 0, 0, 1, 7, 7, 1, 8, 8, 8, 8, 8],\n[1, 8, 8, 8, 8, 1, 4, 4, 4, 1, 1, 9, 9, 9, 9, 9, 1, 0, 0, 0, 1, 7, 1, 1, 8, 8, 8, 8, 8],\n[8, 1, 1, 8, 1, 1, 1, 1, 1, 1, 9, 9, 1, 1, 9, 9, 1, 1, 0, 1, 1, 1, 7, 1, 8, 8, 1, 8, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 4, 4, 4, 1, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 9, 9, 9, 1, 9, 9, 1, 1, 9, 9, 9, 9],\n[4, 1, 4, 4, 4, 1, 1, 0, 1, 1, 8, 8, 8, 8, 8, 8, 1, 9, 9, 9, 1, 1, 1, 1, 1, 9, 1, 9, 9],\n[4, 4, 4, 1, 4, 1, 1, 0, 0, 1, 8, 8, 8, 1, 8, 8, 1, 1, 9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[8, 8, 8, 8, 8, 1, 1, 4, 4, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 4, 1, 1, 0, 1, 1, 0, 0],\n[8, 8, 1, 8, 8, 1, 1, 1, 4, 1, 0, 0, 1, 0, 1, 0, 1, 9, 9, 1, 1, 4, 1, 1, 0, 0, 1, 0, 0],\n[8, 8, 8, 8, 8, 1, 4, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 9, 9, 9, 1, 4, 4, 1, 0, 1, 0, 0, 0],\n[8, 8, 8, 8, 8, 1, 1, 4, 1, 1, 1, 1, 0, 0, 0, 0, 1, 9, 9, 9, 1, 4, 1, 1, 0, 1, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 9, 5, 8, 9, 0],\n[0, 5, 9, 5, 5, 9],\n[8, 4, 9, 0, 7, 8],\n[4, 0, 8, 9, 9, 9],\n[8, 4, 0, 9, 4, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 5, 5, 5, 5, 8, 5, 8, 1, 8, 1],\n[8, 5, 5, 8, 5, 8, 5, 8, 8, 1, 8],\n[5, 5, 5, 5, 5, 5, 8, 8, 1, 1, 1],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[3, 3, 3, 3, 3, 3, 3, 8, 1, 1, 1],\n[3, 3, 3, 3, 3, 3, 3, 8, 8, 1, 1],\n[8, 8, 3, 3, 3, 3, 3, 8, 1, 1, 8],\n[3, 3, 3, 3, 3, 8, 3, 8, 8, 1, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[1, 1, 1, 1, 1, 1, 1, 8, 5, 5, 5],\n[8, 1, 1, 1, 1, 8, 1, 8, 5, 8, 5],\n[8, 1, 1, 1, 1, 8, 1, 8, 5, 5, 5],\n[1, 1, 1, 1, 8, 1, 1, 8, 5, 5, 5],\n[1, 1, 1, 1, 8, 1, 1, 8, 5, 8, 5],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[7, 7, 7, 7, 8, 7, 8, 8, 3, 3, 8],\n[8, 7, 7, 8, 7, 8, 7, 8, 8, 8, 8],\n[7, 7, 7, 7, 7, 7, 7, 8, 3, 8, 3],\n[7, 8, 7, 7, 7, 8, 7, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[5, 8, 5, 5, 5, 5, 5, 8, 8, 8, 6],\n[5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 6],\n[8, 5, 8, 5, 5, 5, 5, 8, 6, 6, 8],\n[8, 5, 5, 5, 5, 5, 5, 8, 6, 6, 6],\n[8, 5, 5, 5, 5, 8, 5, 8, 6, 8, 8],\n[5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 8, 9, 9, 9, 4, 4, 9, 8, 8, 8, 8, 9, 7, 9, 9, 9, 9, 5, 5, 5], [7, 7, 7, 9, 9, 9, 9, 4, 4, 4, 9, 8, 8, 9, 8, 9, 7, 9, 9, 9, 9, 5, 5, 9], [7, 7, 9, 9, 8, 9, 9, 4, 4, 4, 9, 8, 8, 8, 8, 9, 7, 7, 9, 9, 5, 5, 5, 9], [7, 9, 9, 9, 8, 8, 9, 4, 4, 9, 9, 8, 8, 8, 8, 9, 7, 7, 9, 9, 5, 5, 5, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [0, 9, 9, 9, 9, 8, 9, 9, 1, 1, 9, 0, 9, 0, 0, 9, 1, 1, 9, 9, 9, 8, 8, 8], [0, 0, 0, 9, 8, 8, 9, 1, 1, 1, 9, 9, 0, 9, 0, 9, 1, 1, 1, 9, 9, 8, 8, 8], [0, 0, 0, 9, 8, 8, 9, 1, 1, 1, 9, 0, 0, 0, 9, 9, 1, 1, 9, 9, 9, 8, 8, 8], [0, 0, 0, 9, 9, 9, 9, 1, 1, 1, 9, 0, 9, 0, 0, 9, 1, 1, 1, 9, 8, 8, 8, 8], [0, 0, 9, 9, 8, 8, 9, 1, 1, 1, 9, 0, 9, 9, 0, 9, 1, 1, 9, 9, 8, 8, 9, 8], [0, 0, 9, 9, 9, 8, 9, 1, 1, 1, 9, 0, 9, 9, 0, 9, 1, 1, 9, 9, 9, 8, 8, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [7, 9, 7, 9, 5, 5, 9, 9, 9, 0, 9, 9, 9, 5, 9, 9, 4, 4, 9, 9, 9, 8, 8, 8], [9, 7, 7, 9, 9, 5, 9, 0, 0, 0, 9, 5, 5, 5, 5, 9, 4, 9, 4, 9, 9, 8, 8, 8], [9, 9, 7, 9, 9, 9, 9, 0, 0, 0, 9, 5, 5, 9, 5, 9, 4, 9, 4, 9, 8, 9, 8, 8], [7, 7, 7, 9, 5, 9, 9, 0, 0, 0, 9, 5, 5, 5, 5, 9, 9, 9, 4, 9, 8, 8, 9, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 5, 5, 9, 7, 7, 9, 4, 9, 4, 9, 1, 1, 1, 1, 9, 1, 1, 1, 9, 6, 9, 6, 6], [5, 9, 5, 9, 9, 7, 9, 4, 4, 9, 9, 1, 1, 9, 1, 9, 1, 9, 9, 9, 9, 6, 6, 6], [5, 5, 9, 9, 9, 7, 9, 9, 4, 4, 9, 1, 1, 1, 1, 9, 1, 1, 9, 9, 6, 6, 9, 6], [5, 9, 9, 9, 7, 7, 9, 4, 4, 4, 9, 1, 1, 1, 9, 9, 1, 9, 1, 9, 6, 9, 6, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 7, 9, 0, 0, 9, 1, 1, 1, 9, 9, 4, 9, 9, 9, 5, 5, 5, 9, 0, 0, 0, 0], [7, 7, 9, 9, 0, 0, 9, 1, 9, 1, 9, 4, 4, 9, 9, 9, 9, 9, 5, 9, 9, 0, 0, 0], [9, 7, 7, 9, 9, 9, 9, 1, 1, 1, 9, 4, 4, 4, 4, 9, 9, 5, 5, 9, 0, 0, 0, 0]], "output": [[7, 8, 4, 8, 7, 5], [0, 8, 1, 0, 1, 8], [7, 5, 0, 5, 4, 8], [5, 7, 4, 1, 1, 6], [7, 0, 1, 4, 5, 0]]}, {"input": [[1, 6, 1, 6, 6, 8, 8, 8, 8, 8, 6, 8, 6, 6, 6, 0, 0, 0, 0, 0, 6, 6, 1, 1, 1, 6], [1, 1, 1, 6, 6, 8, 8, 6, 6, 8, 8, 8, 6, 8, 6, 6, 6, 0, 0, 0, 6, 6, 1, 6, 6, 6], [1, 1, 1, 6, 6, 6, 8, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 1, 6, 1], [1, 1, 6, 6, 6, 8, 6, 8, 8, 8, 8, 8, 8, 6, 6, 0, 0, 0, 0, 0, 6, 6, 1, 6, 1, 1], [1, 1, 1, 6, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 6, 0, 6, 0, 0, 0, 0, 6, 1, 1, 6, 1], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 0, 0, 6, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 6, 5, 6, 6, 6, 6, 5, 6, 8, 8, 8, 6], [0, 0, 6, 6, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 5, 5, 5, 6, 6, 8, 8, 8, 8], [0, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 5, 6, 5, 6, 5, 6, 8, 8, 8, 6], [0, 0, 0, 6, 6, 8, 8, 6, 8, 8, 8, 8, 8, 8, 6, 5, 5, 5, 5, 5, 6, 6, 8, 8, 8, 8], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 0, 6, 6, 6, 5, 5, 6, 5, 5, 5, 5, 5, 6, 6, 6, 5, 6, 5, 5, 5, 6, 6, 6, 8, 8], [0, 0, 0, 6, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 8, 8, 6], [0, 0, 0, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 8, 6], [0, 0, 6, 6, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 6, 8]], "output": [[1, 8, 0, 1], [0, 8, 5, 8], [0, 5, 5, 8]]}, {"input": [[8, 1, 8, 8, 8, 1, 9, 9, 9, 1, 5, 5, 5, 1, 5, 5, 1, 1, 1, 8, 1, 9, 9, 1, 1, 1, 0, 1, 0], [8, 8, 8, 1, 8, 1, 9, 9, 9, 1, 5, 5, 1, 5, 5, 5, 1, 8, 8, 1, 1, 9, 9, 1, 0, 0, 1, 0, 0], [8, 8, 8, 8, 8, 1, 9, 9, 1, 1, 5, 5, 5, 5, 1, 5, 1, 8, 8, 8, 1, 9, 9, 1, 0, 0, 0, 0, 1], [8, 8, 8, 8, 8, 1, 9, 1, 9, 1, 5, 1, 5, 5, 5, 5, 1, 8, 8, 8, 1, 9, 9, 1, 1, 0, 0, 0, 1], [8, 1, 8, 8, 8, 1, 9, 9, 9, 1, 1, 5, 5, 1, 5, 5, 1, 8, 8, 8, 1, 9, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 0, 1, 5, 5, 1, 1, 1, 9, 9, 1, 9, 9, 1, 5, 1, 1, 1, 5, 5, 1, 9, 1, 9, 9, 1], [0, 0, 0, 0, 0, 1, 5, 1, 1, 1, 9, 9, 1, 9, 9, 1, 1, 5, 1, 5, 1, 5, 5, 1, 1, 1, 9, 9, 9], [0, 1, 1, 0, 1, 1, 1, 5, 1, 1, 9, 9, 1, 9, 9, 9, 1, 1, 5, 5, 1, 1, 1, 1, 1, 9, 9, 1, 9], [1, 0, 0, 0, 1, 1, 1, 5, 5, 1, 9, 9, 9, 1, 1, 9, 1, 5, 1, 5, 1, 5, 5, 1, 9, 9, 9, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 1, 1, 8, 1, 4, 4, 4, 1, 9, 9, 9, 9, 9, 1, 1, 1, 0, 0, 1, 1, 7, 1, 8, 8, 8, 8, 1], [8, 1, 8, 1, 8, 1, 4, 4, 4, 1, 9, 9, 9, 9, 9, 9, 1, 0, 0, 0, 1, 7, 7, 1, 8, 8, 8, 8, 8], [1, 8, 8, 8, 8, 1, 4, 4, 4, 1, 1, 9, 9, 9, 9, 9, 1, 0, 0, 0, 1, 7, 1, 1, 8, 8, 8, 8, 8], [8, 1, 1, 8, 1, 1, 1, 1, 1, 1, 9, 9, 1, 1, 9, 9, 1, 1, 0, 1, 1, 1, 7, 1, 8, 8, 1, 8, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 4, 4, 1, 0, 0, 0, 1, 8, 8, 8, 8, 8, 8, 1, 9, 9, 9, 1, 9, 9, 1, 1, 9, 9, 9, 9], [4, 1, 4, 4, 4, 1, 1, 0, 1, 1, 8, 8, 8, 8, 8, 8, 1, 9, 9, 9, 1, 1, 1, 1, 1, 9, 1, 9, 9], [4, 4, 4, 1, 4, 1, 1, 0, 0, 1, 8, 8, 8, 1, 8, 8, 1, 1, 9, 9, 1, 9, 9, 1, 9, 9, 9, 9, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [8, 8, 8, 8, 8, 1, 1, 4, 4, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 4, 1, 1, 0, 1, 1, 0, 0], [8, 8, 1, 8, 8, 1, 1, 1, 4, 1, 0, 0, 1, 0, 1, 0, 1, 9, 9, 1, 1, 4, 1, 1, 0, 0, 1, 0, 0], [8, 8, 8, 8, 8, 1, 4, 4, 4, 1, 0, 0, 0, 0, 1, 1, 1, 9, 9, 9, 1, 4, 4, 1, 0, 1, 0, 0, 0], [8, 8, 8, 8, 8, 1, 1, 4, 1, 1, 1, 1, 0, 0, 0, 0, 1, 9, 9, 9, 1, 4, 1, 1, 0, 1, 0, 0, 0]], "output": [[8, 9, 5, 8, 9, 0], [0, 5, 9, 5, 5, 9], [8, 4, 9, 0, 7, 8], [4, 0, 8, 9, 9, 9], [8, 4, 0, 9, 4, 0]]}], "input_grid": [[5, 5, 5, 5, 5, 8, 5, 8, 1, 8, 1], [8, 5, 5, 8, 5, 8, 5, 8, 8, 1, 8], [5, 5, 5, 5, 5, 5, 8, 8, 1, 1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 8, 1, 1, 1], [3, 3, 3, 3, 3, 3, 3, 8, 8, 1, 1], [8, 8, 3, 3, 3, 3, 3, 8, 1, 1, 8], [3, 3, 3, 3, 3, 8, 3, 8, 8, 1, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 8, 5, 5, 5], [8, 1, 1, 1, 1, 8, 1, 8, 5, 8, 5], [8, 1, 1, 1, 1, 8, 1, 8, 5, 5, 5], [1, 1, 1, 1, 8, 1, 1, 8, 5, 5, 5], [1, 1, 1, 1, 8, 1, 1, 8, 5, 8, 5], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [7, 7, 7, 7, 8, 7, 8, 8, 3, 3, 8], [8, 7, 7, 8, 7, 8, 7, 8, 8, 8, 8], [7, 7, 7, 7, 7, 7, 7, 8, 3, 8, 3], [7, 8, 7, 7, 7, 8, 7, 8, 8, 3, 3], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 8, 5, 5, 5, 5, 5, 8, 8, 8, 6], [5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 6], [8, 5, 8, 5, 5, 5, 5, 8, 6, 6, 8], [8, 5, 5, 5, 5, 5, 5, 8, 6, 6, 6], [8, 5, 5, 5, 5, 8, 5, 8, 6, 8, 8], [5, 5, 5, 5, 5, 5, 5, 8, 6, 6, 8]], "task_key": "780d0b14"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 0],\n[0, 0, 0, 4, 0, 4],\n[0, 0, 0, 0, 2, 0],\n[0, 0, 0, 4, 0, 4],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 9, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 6, 9, 9, 8, 9, 9],\n[9, 9, 9, 6, 9, 9, 6, 9, 9, 8, 9, 8, 8, 9, 8, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 8, 9, 9],\n[9, 1, 9, 9, 6, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 2, 9, 6, 9, 9, 9, 6, 9, 9, 8, 8, 8],\n[9, 9, 9, 9, 9, 6, 9, 9, 9, 6, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 9, 9, 6, 8, 9, 9, 2, 9, 9, 9, 9, 9, 9, 1, 9, 6, 9, 2, 6, 6, 9, 6, 9, 6, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 9, 9, 9, 9, 1, 9, 9, 8, 6, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9],\n[6, 9, 9, 9, 1, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9, 6, 9, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 9, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 6, 9, 9, 8, 9, 9],\n[9, 7, 9, 6, 9, 9, 6, 9, 9, 8, 9, 8, 8, 9, 8, 4, 9, 4, 9, 9, 6, 9, 9, 9, 9, 8, 9, 9],\n[7, 1, 7, 9, 6, 8, 9, 9, 9, 9, 9, 9, 9, 7, 9, 6, 2, 9, 6, 9, 9, 9, 6, 9, 9, 8, 8, 8],\n[9, 7, 9, 9, 9, 6, 9, 9, 4, 6, 4, 9, 7, 1, 7, 4, 7, 4, 9, 4, 6, 4, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 7, 9, 6, 8, 9, 9, 2, 9, 9, 9, 7, 9, 7, 1, 7, 6, 9, 2, 6, 6, 9, 6, 9, 6, 9],\n[9, 9, 7, 1, 7, 9, 9, 7, 4, 8, 4, 9, 9, 4, 9, 4, 7, 9, 9, 4, 9, 4, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 7, 7, 9, 7, 1, 7, 9, 8, 6, 9, 9, 2, 9, 9, 9, 7, 9, 9, 9, 9, 6, 7, 9, 9, 9],\n[6, 9, 9, 7, 1, 7, 9, 7, 9, 6, 9, 9, 9, 4, 9, 4, 9, 7, 1, 7, 9, 9, 9, 7, 1, 7, 9, 9],\n[9, 9, 9, 8, 7, 9, 9, 9, 8, 9, 9, 9, 9, 6, 9, 6, 6, 9, 7, 9, 9, 9, 9, 9, 7, 9, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6],\n[9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9],\n[9, 2, 9, 9, 9, 9, 9, 8, 9, 8, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 8, 9, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 4, 6, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 6],\n[4, 9, 4, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9],\n[9, 2, 9, 9, 4, 9, 4, 8, 9, 8, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9],\n[4, 9, 4, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 4, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 8, 9, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0], [0, 0, 0, 4, 0, 4], [0, 0, 0, 0, 2, 0], [0, 0, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}, {"input": [[6, 9, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 6, 9, 9, 8, 9, 9], [9, 9, 9, 6, 9, 9, 6, 9, 9, 8, 9, 8, 8, 9, 8, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 8, 9, 9], [9, 1, 9, 9, 6, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 2, 9, 6, 9, 9, 9, 6, 9, 9, 8, 8, 8], [9, 9, 9, 9, 9, 6, 9, 9, 9, 6, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 6, 8, 9, 9, 2, 9, 9, 9, 9, 9, 9, 1, 9, 6, 9, 2, 6, 6, 9, 6, 9, 6, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 9, 9, 1, 9, 9, 8, 6, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9], [6, 9, 9, 9, 1, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 8, 9, 9, 9, 9, 8, 9, 9, 9, 9, 6, 9, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[6, 9, 9, 9, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 6, 9, 9, 8, 9, 9], [9, 7, 9, 6, 9, 9, 6, 9, 9, 8, 9, 8, 8, 9, 8, 4, 9, 4, 9, 9, 6, 9, 9, 9, 9, 8, 9, 9], [7, 1, 7, 9, 6, 8, 9, 9, 9, 9, 9, 9, 9, 7, 9, 6, 2, 9, 6, 9, 9, 9, 6, 9, 9, 8, 8, 8], [9, 7, 9, 9, 9, 6, 9, 9, 4, 6, 4, 9, 7, 1, 7, 4, 7, 4, 9, 4, 6, 4, 9, 9, 9, 9, 9, 9], [8, 9, 9, 7, 9, 6, 8, 9, 9, 2, 9, 9, 9, 7, 9, 7, 1, 7, 6, 9, 2, 6, 6, 9, 6, 9, 6, 9], [9, 9, 7, 1, 7, 9, 9, 7, 4, 8, 4, 9, 9, 4, 9, 4, 7, 9, 9, 4, 9, 4, 9, 9, 9, 9, 9, 9], [8, 9, 9, 7, 7, 9, 7, 1, 7, 9, 8, 6, 9, 9, 2, 9, 9, 9, 7, 9, 9, 9, 9, 6, 7, 9, 9, 9], [6, 9, 9, 7, 1, 7, 9, 7, 9, 6, 9, 9, 9, 4, 9, 4, 9, 7, 1, 7, 9, 9, 9, 7, 1, 7, 9, 9], [9, 9, 9, 8, 7, 9, 9, 9, 8, 9, 9, 9, 9, 6, 9, 6, 6, 9, 7, 9, 9, 9, 9, 9, 7, 9, 9, 9]]}, {"input": [[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6], [9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9], [9, 2, 9, 9, 9, 9, 9, 8, 9, 8, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 8, 9, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9]], "output": [[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 4, 6, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 6], [4, 9, 4, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9], [9, 2, 9, 9, 4, 9, 4, 8, 9, 8, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9], [4, 9, 4, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 4, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 8, 9, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9]]}], "input_grid": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "task_key": "0ca9ddb6"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 1, 1, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 1, 1, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 8, 8, 9, 8, 8, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 8, 8, 8, 8, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[9, 9, 9, 9, 9, 6, 6, 6, 6, 9, 8, 8, 8, 8, 9, 9],\n[9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 2, 5, 2, 2, 5, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 2, 5, 2, 2, 5, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 5, 5, 2, 2, 5, 2, 2, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 2, 5, 2],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 8, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 8, 6, 8, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 8, 6, 8, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 8, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 1, 1, 9], [9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 1, 1, 9], [9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 8, 8, 9, 8, 8, 9, 9, 9, 9], [9, 9, 9, 9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9], [9, 9, 9, 8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9], [9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 8, 8, 8, 8, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [9, 9, 9, 9, 9, 6, 6, 6, 6, 9, 8, 8, 8, 8, 9, 9], [9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 3, 5, 3, 5, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 5, 3, 3, 5, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 2, 5, 2, 2, 5, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 2, 5, 2, 2, 5, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 5, 5, 2, 2, 5, 2, 2, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 2, 2, 5, 2], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 8, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 8, 6, 8, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 8, 6, 8, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 8, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "e8dc4411"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 2, 4, 4, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 2, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 2, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 8, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 2, 4, 4, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}], "input_grid": [[3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 2, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 8, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3]], "task_key": "d4a91cb9"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 0, 3],\n[3, 3, 0],\n[3, 3, 3],\n[0, 3, 0],\n[3, 0, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3],\n[3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0],\n[3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3],\n[3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3],\n[3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0],\n[3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 0, 5],\n[5, 5, 5, 5],\n[5, 5, 0, 5],\n[5, 0, 0, 5],\n[5, 0, 0, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5],\n[5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5],\n[5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5],\n[5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5],\n[5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5],\n[5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5],\n[5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 0, 0, 5, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 0, 0, 5, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 9],\n[9, 0, 0, 9],\n[9, 0, 9, 0],\n[9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9],\n[9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9],\n[9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[9, 0, 0, 9, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[9, 0, 9, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 0],\n[0, 3, 3, 3],\n[3, 3, 3, 0],\n[0, 3, 3, 0],\n[3, 3, 3, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 0, 3], [3, 3, 0], [3, 3, 3], [0, 3, 0], [3, 0, 3]], "output": [[3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0], [3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[5, 5, 0, 5], [5, 5, 5, 5], [5, 5, 0, 5], [5, 0, 0, 5], [5, 0, 0, 5]], "output": [[5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5], [5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5], [5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5], [5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 0, 5], [5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5], [5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 5], [5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 5, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 5, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 9], [9, 0, 0, 9], [9, 0, 9, 0], [9, 9, 9, 9]], "output": [[0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9], [9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9], [9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 9, 9, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 9, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[3, 3, 3, 0], [0, 3, 3, 3], [3, 3, 3, 0], [0, 3, 3, 0], [3, 3, 3, 3]], "task_key": "91413438"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 9, 9, 9, 9, 9],\n[4, 4, 9, 9, 9, 9, 9],\n[4, 4, 4, 9, 9, 9, 9],\n[4, 4, 9, 9, 9, 9, 9],\n[4, 9, 9, 9, 9, 9, 9],\n[4, 9, 9, 9, 9, 9, 9],\n[4, 4, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 3],\n[7, 3, 3],\n[7, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3],\n[3, 3, 3, 3],\n[3, 8, 8, 8],\n[8, 8, 8, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[4, 4, 9, 9, 9, 9, 9], [4, 4, 9, 9, 9, 9, 9], [4, 4, 4, 9, 9, 9, 9], [4, 4, 9, 9, 9, 9, 9], [4, 9, 9, 9, 9, 9, 9], [4, 9, 9, 9, 9, 9, 9], [4, 4, 9, 9, 9, 9, 9]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[7, 7, 3], [7, 3, 3], [7, 3, 3]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[3, 3, 3, 3], [3, 3, 3, 3], [3, 8, 8, 8], [8, 8, 8, 8]]}], "input_grid": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "task_key": "681b3aeb"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 6],\n[6, 6, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 6],\n[6, 6, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 6],\n[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 6, 3, 8, 8, 8, 8, 8, 8, 8, 6],\n[6, 6, 3, 6, 3, 8, 6, 6, 6, 6, 6, 8, 6],\n[6, 6, 3, 6, 3, 8, 8, 8, 8, 8, 8, 8, 6],\n[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3],\n[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3],\n[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3],\n[6, 3, 3, 3, 6, 7, 3, 7, 3, 3, 3, 3],\n[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3],\n[3, 3, 5, 3, 3, 3, 5, 3, 3, 3, 3, 3],\n[3, 3, 5, 3, 3, 3, 5, 3, 4, 4, 4, 3],\n[3, 3, 5, 3, 3, 3, 5, 3, 4, 3, 4, 3],\n[3, 3, 5, 3, 3, 3, 5, 3, 4, 3, 4, 3],\n[3, 3, 5, 5, 5, 5, 5, 3, 4, 3, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1],\n[1, 1, 3, 3, 3, 3, 3, 8, 8, 8, 8, 1],\n[1, 1, 3, 3, 3, 3, 3, 8, 8, 8, 8, 1],\n[1, 1, 3, 3, 3, 3, 3, 8, 8, 8, 8, 1],\n[1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1],\n[1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1],\n[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1],\n[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1],\n[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1],\n[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1],\n[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 6], [6, 6, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 6], [6, 6, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 6], [6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 3, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 3, 6, 3, 8, 8, 8, 8, 8, 8, 8, 6], [6, 6, 3, 6, 3, 8, 6, 6, 6, 6, 6, 8, 6], [6, 6, 3, 6, 3, 8, 8, 8, 8, 8, 8, 8, 6], [6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 9, 6, 6, 6, 9, 6, 6, 6, 6], [6, 6, 6, 6, 9, 6, 6, 6, 9, 6, 6, 6, 6], [6, 6, 6, 6, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3], [6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3], [6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3], [3, 3, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3], [3, 3, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3], [3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3], [3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3], [3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3], [3, 3, 5, 5, 5, 5, 5, 3, 4, 4, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3], [6, 3, 3, 3, 6, 7, 3, 7, 3, 3, 3, 3], [6, 6, 6, 6, 6, 7, 7, 7, 3, 3, 3, 3], [3, 3, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3], [3, 3, 5, 3, 3, 3, 5, 3, 3, 3, 3, 3], [3, 3, 5, 3, 3, 3, 5, 3, 4, 4, 4, 3], [3, 3, 5, 3, 3, 3, 5, 3, 4, 3, 4, 3], [3, 3, 5, 3, 3, 3, 5, 3, 4, 3, 4, 3], [3, 3, 5, 5, 5, 5, 5, 3, 4, 3, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}], "input_grid": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1], [1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1], [1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1], [1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1], [1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1], [1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1], [1, 5, 5, 5, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1], [1, 1, 3, 3, 3, 3, 3, 8, 8, 8, 8, 1], [1, 1, 3, 3, 3, 3, 3, 8, 8, 8, 8, 1], [1, 1, 3, 3, 3, 3, 3, 8, 8, 8, 8, 1], [1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1], [1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "task_key": "4347f46a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 0, 0, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 0, 0, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 8, 8, 7, 6, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 8, 8, 7, 6, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 4, 4, 1, 4, 1, 1],\n[1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 0, 0, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 0, 0, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 8, 8, 7, 6, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 8, 8, 7, 6, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}], "input_grid": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 4, 4, 1, 4, 1, 1], [1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "task_key": "4938f0c2"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0],\n[0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4],\n[4, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 3, 3, 3, 3, 3, 3, 3, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 7, 5, 7, 5, 3, 5, 5, 5, 5, 5, 3, 5, 5],\n[5, 5, 5, 8, 5, 5, 5, 5, 8, 7, 7, 7, 5, 3, 5, 5, 5, 5, 5, 3, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 3, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 3, 3, 3, 3, 3, 3, 3, 5, 5],\n[5, 1, 1, 1, 1, 1, 1, 1, 6, 5, 5, 6, 5, 5, 5, 5, 2, 2, 2, 5, 5, 5],\n[5, 1, 5, 5, 5, 5, 5, 1, 6, 5, 5, 6, 5, 5, 5, 5, 2, 5, 2, 5, 5, 5],\n[5, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 5, 5, 5, 5, 2, 2, 2, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3],\n[3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7],\n[7, 7, 1, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7],\n[7, 7, 1, 7, 7, 7, 1, 7, 6, 6, 6, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7],\n[7, 7, 1, 1, 1, 1, 1, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 7, 7, 7, 7, 9, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 7, 7, 7, 7, 9, 7, 7, 7, 7, 7, 7, 7],\n[5, 7, 5, 7, 7, 7, 0, 0, 0, 0, 0, 0, 9, 7, 7, 7, 7, 9, 3, 3, 3, 3, 7, 7, 7],\n[5, 7, 5, 7, 7, 7, 0, 7, 7, 7, 7, 0, 9, 7, 7, 7, 7, 9, 3, 7, 7, 3, 7, 7, 7],\n[5, 7, 5, 7, 7, 7, 0, 7, 7, 7, 7, 0, 9, 7, 7, 7, 7, 9, 3, 7, 7, 3, 7, 7, 7],\n[5, 7, 5, 7, 7, 7, 0, 7, 7, 7, 7, 0, 9, 9, 9, 9, 9, 9, 3, 7, 7, 3, 7, 7, 7],\n[5, 7, 5, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 7, 7, 7],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[0, 0], [0, 0]]}, {"input": [[4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[4, 4], [4, 4]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 3, 3, 3, 3, 3, 3, 3, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 8, 7, 5, 7, 5, 3, 5, 5, 5, 5, 5, 3, 5, 5], [5, 5, 5, 8, 5, 5, 5, 5, 8, 7, 7, 7, 5, 3, 5, 5, 5, 5, 5, 3, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 8, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 3, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 3, 3, 3, 3, 3, 3, 3, 5, 5], [5, 1, 1, 1, 1, 1, 1, 1, 6, 5, 5, 6, 5, 5, 5, 5, 2, 2, 2, 5, 5, 5], [5, 1, 5, 5, 5, 5, 5, 1, 6, 5, 5, 6, 5, 5, 5, 5, 2, 5, 2, 5, 5, 5], [5, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 5, 5, 5, 5, 2, 2, 2, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[3, 3], [3, 3]]}], "input_grid": [[7, 7, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7], [7, 7, 1, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7], [7, 7, 1, 7, 7, 7, 1, 7, 6, 6, 6, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7], [7, 7, 1, 1, 1, 1, 1, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 7, 7, 7, 7, 9, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 7, 7, 7, 7, 9, 7, 7, 7, 7, 7, 7, 7], [5, 7, 5, 7, 7, 7, 0, 0, 0, 0, 0, 0, 9, 7, 7, 7, 7, 9, 3, 3, 3, 3, 7, 7, 7], [5, 7, 5, 7, 7, 7, 0, 7, 7, 7, 7, 0, 9, 7, 7, 7, 7, 9, 3, 7, 7, 3, 7, 7, 7], [5, 7, 5, 7, 7, 7, 0, 7, 7, 7, 7, 0, 9, 7, 7, 7, 7, 9, 3, 7, 7, 3, 7, 7, 7], [5, 7, 5, 7, 7, 7, 0, 7, 7, 7, 7, 0, 9, 9, 9, 9, 9, 9, 3, 7, 7, 3, 7, 7, 7], [5, 7, 5, 7, 7, 7, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 7, 7, 7], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "task_key": "445eab21"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 3, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5],\n[3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 5, 3, 5],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5],\n[3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[6, 6, 3, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 1, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 1, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 3, 6, 6, 6],\n[6, 1, 1, 3, 1, 1, 6],\n[6, 1, 5, 5, 5, 1, 6],\n[3, 3, 5, 3, 5, 3, 3],\n[6, 1, 5, 5, 5, 1, 6],\n[6, 1, 1, 3, 1, 1, 6],\n[6, 6, 6, 3, 6, 6, 6]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 3, 9, 9],\n[9, 8, 8, 8, 9],\n[3, 8, 6, 8, 3],\n[9, 8, 8, 8, 9],\n[9, 9, 3, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[9, 9, 5, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 8, 8, 5, 8, 8, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5],\n[9, 9, 5, 9, 9, 9, 5, 5, 5, 5, 5, 5, 8, 8, 5, 8, 8, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 5, 9, 9, 9],\n[9, 8, 8, 5, 8, 8, 9],\n[9, 8, 3, 3, 3, 8, 9],\n[5, 5, 3, 5, 3, 5, 5],\n[9, 8, 3, 3, 3, 8, 9],\n[9, 8, 8, 5, 8, 8, 9],\n[9, 9, 9, 5, 9, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2],\n[2, 7, 7, 2, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1],\n[2, 7, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 7, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 7, 7, 2, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 5, 5, 2, 2, 2, 2, 2, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 9, 2, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2],\n[2, 2, 5, 9, 9, 9, 3, 2, 2, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 5, 5, 2, 2, 3, 2, 2, 5, 5, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 3, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 5, 3, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [6, 6, 3, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 1, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 1, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 1, 1, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[6, 6, 6, 3, 6, 6, 6], [6, 1, 1, 3, 1, 1, 6], [6, 1, 5, 5, 5, 1, 6], [3, 3, 5, 3, 5, 3, 3], [6, 1, 5, 5, 5, 1, 6], [6, 1, 1, 3, 1, 1, 6], [6, 6, 6, 3, 6, 6, 6]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[9, 9, 3, 9, 9], [9, 8, 8, 8, 9], [3, 8, 6, 8, 3], [9, 8, 8, 8, 9], [9, 9, 3, 9, 9]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [9, 9, 5, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 8, 8, 5, 8, 8, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 9, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5], [9, 9, 5, 9, 9, 9, 5, 5, 5, 5, 5, 5, 8, 8, 5, 8, 8, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[9, 9, 9, 5, 9, 9, 9], [9, 8, 8, 5, 8, 8, 9], [9, 8, 3, 3, 3, 8, 9], [5, 5, 3, 5, 3, 5, 5], [9, 8, 3, 3, 3, 8, 9], [9, 8, 8, 5, 8, 8, 9], [9, 9, 9, 5, 9, 9, 9]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2], [2, 7, 7, 2, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1], [2, 7, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 7, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 7, 7, 2, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 5, 5, 2, 2, 2, 2, 2, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 9, 2, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2], [2, 2, 5, 9, 9, 9, 3, 2, 2, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 5, 5, 2, 2, 3, 2, 2, 5, 5, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2]], "task_key": "4290ef0e"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6],\n[9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 9, 3, 9],\n[9, 9, 9, 3, 3, 3, 3, 3, 3, 9, 3, 9, 3, 9, 9, 3, 3, 9],\n[9, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 9, 9, 3, 3, 9],\n[9, 9, 3, 3, 9, 3, 3, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 9],\n[9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 9, 3, 9],\n[9, 9, 3, 3, 3, 9, 3, 3, 3, 9, 3, 3, 3, 9, 9, 3, 3, 9],\n[9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 9],\n[9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 6],\n[9, 6, 6, 6, 6, 6, 6, 9, 6, 9, 6, 9, 9, 6, 6],\n[6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 9, 9, 6, 6],\n[6, 6, 9, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 9, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 6],\n[6, 6, 6, 9, 6, 6, 6, 9, 6, 6, 6, 9, 9, 6, 6],\n[9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 6, 0, 6, 6],\n[0, 0, 0, 0, 0],\n[6, 0, 6, 6, 6],\n[6, 6, 6, 6, 0],\n[0, 6, 6, 0, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 9, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 9, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3],\n[3, 3, 3],\n[3, 3, 3],\n[3, 3, 3],\n[3, 3, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0],\n[0, 9, 0, 0, 9, 0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0],\n[0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 0, 9, 9, 0, 9, 9, 0, 0, 0, 0],\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0],\n[3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6], [9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 9, 3, 9], [9, 9, 9, 3, 3, 3, 3, 3, 3, 9, 3, 9, 3, 9, 9, 3, 3, 9], [9, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 9, 9, 3, 3, 9], [9, 9, 3, 3, 9, 3, 3, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 9], [9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 9, 3, 9], [9, 9, 3, 3, 3, 9, 3, 3, 3, 9, 3, 3, 3, 9, 9, 3, 3, 9], [9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 9], [9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6]], "output": [[9, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 6], [9, 6, 6, 6, 6, 6, 6, 9, 6, 9, 6, 9, 9, 6, 6], [6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 9, 9, 6, 6], [6, 6, 9, 6, 6, 9, 6, 6, 6, 6, 6, 6, 9, 9, 6], [6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 9, 6], [6, 6, 6, 9, 6, 6, 6, 9, 6, 6, 6, 9, 9, 6, 6], [9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[0, 6, 0, 6, 6], [0, 0, 0, 0, 0], [6, 0, 6, 6, 6], [6, 6, 6, 6, 0], [0, 6, 6, 0, 6]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 9, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 9, 3]], "output": [[3, 3, 3], [3, 3, 3], [3, 3, 3], [3, 3, 3], [3, 3, 3]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 9, 0, 0, 9, 0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 9, 0, 9, 9, 0, 9, 9, 0, 0, 0, 0], [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 9, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "3de23699"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1],\n[1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1],\n[1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1],\n[1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 1, 0, 0, 1, 1, 1, 1],\n[0, 1, 0, 0, 1, 0, 1, 1, 1],\n[0, 0, 1, 1, 1, 1, 0, 0, 1],\n[0, 1, 0, 1, 1, 1, 0, 1, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 8, 9, 9, 8, 8, 8, 8, 9, 8, 9, 9, 9, 8, 9, 9],\n[8, 9, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8],\n[9, 9, 9, 8, 8, 8, 8, 8, 9, 9, 9, 8, 9, 9, 9, 8],\n[8, 8, 8, 8, 9, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 8, 9, 9, 9, 8, 9, 9, 9, 8, 9, 9, 8, 8, 8, 8],\n[8, 9, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8],\n[9, 9, 9, 8, 9, 9, 9, 8, 9, 9, 9, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 1, 9, 1, 1, 1, 9, 1, 9],\n[9, 9, 9, 1, 1, 1, 9, 9, 9],\n[9, 9, 1, 1, 1, 1, 9, 9, 1],\n[9, 9, 9, 1, 1, 1, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 9, 9, 9],\n[9, 1, 9, 9, 1, 9, 9, 1, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 1, 9, 9, 1, 9, 9, 1],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 1, 9, 9, 1, 9, 1, 1, 1],\n[9, 9, 9, 9, 9, 9, 1, 1, 1],\n[9, 9, 1, 9, 9, 1, 1, 1, 1],\n[9, 9, 9, 9, 9, 9, 1, 1, 1],\n[9, 9, 9, 9, 9, 9, 1, 1, 1],\n[9, 1, 9, 9, 1, 9, 9, 1, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 1, 9, 9, 1, 9, 9, 1],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 1, 9, 9, 1, 9, 9, 1, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 1, 9, 9, 1, 9, 9, 1],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[0, 0, 1, 0, 0, 1, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 1, 0]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[9, 8, 9, 9, 8, 8, 8, 8, 9, 8, 9, 9, 9, 8, 9, 9], [8, 9, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8], [9, 9, 9, 8, 8, 8, 8, 8, 9, 9, 9, 8, 9, 9, 9, 8], [8, 8, 8, 8, 9, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 8, 9, 9, 9, 8, 9, 9, 9, 8, 9, 9, 8, 8, 8, 8], [8, 9, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8], [9, 9, 9, 8, 9, 9, 9, 8, 9, 9, 9, 8, 8, 8, 8, 8]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 1, 1, 1, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[9, 1, 9, 1, 1, 1, 9, 1, 9], [9, 9, 9, 1, 1, 1, 9, 9, 9], [9, 9, 1, 1, 1, 1, 9, 9, 1], [9, 9, 9, 1, 1, 1, 9, 9, 9], [9, 9, 9, 1, 1, 1, 9, 9, 9], [9, 1, 9, 9, 1, 9, 9, 1, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 9, 9, 1, 9, 9, 1], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 1, 9, 9, 1, 9, 1, 1, 1], [9, 9, 9, 9, 9, 9, 1, 1, 1], [9, 9, 1, 9, 9, 1, 1, 1, 1], [9, 9, 9, 9, 9, 9, 1, 1, 1], [9, 9, 9, 9, 9, 9, 1, 1, 1], [9, 1, 9, 9, 1, 9, 9, 1, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 9, 9, 1, 9, 9, 1], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 1, 9, 9, 1, 9, 9, 1, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 1, 9, 9, 1, 9, 9, 1], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9]]}], "input_grid": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "task_key": "80af3007"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 4, 0, 9, 0, 8],\n[5, 0, 0, 4, 1, 7],\n[9, 0, 7, 0, 0, 0],\n[3, 0, 4, 0, 3, 1],\n[0, 0, 4, 3, 0, 0],\n[5, 0, 0, 0, 0, 4],\n[5, 7, 2, 8, 0, 5],\n[5, 0, 8, 0, 1, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 0, 8],\n[4, 1, 7],\n[0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 9, 9, 9, 0, 8],\n[6, 4, 3, 9, 9, 1],\n[9, 9, 9, 3, 9, 9],\n[9, 9, 1, 9, 4, 9],\n[9, 9, 9, 9, 9, 8],\n[5, 9, 9, 6, 6, 6],\n[9, 9, 9, 9, 1, 5],\n[9, 9, 9, 9, 4, 9],\n[9, 6, 6, 9, 9, 9],\n[6, 9, 3, 9, 6, 9],\n[5, 9, 9, 9, 8, 9],\n[9, 0, 9, 9, 3, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 0, 8],\n[9, 9, 1],\n[3, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 6, 7, 7, 3, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 3, 3],\n[7, 3, 3, 3, 7, 3, 7, 7, 7],\n[3, 7, 7, 3, 7, 7, 7, 7, 7],\n[7, 7, 3, 3, 7, 7, 7, 7, 7],\n[7, 7, 3, 3, 7, 7, 7, 7, 7],\n[7, 6, 7, 7, 7, 3, 7, 3, 7],\n[3, 7, 7, 7, 7, 7, 3, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 7, 7, 7, 3, 3],\n[7, 7, 7, 7, 7, 7, 6, 7, 7],\n[7, 7, 3, 7, 7, 7, 7, 7, 3],\n[3, 3, 3, 7, 7, 7, 3, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 4, 0, 9, 0, 8], [5, 0, 0, 4, 1, 7], [9, 0, 7, 0, 0, 0], [3, 0, 4, 0, 3, 1], [0, 0, 4, 3, 0, 0], [5, 0, 0, 0, 0, 4], [5, 7, 2, 8, 0, 5], [5, 0, 8, 0, 1, 9]], "output": [[9, 0, 8], [4, 1, 7], [0, 0, 0]]}, {"input": [[8, 9, 9, 9, 0, 8], [6, 4, 3, 9, 9, 1], [9, 9, 9, 3, 9, 9], [9, 9, 1, 9, 4, 9], [9, 9, 9, 9, 9, 8], [5, 9, 9, 6, 6, 6], [9, 9, 9, 9, 1, 5], [9, 9, 9, 9, 4, 9], [9, 6, 6, 9, 9, 9], [6, 9, 3, 9, 6, 9], [5, 9, 9, 9, 8, 9], [9, 0, 9, 9, 3, 9]], "output": [[9, 0, 8], [9, 9, 1], [3, 9, 9]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[1, 1, 1], [1, 1, 1], [1, 1, 1]]}], "input_grid": [[7, 6, 7, 7, 3, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 3, 3], [7, 3, 3, 3, 7, 3, 7, 7, 7], [3, 7, 7, 3, 7, 7, 7, 7, 7], [7, 7, 3, 3, 7, 7, 7, 7, 7], [7, 7, 3, 3, 7, 7, 7, 7, 7], [7, 6, 7, 7, 7, 3, 7, 3, 7], [3, 7, 7, 7, 7, 7, 3, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 7, 7, 7, 3, 3], [7, 7, 7, 7, 7, 7, 6, 7, 7], [7, 7, 3, 7, 7, 7, 7, 7, 3], [3, 3, 3, 7, 7, 7, 3, 7, 7]], "task_key": "5bd6f4ac"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 7, 4, 7, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 7, 4, 7, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 3, 1, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 3, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 3, 1, 9, 9, 3, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 2, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6],\n[6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 4, 4, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6],\n[6, 4, 4, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 1, 1, 1, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 2, 6, 6],\n[6, 4, 4, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6],\n[6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0],\n[0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0],\n[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3],\n[8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0],\n[0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 3, 0, 0, 3],\n[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 7, 4, 7, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 7, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 7, 4, 7, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 3, 1, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 3, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 3, 1, 9, 9, 3, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 2, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6], [6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6], [6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6]], "output": [[6, 6, 6, 4, 4, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6], [6, 4, 4, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 2, 6, 1, 1, 1, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 6, 2, 6, 6], [6, 4, 4, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 6], [6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6], [6, 6, 3, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3], [8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 3, 0, 0, 3], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0]], "task_key": "3e980e27"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 3, 6, 6, 5, 5, 5, 5],\n[6, 6, 6, 6, 5, 6, 5, 6],\n[6, 6, 6, 6, 5, 6, 5, 5],\n[6, 6, 6, 6, 5, 5, 5, 6],\n[6, 6, 6, 6, 5, 5, 5, 6],\n[6, 6, 6, 6, 5, 5, 5, 5],\n[6, 6, 6, 6, 5, 5, 5, 5],\n[6, 7, 6, 7, 6, 6, 6, 6],\n[7, 6, 7, 7, 6, 6, 6, 8],\n[6, 6, 7, 6, 6, 8, 6, 8],\n[6, 7, 6, 6, 6, 8, 8, 6],\n[6, 6, 6, 6, 8, 8, 6, 8],\n[6, 7, 6, 6, 6, 6, 8, 6],\n[7, 7, 6, 6, 8, 6, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5],\n[5, 6, 5, 7],\n[5, 8, 5, 5],\n[5, 5, 5, 6],\n[5, 5, 5, 8],\n[5, 5, 5, 5],\n[5, 5, 5, 5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 8, 1, 8, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 3, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 1],\n[3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 8, 8, 1, 1, 1, 1, 8, 8, 1, 8],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 5, 1, 1, 1, 5],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1],\n[1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 1, 1, 1, 5, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 8, 3, 8, 5, 3, 5, 1, 3, 1, 5],\n[8, 8, 8, 8, 8, 5, 1, 5, 3, 8, 3],\n[3, 8, 8, 5, 2, 5, 3, 8, 8, 5, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 4, 6, 6, 6, 4, 6, 7, 6, 7, 7, 7, 7, 7, 7],\n[6, 4, 6, 6, 4, 4, 4, 6, 7, 7, 7, 7, 7, 7, 7, 7],\n[6, 4, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 7, 7, 7, 7],\n[6, 4, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7],\n[4, 6, 6, 4, 4, 6, 6, 4, 7, 7, 7, 7, 7, 7, 7, 7],\n[1, 1, 6, 6, 6, 6, 6, 1, 3, 3, 3, 3, 3, 3, 3, 3],\n[6, 1, 6, 1, 1, 1, 6, 1, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 6, 1, 6, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3],\n[6, 1, 1, 6, 1, 1, 1, 6, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 1, 6, 1, 1, 6, 6, 1, 3, 3, 3, 3, 3, 6, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 1, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 1, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 9, 9, 6, 9, 7, 7, 7, 9, 7],\n[9, 6, 6, 6, 6, 7, 7, 9, 9, 7],\n[9, 6, 9, 6, 9, 7, 9, 7, 7, 7],\n[6, 9, 6, 6, 6, 7, 7, 7, 7, 9],\n[6, 6, 9, 9, 9, 7, 9, 9, 7, 7],\n[5, 9, 5, 9, 9, 9, 9, 9, 9, 9],\n[5, 5, 5, 9, 5, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 5, 0, 9, 9, 9, 9],\n[5, 9, 5, 9, 5, 9, 9, 0, 0, 9],\n[9, 5, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 3, 6, 6, 5, 5, 5, 5], [6, 6, 6, 6, 5, 6, 5, 6], [6, 6, 6, 6, 5, 6, 5, 5], [6, 6, 6, 6, 5, 5, 5, 6], [6, 6, 6, 6, 5, 5, 5, 6], [6, 6, 6, 6, 5, 5, 5, 5], [6, 6, 6, 6, 5, 5, 5, 5], [6, 7, 6, 7, 6, 6, 6, 6], [7, 6, 7, 7, 6, 6, 6, 8], [6, 6, 7, 6, 6, 8, 6, 8], [6, 7, 6, 6, 6, 8, 8, 6], [6, 6, 6, 6, 8, 8, 6, 8], [6, 7, 6, 6, 6, 6, 8, 6], [7, 7, 6, 6, 8, 6, 8, 8]], "output": [[5, 5, 5, 5], [5, 6, 5, 7], [5, 8, 5, 5], [5, 5, 5, 6], [5, 5, 5, 8], [5, 5, 5, 5], [5, 5, 5, 5]]}, {"input": [[1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 8, 1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 3, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 1], [3, 1, 3, 1, 3, 1, 3, 3, 3, 3, 3, 1, 8, 8, 1, 1, 1, 1, 8, 8, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 5, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1], [1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 1, 5, 1, 1, 1, 5, 1]], "output": [[5, 8, 3, 8, 5, 3, 5, 1, 3, 1, 5], [8, 8, 8, 8, 8, 5, 1, 5, 3, 8, 3], [3, 8, 8, 5, 2, 5, 3, 8, 8, 5, 8]]}, {"input": [[6, 6, 4, 6, 6, 6, 4, 6, 7, 6, 7, 7, 7, 7, 7, 7], [6, 4, 6, 6, 4, 4, 4, 6, 7, 7, 7, 7, 7, 7, 7, 7], [6, 4, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 7, 7, 7, 7], [6, 4, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7], [4, 6, 6, 4, 4, 6, 6, 4, 7, 7, 7, 7, 7, 7, 7, 7], [1, 1, 6, 6, 6, 6, 6, 1, 3, 3, 3, 3, 3, 3, 3, 3], [6, 1, 6, 1, 1, 1, 6, 1, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 6, 1, 6, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3], [6, 1, 1, 6, 1, 1, 1, 6, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 6, 1, 1, 6, 6, 1, 3, 3, 3, 3, 3, 6, 3, 3]], "output": [[7, 1, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 1, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7]]}], "input_grid": [[6, 9, 9, 6, 9, 7, 7, 7, 9, 7], [9, 6, 6, 6, 6, 7, 7, 9, 9, 7], [9, 6, 9, 6, 9, 7, 9, 7, 7, 7], [6, 9, 6, 6, 6, 7, 7, 7, 7, 9], [6, 6, 9, 9, 9, 7, 9, 9, 7, 7], [5, 9, 5, 9, 9, 9, 9, 9, 9, 9], [5, 5, 5, 9, 5, 9, 9, 9, 9, 9], [9, 9, 9, 9, 5, 0, 9, 9, 9, 9], [5, 9, 5, 9, 5, 9, 9, 0, 0, 9], [9, 5, 9, 9, 9, 9, 9, 9, 9, 9]], "task_key": "75b8110e"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9],\n[9, 3, 9, 5, 5],\n[9, 3, 9, 5, 5],\n[9, 3, 9, 5, 5],\n[9, 3, 9, 5, 5],\n[9, 3, 9, 5, 5],\n[9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9],\n[9, 3, 9, 5, 5],\n[9, 3, 8, 5, 5],\n[9, 3, 8, 5, 5],\n[9, 3, 8, 5, 5],\n[9, 3, 9, 5, 5],\n[9, 9, 9, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[9, 9, 9, 9, 9], [9, 9, 9, 9, 9], [9, 3, 9, 5, 5], [9, 3, 9, 5, 5], [9, 3, 9, 5, 5], [9, 3, 9, 5, 5], [9, 3, 9, 5, 5], [9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9], [9, 9, 9, 9, 9], [9, 3, 9, 5, 5], [9, 3, 8, 5, 5], [9, 3, 8, 5, 5], [9, 3, 8, 5, 5], [9, 3, 9, 5, 5], [9, 9, 9, 9, 9]]}], "input_grid": [[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "task_key": "d6ad076f"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 2, 2, 5, 5, 2, 2, 5],\n[5, 5, 5, 5, 2, 2, 5, 5, 2, 2, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 2, 2, 5, 5, 5, 5],\n[5, 5, 1, 1, 5, 2, 2, 5, 5, 5, 5],\n[5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 5, 5, 5, 2, 2, 5, 5, 2, 2, 5],\n[5, 1, 5, 5, 2, 2, 5, 5, 2, 2, 5],\n[5, 5, 1, 5, 5, 5, 2, 5, 5, 5, 2],\n[5, 5, 5, 1, 1, 5, 5, 2, 5, 5, 5],\n[1, 5, 5, 1, 1, 5, 5, 5, 2, 5, 5],\n[5, 1, 5, 5, 5, 2, 2, 5, 5, 2, 5],\n[5, 5, 1, 1, 5, 2, 2, 5, 5, 5, 2],\n[5, 5, 1, 1, 5, 5, 5, 2, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5],\n[1, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5],\n[5, 1, 5, 5, 5, 5, 5, 5, 2, 2, 2],\n[5, 5, 1, 5, 5, 5, 5, 5, 2, 2, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 2],\n[1, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 1, 5, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 1, 5, 5, 5, 2, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 2, 5, 5, 5],\n[5, 5, 5, 1, 1, 5, 5, 5, 2, 5, 5],\n[1, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5],\n[5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 2],\n[5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4],\n[4, 4, 4, 4, 4, 1, 1, 4, 4, 1, 1, 4, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4],\n[4, 4, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4],\n[4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 4, 2, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 2, 4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4],\n[4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 1, 4, 1, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4],\n[1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 1, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4],\n[4, 1, 4, 4, 4, 1, 1, 4, 4, 1, 1, 4, 1, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4],\n[4, 4, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 4, 1, 4, 4, 4, 4, 2, 4, 4, 2, 2, 4],\n[4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 2, 4, 2, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 2, 4, 4, 1, 1, 4, 4, 4, 4, 2, 4, 4, 2],\n[4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4],\n[4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 2, 2, 4, 4, 4, 2, 4],\n[4, 4, 4, 2, 4, 4, 2, 4, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 4, 2, 2, 2],\n[4, 4, 4, 4, 2, 4, 4, 2, 2, 2, 4, 2, 4, 4, 2, 2, 2, 4, 4, 4, 2, 2, 2, 4],\n[4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 2, 4, 2, 4, 4, 2, 4, 2, 4, 4, 4, 2, 4, 2]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4],\n[1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4],\n[4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4],\n[4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9],\n[9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 1, 1, 9],\n[9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 1, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 1, 1, 9],\n[9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9],\n[9, 9, 9, 1, 1, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9],\n[9, 1, 1, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 1, 1, 9, 1, 1, 9, 1, 1, 9, 9, 1, 1, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 1, 1, 9, 9],\n[9, 9, 9, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 2, 2, 9, 2, 2, 9, 9, 9, 9, 2, 2, 9],\n[9, 9, 9, 9, 9, 9, 2, 2, 9, 9, 9, 9, 2, 2, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 2, 2, 5, 5, 2, 2, 5], [5, 5, 5, 5, 2, 2, 5, 5, 2, 2, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 2, 2, 5, 5, 5, 5], [5, 5, 1, 1, 5, 2, 2, 5, 5, 5, 5], [5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5], [5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 5, 5, 5, 2, 2, 5, 5, 2, 2, 5], [5, 1, 5, 5, 2, 2, 5, 5, 2, 2, 5], [5, 5, 1, 5, 5, 5, 2, 5, 5, 5, 2], [5, 5, 5, 1, 1, 5, 5, 2, 5, 5, 5], [1, 5, 5, 1, 1, 5, 5, 5, 2, 5, 5], [5, 1, 5, 5, 5, 2, 2, 5, 5, 2, 5], [5, 5, 1, 1, 5, 2, 2, 5, 5, 5, 2], [5, 5, 1, 1, 5, 5, 5, 2, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5], [1, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5], [5, 1, 5, 5, 5, 5, 5, 5, 2, 2, 2], [5, 5, 1, 5, 5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 2], [1, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5], [5, 1, 5, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 1, 5, 5, 5, 2, 5, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 2, 5, 5, 5], [5, 5, 5, 1, 1, 5, 5, 5, 2, 5, 5], [1, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5], [5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 2], [5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5], [5, 1, 1, 5, 2, 2, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4], [4, 4, 4, 4, 4, 1, 1, 4, 4, 1, 1, 4, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4], [4, 4, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4], [4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 4, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 2, 4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4], [4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4], [4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 1, 4, 1, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4], [1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 1, 4, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4], [4, 1, 4, 4, 4, 1, 1, 4, 4, 1, 1, 4, 1, 1, 1, 4, 2, 2, 4, 1, 1, 4, 4, 4], [4, 4, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 4, 1, 4, 4, 4, 4, 2, 4, 4, 2, 2, 4], [4, 4, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 2, 4, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 2, 4, 4, 1, 1, 4, 4, 4, 4, 2, 4, 4, 2], [4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4], [4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 2, 2, 4, 4, 4, 2, 4], [4, 4, 4, 2, 4, 4, 2, 4, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 4, 2, 2, 2], [4, 4, 4, 4, 2, 4, 4, 2, 2, 2, 4, 2, 4, 4, 2, 2, 2, 4, 4, 4, 2, 2, 2, 4], [4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 2, 4, 2, 4, 4, 2, 4, 2, 4, 4, 4, 2, 4, 2]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4], [1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4], [4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4], [4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4]]}], "input_grid": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9], [9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 1, 1, 9], [9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 1, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 1, 1, 9], [9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9], [9, 9, 9, 1, 1, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 9], [9, 1, 1, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 1, 1, 9, 1, 1, 9, 1, 1, 9, 9, 1, 1, 9, 9], [9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 1, 1, 9, 9], [9, 9, 9, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 2, 2, 9, 2, 2, 9, 9, 9, 9, 2, 2, 9], [9, 9, 9, 9, 9, 9, 2, 2, 9, 9, 9, 9, 2, 2, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "task_key": "5c0a986e"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[1, 2, 7, 9, 3, 8, 2, 6, 8, 1, 7, 9, 3, 7, 7, 1, 2, 8, 9, 1, 7, 7],\n[9, 6, 7, 9, 7, 7, 3, 6, 8, 1, 7, 7, 9, 8, 9, 8, 3, 6, 2, 7, 1, 2],\n[7, 7, 3, 2, 7, 3, 7, 7, 8, 9, 6, 3, 2, 1, 3, 6, 2, 9, 7, 7, 7, 7],\n[9, 8, 2, 3, 7, 7, 7, 2, 8, 7, 2, 3, 8, 8, 7, 3, 7, 9, 3, 2, 3, 7],\n[2, 2, 7, 1, 7, 6, 6, 7, 3, 1, 7, 3, 7, 8, 3, 7, 9, 7, 8, 7, 9, 7],\n[8, 9, 7, 7, 2, 8, 8, 7, 9, 6, 7, 9, 2, 6, 8, 7, 3, 7, 8, 3, 7, 8],\n[2, 7, 7, 2, 7, 1, 7, 7, 7, 7, 6, 1, 3, 6, 3, 7, 7, 7, 6, 7, 9, 6],\n[1, 8, 8, 7, 7, 9, 2, 7, 7, 2, 7, 9, 7, 7, 8, 1, 1, 6, 2, 7, 7, 2],\n[7, 7, 7, 3, 7, 7, 6, 7, 9, 8, 7, 8, 9, 7, 2, 9, 3, 9, 6, 7, 7, 3],\n[1, 7, 1, 3, 7, 3, 7, 7, 8, 8, 7, 7, 7, 3, 2, 3, 7, 8, 7, 6, 1, 7],\n[7, 9, 2, 9, 1, 7, 7, 1, 6, 2, 7, 9, 7, 7, 7, 6, 2, 2, 2, 2, 7, 7],\n[9, 9, 7, 7, 3, 9, 1, 8, 2, 9, 7, 1, 8, 3, 9, 3, 7, 7, 9, 7, 6, 9],\n[7, 6, 8, 9, 7, 7, 6, 3, 9, 9, 7, 3, 7, 8, 8, 9, 3, 7, 7, 6, 7, 8],\n[7, 1, 7, 7, 7, 7, 8, 3, 9, 7, 7, 9, 2, 2, 3, 1, 7, 7, 7, 8, 7, 9],\n[9, 6, 2, 9, 9, 3, 1, 7, 7, 7, 1, 7, 7, 9, 7, 1, 2, 9, 6, 6, 2, 9],\n[9, 8, 7, 3, 1, 1, 8, 7, 7, 7, 2, 7, 6, 3, 7, 7, 7, 8, 2, 7, 3, 6],\n[6, 7, 6, 7, 7, 9, 7, 7, 8, 7, 7, 3, 7, 8, 1, 3, 6, 1, 8, 8, 8, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 2, 5, 9, 3, 8, 2, 6, 8, 1, 5, 9, 3, 5, 5, 1, 2, 8, 9, 1, 5, 5],\n[9, 6, 5, 9, 5, 5, 3, 6, 8, 1, 5, 5, 9, 8, 9, 8, 3, 6, 2, 5, 1, 2],\n[5, 5, 3, 2, 5, 3, 5, 5, 8, 9, 6, 3, 2, 1, 3, 6, 2, 9, 5, 5, 5, 5],\n[9, 8, 2, 3, 5, 5, 5, 2, 8, 5, 2, 3, 8, 8, 5, 3, 5, 9, 3, 2, 3, 5],\n[2, 2, 5, 1, 5, 6, 6, 5, 3, 1, 5, 3, 5, 8, 3, 5, 9, 5, 8, 5, 9, 5],\n[8, 9, 5, 5, 2, 8, 8, 5, 9, 6, 5, 9, 2, 6, 8, 5, 3, 5, 8, 3, 5, 8],\n[2, 5, 5, 2, 5, 1, 5, 5, 5, 5, 6, 1, 3, 6, 3, 5, 5, 5, 6, 5, 9, 6],\n[1, 8, 8, 5, 5, 9, 2, 5, 5, 2, 5, 9, 5, 5, 8, 1, 1, 6, 2, 5, 5, 2],\n[5, 5, 5, 3, 5, 5, 6, 5, 9, 8, 5, 8, 9, 5, 2, 9, 3, 9, 6, 5, 5, 3],\n[1, 5, 1, 3, 5, 3, 5, 5, 8, 8, 5, 5, 5, 3, 2, 3, 5, 8, 5, 6, 1, 5],\n[5, 9, 2, 9, 1, 5, 5, 1, 6, 2, 5, 9, 5, 5, 5, 6, 2, 2, 2, 2, 5, 5],\n[9, 9, 5, 5, 3, 9, 1, 8, 2, 9, 5, 1, 8, 3, 9, 3, 5, 5, 9, 5, 6, 9],\n[5, 6, 8, 9, 5, 5, 6, 3, 9, 9, 5, 3, 5, 8, 8, 9, 3, 5, 5, 6, 5, 8],\n[5, 1, 5, 5, 5, 5, 8, 3, 9, 5, 5, 9, 2, 2, 3, 1, 5, 5, 5, 8, 5, 9],\n[9, 6, 2, 9, 9, 3, 1, 5, 5, 5, 1, 5, 5, 9, 5, 1, 2, 9, 6, 6, 2, 9],\n[9, 8, 5, 3, 1, 1, 8, 5, 5, 5, 2, 5, 6, 3, 5, 5, 5, 8, 2, 5, 3, 6],\n[6, 5, 6, 5, 5, 9, 5, 5, 8, 5, 5, 3, 5, 8, 1, 3, 6, 1, 8, 8, 8, 5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[7, 8, 7, 7, 7, 7, 1],\n[7, 0, 3, 7, 6, 4, 5],\n[7, 7, 1, 4, 7, 9, 6],\n[0, 7, 7, 7, 9, 7, 7],\n[8, 4, 0, 7, 6, 4, 7],\n[7, 7, 5, 8, 8, 7, 0],\n[7, 7, 4, 3, 5, 7, 7],\n[7, 7, 7, 6, 7, 3, 7],\n[9, 8, 4, 7, 5, 7, 3],\n[6, 7, 7, 7, 0, 7, 7],\n[3, 7, 7, 7, 5, 5, 3],\n[3, 7, 0, 6, 9, 7, 7],\n[5, 1, 7, 9, 1, 4, 7],\n[7, 5, 3, 3, 3, 1, 7],\n[1, 7, 8, 8, 3, 7, 7],\n[0, 6, 7, 8, 9, 5, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 8, 5, 5, 5, 5, 1],\n[5, 0, 3, 5, 6, 4, 5],\n[5, 5, 1, 4, 5, 9, 6],\n[0, 5, 5, 5, 9, 5, 5],\n[8, 4, 0, 5, 6, 4, 5],\n[5, 5, 5, 8, 8, 5, 0],\n[5, 5, 4, 3, 5, 5, 5],\n[5, 5, 5, 6, 5, 3, 5],\n[9, 8, 4, 5, 5, 5, 3],\n[6, 5, 5, 5, 0, 5, 5],\n[3, 5, 5, 5, 5, 5, 3],\n[3, 5, 0, 6, 9, 5, 5],\n[5, 1, 5, 9, 1, 4, 5],\n[5, 5, 3, 3, 3, 1, 5],\n[1, 5, 8, 8, 3, 5, 5],\n[0, 6, 5, 8, 9, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 2, 6, 2, 2, 4, 6, 5, 6, 7],\n[7, 7, 3, 7, 5, 5, 7, 2, 7, 3],\n[2, 6, 3, 7, 8, 9, 7, 9, 7, 7],\n[6, 2, 7, 8, 9, 2, 7, 7, 7, 7],\n[6, 7, 5, 6, 7, 7, 7, 7, 7, 9],\n[7, 4, 8, 2, 7, 3, 4, 7, 2, 8],\n[7, 4, 9, 2, 7, 3, 3, 7, 7, 7],\n[8, 6, 4, 2, 6, 5, 8, 9, 6, 6],\n[7, 7, 7, 7, 9, 7, 2, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 2, 6, 2, 2, 4, 6, 5, 6, 5],\n[5, 5, 3, 5, 5, 5, 5, 2, 5, 3],\n[2, 6, 3, 5, 8, 9, 5, 9, 5, 5],\n[6, 2, 5, 8, 9, 2, 5, 5, 5, 5],\n[6, 5, 5, 6, 5, 5, 5, 5, 5, 9],\n[5, 4, 8, 2, 5, 3, 4, 5, 2, 8],\n[5, 4, 9, 2, 5, 3, 3, 5, 5, 5],\n[8, 6, 4, 2, 6, 5, 8, 9, 6, 6],\n[5, 5, 5, 5, 9, 5, 2, 5, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 7, 7, 6, 7, 3, 7, 7, 9, 6],\n[7, 4, 9, 9, 6, 4, 9, 4, 7, 7, 9],\n[3, 6, 7, 6, 6, 7, 7, 9, 6, 7, 9],\n[3, 7, 3, 6, 3, 7, 9, 3, 6, 3, 7],\n[6, 7, 6, 7, 6, 7, 4, 9, 7, 6, 9],\n[6, 6, 6, 4, 7, 7, 3, 9, 7, 4, 7],\n[7, 7, 9, 6, 7, 7, 9, 3, 7, 7, 7],\n[3, 6, 6, 9, 6, 6, 7, 6, 3, 6, 6],\n[7, 6, 4, 7, 7, 4, 6, 9, 7, 6, 7],\n[6, 7, 7, 4, 7, 7, 7, 7, 9, 7, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[1, 2, 7, 9, 3, 8, 2, 6, 8, 1, 7, 9, 3, 7, 7, 1, 2, 8, 9, 1, 7, 7], [9, 6, 7, 9, 7, 7, 3, 6, 8, 1, 7, 7, 9, 8, 9, 8, 3, 6, 2, 7, 1, 2], [7, 7, 3, 2, 7, 3, 7, 7, 8, 9, 6, 3, 2, 1, 3, 6, 2, 9, 7, 7, 7, 7], [9, 8, 2, 3, 7, 7, 7, 2, 8, 7, 2, 3, 8, 8, 7, 3, 7, 9, 3, 2, 3, 7], [2, 2, 7, 1, 7, 6, 6, 7, 3, 1, 7, 3, 7, 8, 3, 7, 9, 7, 8, 7, 9, 7], [8, 9, 7, 7, 2, 8, 8, 7, 9, 6, 7, 9, 2, 6, 8, 7, 3, 7, 8, 3, 7, 8], [2, 7, 7, 2, 7, 1, 7, 7, 7, 7, 6, 1, 3, 6, 3, 7, 7, 7, 6, 7, 9, 6], [1, 8, 8, 7, 7, 9, 2, 7, 7, 2, 7, 9, 7, 7, 8, 1, 1, 6, 2, 7, 7, 2], [7, 7, 7, 3, 7, 7, 6, 7, 9, 8, 7, 8, 9, 7, 2, 9, 3, 9, 6, 7, 7, 3], [1, 7, 1, 3, 7, 3, 7, 7, 8, 8, 7, 7, 7, 3, 2, 3, 7, 8, 7, 6, 1, 7], [7, 9, 2, 9, 1, 7, 7, 1, 6, 2, 7, 9, 7, 7, 7, 6, 2, 2, 2, 2, 7, 7], [9, 9, 7, 7, 3, 9, 1, 8, 2, 9, 7, 1, 8, 3, 9, 3, 7, 7, 9, 7, 6, 9], [7, 6, 8, 9, 7, 7, 6, 3, 9, 9, 7, 3, 7, 8, 8, 9, 3, 7, 7, 6, 7, 8], [7, 1, 7, 7, 7, 7, 8, 3, 9, 7, 7, 9, 2, 2, 3, 1, 7, 7, 7, 8, 7, 9], [9, 6, 2, 9, 9, 3, 1, 7, 7, 7, 1, 7, 7, 9, 7, 1, 2, 9, 6, 6, 2, 9], [9, 8, 7, 3, 1, 1, 8, 7, 7, 7, 2, 7, 6, 3, 7, 7, 7, 8, 2, 7, 3, 6], [6, 7, 6, 7, 7, 9, 7, 7, 8, 7, 7, 3, 7, 8, 1, 3, 6, 1, 8, 8, 8, 7]], "output": [[1, 2, 5, 9, 3, 8, 2, 6, 8, 1, 5, 9, 3, 5, 5, 1, 2, 8, 9, 1, 5, 5], [9, 6, 5, 9, 5, 5, 3, 6, 8, 1, 5, 5, 9, 8, 9, 8, 3, 6, 2, 5, 1, 2], [5, 5, 3, 2, 5, 3, 5, 5, 8, 9, 6, 3, 2, 1, 3, 6, 2, 9, 5, 5, 5, 5], [9, 8, 2, 3, 5, 5, 5, 2, 8, 5, 2, 3, 8, 8, 5, 3, 5, 9, 3, 2, 3, 5], [2, 2, 5, 1, 5, 6, 6, 5, 3, 1, 5, 3, 5, 8, 3, 5, 9, 5, 8, 5, 9, 5], [8, 9, 5, 5, 2, 8, 8, 5, 9, 6, 5, 9, 2, 6, 8, 5, 3, 5, 8, 3, 5, 8], [2, 5, 5, 2, 5, 1, 5, 5, 5, 5, 6, 1, 3, 6, 3, 5, 5, 5, 6, 5, 9, 6], [1, 8, 8, 5, 5, 9, 2, 5, 5, 2, 5, 9, 5, 5, 8, 1, 1, 6, 2, 5, 5, 2], [5, 5, 5, 3, 5, 5, 6, 5, 9, 8, 5, 8, 9, 5, 2, 9, 3, 9, 6, 5, 5, 3], [1, 5, 1, 3, 5, 3, 5, 5, 8, 8, 5, 5, 5, 3, 2, 3, 5, 8, 5, 6, 1, 5], [5, 9, 2, 9, 1, 5, 5, 1, 6, 2, 5, 9, 5, 5, 5, 6, 2, 2, 2, 2, 5, 5], [9, 9, 5, 5, 3, 9, 1, 8, 2, 9, 5, 1, 8, 3, 9, 3, 5, 5, 9, 5, 6, 9], [5, 6, 8, 9, 5, 5, 6, 3, 9, 9, 5, 3, 5, 8, 8, 9, 3, 5, 5, 6, 5, 8], [5, 1, 5, 5, 5, 5, 8, 3, 9, 5, 5, 9, 2, 2, 3, 1, 5, 5, 5, 8, 5, 9], [9, 6, 2, 9, 9, 3, 1, 5, 5, 5, 1, 5, 5, 9, 5, 1, 2, 9, 6, 6, 2, 9], [9, 8, 5, 3, 1, 1, 8, 5, 5, 5, 2, 5, 6, 3, 5, 5, 5, 8, 2, 5, 3, 6], [6, 5, 6, 5, 5, 9, 5, 5, 8, 5, 5, 3, 5, 8, 1, 3, 6, 1, 8, 8, 8, 5]]}, {"input": [[7, 8, 7, 7, 7, 7, 1], [7, 0, 3, 7, 6, 4, 5], [7, 7, 1, 4, 7, 9, 6], [0, 7, 7, 7, 9, 7, 7], [8, 4, 0, 7, 6, 4, 7], [7, 7, 5, 8, 8, 7, 0], [7, 7, 4, 3, 5, 7, 7], [7, 7, 7, 6, 7, 3, 7], [9, 8, 4, 7, 5, 7, 3], [6, 7, 7, 7, 0, 7, 7], [3, 7, 7, 7, 5, 5, 3], [3, 7, 0, 6, 9, 7, 7], [5, 1, 7, 9, 1, 4, 7], [7, 5, 3, 3, 3, 1, 7], [1, 7, 8, 8, 3, 7, 7], [0, 6, 7, 8, 9, 5, 7]], "output": [[5, 8, 5, 5, 5, 5, 1], [5, 0, 3, 5, 6, 4, 5], [5, 5, 1, 4, 5, 9, 6], [0, 5, 5, 5, 9, 5, 5], [8, 4, 0, 5, 6, 4, 5], [5, 5, 5, 8, 8, 5, 0], [5, 5, 4, 3, 5, 5, 5], [5, 5, 5, 6, 5, 3, 5], [9, 8, 4, 5, 5, 5, 3], [6, 5, 5, 5, 0, 5, 5], [3, 5, 5, 5, 5, 5, 3], [3, 5, 0, 6, 9, 5, 5], [5, 1, 5, 9, 1, 4, 5], [5, 5, 3, 3, 3, 1, 5], [1, 5, 8, 8, 3, 5, 5], [0, 6, 5, 8, 9, 5, 5]]}, {"input": [[7, 2, 6, 2, 2, 4, 6, 5, 6, 7], [7, 7, 3, 7, 5, 5, 7, 2, 7, 3], [2, 6, 3, 7, 8, 9, 7, 9, 7, 7], [6, 2, 7, 8, 9, 2, 7, 7, 7, 7], [6, 7, 5, 6, 7, 7, 7, 7, 7, 9], [7, 4, 8, 2, 7, 3, 4, 7, 2, 8], [7, 4, 9, 2, 7, 3, 3, 7, 7, 7], [8, 6, 4, 2, 6, 5, 8, 9, 6, 6], [7, 7, 7, 7, 9, 7, 2, 7, 7, 7]], "output": [[5, 2, 6, 2, 2, 4, 6, 5, 6, 5], [5, 5, 3, 5, 5, 5, 5, 2, 5, 3], [2, 6, 3, 5, 8, 9, 5, 9, 5, 5], [6, 2, 5, 8, 9, 2, 5, 5, 5, 5], [6, 5, 5, 6, 5, 5, 5, 5, 5, 9], [5, 4, 8, 2, 5, 3, 4, 5, 2, 8], [5, 4, 9, 2, 5, 3, 3, 5, 5, 5], [8, 6, 4, 2, 6, 5, 8, 9, 6, 6], [5, 5, 5, 5, 9, 5, 2, 5, 5, 5]]}], "input_grid": [[4, 4, 7, 7, 6, 7, 3, 7, 7, 9, 6], [7, 4, 9, 9, 6, 4, 9, 4, 7, 7, 9], [3, 6, 7, 6, 6, 7, 7, 9, 6, 7, 9], [3, 7, 3, 6, 3, 7, 9, 3, 6, 3, 7], [6, 7, 6, 7, 6, 7, 4, 9, 7, 6, 9], [6, 6, 6, 4, 7, 7, 3, 9, 7, 4, 7], [7, 7, 9, 6, 7, 7, 9, 3, 7, 7, 7], [3, 6, 6, 9, 6, 6, 7, 6, 3, 6, 6], [7, 6, 4, 7, 7, 4, 6, 9, 7, 6, 7], [6, 7, 7, 4, 7, 7, 7, 7, 9, 7, 6]], "task_key": "c8f0f002"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 9, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 8, 8, 9, 8, 8, 8, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 9, 9, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 8, 9, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 0, 0, 8, 8],\n[8, 8, 8, 8, 3, 8, 3, 0, 8, 8, 8, 8, 8, 2, 8, 8, 2, 2, 0, 0, 8, 8],\n[8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 8, 2, 2, 8, 2, 2, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 2, 2, 2, 2, 8, 8, 8, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 0, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 6, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8],\n[8, 6, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8],\n[8, 8, 6, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8],\n[6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 9, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 8, 8, 9, 8, 8, 2, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 9, 9, 8, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8],\n[8, 9, 8, 9, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8],\n[8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8],\n[8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 0, 0, 8, 8],\n[8, 8, 8, 8, 3, 8, 3, 0, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 0, 0, 8, 8],\n[8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 6, 8, 8, 8, 8, 4, 8, 4, 0, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8],\n[6, 8, 8, 6, 8, 8, 8, 4, 4, 4, 4, 8, 8, 1, 8, 8, 1, 8, 8, 8, 8, 8],\n[8, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8, 8],\n[6, 8, 6, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 0, 8, 8, 8, 8, 8],\n[6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 1, 1, 0, 1, 8, 8, 8, 7, 7, 0, 7, 8, 8],\n[8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8],\n[8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 0, 5, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 2, 2, 0, 2, 8, 8, 8, 8, 8, 8, 8, 8, 0, 2],\n[8, 8, 2, 8, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 1, 1, 0, 1, 8, 8, 8, 7, 7, 0, 7, 8, 8],\n[8, 8, 8, 1, 8, 1, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8],\n[8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8],\n[8, 8, 8, 1, 8, 1, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 9, 0, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 0, 5, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 5, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8],\n[8, 8, 2, 2, 0, 2, 8, 8, 5, 8, 5, 8, 2, 2, 0, 2],\n[8, 8, 2, 8, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 2, 8],\n[8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8],\n[8, 8, 2, 8, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 9, 2, 2, 9, 9, 9, 9, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 7, 2, 9, 9, 9, 9, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[9, 6, 2, 2, 2, 2, 9, 9, 9, 9, 4, 4, 4, 2, 2, 2, 2, 9, 4, 2, 2, 2, 9, 1, 2],\n[2, 2, 2, 9, 7, 2, 9, 9, 9, 9, 2, 4, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[9, 6, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2],\n[2, 6, 2, 2, 9, 2, 2, 9, 8, 2, 2, 2, 2, 2, 2, 2, 9, 0, 2, 9, 9, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 3, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 2, 2],\n[2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 3, 2, 2, 9, 6, 2, 2, 9, 2, 2, 2, 9, 9, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 0, 2, 2, 9, 9, 8, 2, 2, 2, 2, 9, 3, 2, 9, 0],\n[9, 5, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 3, 2, 2, 0],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 3, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2],\n[9, 6, 2, 9, 6, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 6, 2, 2, 6, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 5, 2, 2, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2],\n[2, 9, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 4, 2, 2, 9, 9, 9, 4, 2, 2],\n[2, 2, 7, 2, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2],\n[2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 9, 0, 2, 2, 2, 2, 2, 9, 8, 2, 2, 2, 9, 5, 2, 9, 4, 2, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 5, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 9, 7, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 7, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[9, 6, 2, 2, 2, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 9, 4, 2, 2, 2, 9, 1, 2],\n[2, 6, 2, 9, 7, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2],\n[2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[9, 6, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 9, 9, 5, 5, 2, 2],\n[2, 6, 2, 2, 9, 3, 2, 9, 8, 2, 4, 4, 4, 4, 2, 2, 9, 0, 2, 9, 9, 5, 5, 2, 2],\n[2, 2, 2, 2, 2, 3, 2, 2, 8, 2, 4, 4, 4, 4, 2, 2, 2, 0, 2, 2, 2, 5, 5, 2, 2],\n[2, 9, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 2, 2],\n[2, 2, 3, 2, 2, 9, 6, 2, 2, 9, 0, 2, 2, 9, 9, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 0, 2, 2, 9, 9, 8, 8, 2, 2, 2, 9, 3, 2, 9, 0],\n[9, 5, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 3, 2, 2, 0],\n[2, 5, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 9, 3, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 7, 7, 7, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2],\n[9, 6, 2, 9, 6, 2, 2, 9, 9, 9, 7, 7, 7, 2, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 6, 2, 2, 6, 2, 2, 9, 9, 9, 7, 7, 7, 2, 2, 2, 5, 2, 2, 9, 9, 9, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 2, 2, 2, 2, 2, 2, 9, 9, 9, 4, 4, 4],\n[2, 9, 7, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 2, 2, 9, 4, 2, 2, 9, 9, 9, 4, 4, 4],\n[2, 2, 7, 2, 2, 9, 5, 2, 2, 2, 7, 7, 7, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4],\n[2, 9, 0, 2, 2, 2, 2, 2, 9, 8, 2, 2, 2, 9, 5, 2, 9, 4, 2, 9, 5, 2, 4, 4, 4],\n[2, 2, 0, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 5, 2, 2, 4, 2, 2, 5, 2, 2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 0, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9, 3, 3, 3, 3],\n[0, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 9, 3, 3, 3, 3, 3, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 9, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 8, 8, 9, 8, 8, 8, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 9, 9, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 8, 9, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 2, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 0, 0, 8, 8], [8, 8, 8, 8, 3, 8, 3, 0, 8, 8, 8, 8, 8, 2, 8, 8, 2, 2, 0, 0, 8, 8], [8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 8, 2, 2, 8, 2, 2, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 2, 2, 2, 2, 8, 8, 8, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 0, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8], [8, 8, 8, 6, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8], [8, 6, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8], [8, 8, 6, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8], [6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 9, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 8, 8, 9, 8, 8, 2, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 9, 9, 8, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8], [8, 9, 8, 9, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8], [8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8], [8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8], [8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 0, 0, 8, 8], [8, 8, 8, 8, 3, 8, 3, 0, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 0, 0, 8, 8], [8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 6, 8, 8, 8, 8, 4, 8, 4, 0, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8], [6, 8, 8, 6, 8, 8, 8, 4, 4, 4, 4, 8, 8, 1, 8, 8, 1, 8, 8, 8, 8, 8], [8, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 8, 8], [6, 8, 6, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 0, 8, 8, 8, 8, 8], [6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 1, 0, 1, 8, 8, 8, 7, 7, 0, 7, 8, 8], [8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8], [8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 0, 5, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 0, 2, 8, 8, 8, 8, 8, 8, 8, 8, 0, 2], [8, 8, 2, 8, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 1, 0, 1, 8, 8, 8, 7, 7, 0, 7, 8, 8], [8, 8, 8, 1, 8, 1, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8], [8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8], [8, 8, 8, 1, 8, 1, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 9, 0, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 0, 5, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 5, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8], [8, 8, 2, 2, 0, 2, 8, 8, 5, 8, 5, 8, 2, 2, 0, 2], [8, 8, 2, 8, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 2, 8], [8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8], [8, 8, 2, 8, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[2, 2, 2, 9, 2, 2, 9, 9, 9, 9, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 9, 9, 9, 9, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 6, 2, 2, 2, 2, 9, 9, 9, 9, 4, 4, 4, 2, 2, 2, 2, 9, 4, 2, 2, 2, 9, 1, 2], [2, 2, 2, 9, 7, 2, 9, 9, 9, 9, 2, 4, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 6, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 2, 2, 2, 2], [2, 6, 2, 2, 9, 2, 2, 9, 8, 2, 2, 2, 2, 2, 2, 2, 9, 0, 2, 9, 9, 2, 2, 2, 2], [2, 2, 2, 2, 2, 3, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 2, 2], [2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 3, 2, 2, 9, 6, 2, 2, 9, 2, 2, 2, 9, 9, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 0, 2, 2, 9, 9, 8, 2, 2, 2, 2, 9, 3, 2, 9, 0], [9, 5, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 3, 2, 2, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 3, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2], [9, 6, 2, 9, 6, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 6, 2, 2, 6, 2, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 5, 2, 2, 9, 9, 9, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 2, 2, 2], [2, 9, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 4, 2, 2, 9, 9, 9, 4, 2, 2], [2, 2, 7, 2, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2], [2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 9, 0, 2, 2, 2, 2, 2, 9, 8, 2, 2, 2, 9, 5, 2, 9, 4, 2, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 5, 2, 2, 2, 2]], "output": [[2, 2, 2, 9, 7, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 7, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 6, 2, 2, 2, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 9, 4, 2, 2, 2, 9, 1, 2], [2, 6, 2, 9, 7, 2, 9, 9, 9, 9, 4, 4, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2], [2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 6, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 9, 9, 5, 5, 2, 2], [2, 6, 2, 2, 9, 3, 2, 9, 8, 2, 4, 4, 4, 4, 2, 2, 9, 0, 2, 9, 9, 5, 5, 2, 2], [2, 2, 2, 2, 2, 3, 2, 2, 8, 2, 4, 4, 4, 4, 2, 2, 2, 0, 2, 2, 2, 5, 5, 2, 2], [2, 9, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 2, 2], [2, 2, 3, 2, 2, 9, 6, 2, 2, 9, 0, 2, 2, 9, 9, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 0, 2, 2, 9, 9, 8, 8, 2, 2, 2, 9, 3, 2, 9, 0], [9, 5, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 3, 2, 2, 0], [2, 5, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 9, 3, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 7, 7, 7, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2], [9, 6, 2, 9, 6, 2, 2, 9, 9, 9, 7, 7, 7, 2, 2, 9, 5, 2, 2, 2, 2, 2, 2, 2, 2], [2, 6, 2, 2, 6, 2, 2, 9, 9, 9, 7, 7, 7, 2, 2, 2, 5, 2, 2, 9, 9, 9, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 2, 2, 2, 2, 2, 2, 9, 9, 9, 4, 4, 4], [2, 9, 7, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 2, 2, 9, 4, 2, 2, 9, 9, 9, 4, 4, 4], [2, 2, 7, 2, 2, 9, 5, 2, 2, 2, 7, 7, 7, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 4], [2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4], [2, 9, 0, 2, 2, 2, 2, 2, 9, 8, 2, 2, 2, 9, 5, 2, 9, 4, 2, 9, 5, 2, 4, 4, 4], [2, 2, 0, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 5, 2, 2, 4, 2, 2, 5, 2, 2, 2, 2]]}], "input_grid": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 0, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9, 3, 3, 3, 3], [0, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 9, 3, 3, 3, 3, 3, 3]], "task_key": "57aa92db"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 1, 3, 7, 0, 4],\n[8, 1, 3, 7, 0, 4],\n[8, 1, 3, 7, 0, 4],\n[8, 1, 3, 7, 0, 4],\n[8, 1, 3, 7, 0, 4],\n[8, 1, 3, 7, 0, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 4, 9, 5],\n[7, 4, 9, 5],\n[7, 4, 9, 5],\n[7, 4, 9, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6],\n[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 1, 9, 0, 4, 3, 6],\n[2, 1, 9, 0, 4, 3, 6],\n[2, 1, 9, 0, 4, 3, 6],\n[2, 1, 9, 0, 4, 3, 6],\n[2, 1, 9, 0, 4, 3, 6],\n[2, 1, 9, 0, 4, 3, 6],\n[2, 1, 9, 0, 4, 3, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 5, 5, 5, 5, 5, 5, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 1, 3, 6, 7, 6, 0, 4]], "output": [[8, 1, 3, 7, 0, 4], [8, 1, 3, 7, 0, 4], [8, 1, 3, 7, 0, 4], [8, 1, 3, 7, 0, 4], [8, 1, 3, 7, 0, 4], [8, 1, 3, 7, 0, 4]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5], [2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 4, 9, 2, 5]], "output": [[7, 4, 9, 5], [7, 4, 9, 5], [7, 4, 9, 5], [7, 4, 9, 5]]}, {"input": [[8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6], [8, 2, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 0, 8, 8, 4, 3, 6]], "output": [[2, 1, 9, 0, 4, 3, 6], [2, 1, 9, 0, 4, 3, 6], [2, 1, 9, 0, 4, 3, 6], [2, 1, 9, 0, 4, 3, 6], [2, 1, 9, 0, 4, 3, 6], [2, 1, 9, 0, 4, 3, 6], [2, 1, 9, 0, 4, 3, 6]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 7, 6, 0, 0, 3, 5]], "task_key": "8e1813be"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 0, 6, 6],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6],\n[3, 3, 3, 3, 8, 8, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6],\n[3, 3, 3, 3, 8, 3, 0, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 6, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 0, 6, 6],\n[3, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 0, 0, 0, 6],\n[3, 3, 3, 3, 8, 8, 0, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 0, 0, 0, 6],\n[3, 3, 3, 3, 8, 0, 0, 0, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 0, 0, 0, 6],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 6, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 6, 6, 6, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 6, 6, 6, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 5, 2, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 2, 2, 0, 5, 2, 5, 5, 2, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 2, 2, 2, 5, 2, 5, 2, 2, 2, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 5, 2, 4, 2, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 2, 2, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 0, 9, 0, 0, 2, 8, 8, 2, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 0, 2, 2, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 5, 0, 5, 5, 2, 4, 4, 4, 4, 4, 2, 2, 2],\n[2, 2, 2, 2, 5, 0, 0, 0, 5, 2, 5, 5, 4, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 0, 0, 0, 5, 2, 5, 4, 4, 4, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 5, 4, 4, 4, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 4, 4, 4, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 9, 4, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 9, 9, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 9, 9, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 9, 9, 9, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 9, 9, 9, 0, 2, 0, 0, 0, 0, 0, 2, 2],\n[2, 2, 2, 2, 2, 0, 0, 9, 0, 0, 2, 8, 8, 0, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 2, 8, 0, 0, 0, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[6, 6, 6, 6, 6, 2, 6, 2, 2, 2, 6, 2, 2, 2, 2, 2],\n[6, 2, 2, 2, 6, 2, 6, 6, 3, 6, 6, 2, 2, 2, 2, 2],\n[6, 2, 4, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[6, 6, 2, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 3, 2, 2, 2, 3, 2, 2, 2, 4, 4, 2, 4, 4, 2, 2],\n[2, 3, 2, 2, 0, 3, 2, 2, 2, 4, 2, 2, 6, 4, 2, 2],\n[2, 3, 3, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 2],\n[3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 3, 2, 4, 2],\n[3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2],\n[3, 2, 2, 6, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 6, 2, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2],\n[6, 6, 6, 6, 6, 2, 6, 3, 3, 3, 6, 2, 2, 2, 2, 2],\n[6, 4, 4, 4, 6, 2, 6, 6, 3, 6, 6, 2, 2, 2, 2, 2],\n[6, 4, 4, 4, 6, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2],\n[6, 6, 4, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 3, 3, 0, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 3, 0, 0, 0, 3, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2],\n[2, 3, 0, 0, 0, 3, 2, 2, 2, 4, 4, 6, 4, 4, 2, 2],\n[2, 3, 0, 0, 0, 3, 2, 2, 2, 4, 6, 6, 6, 4, 2, 2],\n[2, 3, 3, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2],\n[3, 3, 6, 3, 3, 2, 2, 2, 2, 2, 4, 4, 3, 4, 4, 2],\n[3, 6, 6, 6, 3, 2, 2, 2, 2, 2, 4, 3, 3, 3, 4, 2],\n[3, 6, 6, 6, 3, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2],\n[3, 6, 6, 6, 3, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2],\n[3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 4, 4, 6, 4, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 6, 8, 8],\n[1, 1, 1, 1, 1, 8, 1, 1, 1, 8, 1, 1, 1, 8, 1, 1, 1, 8],\n[1, 1, 1, 1, 1, 8, 4, 1, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8],\n[1, 1, 1, 1, 1, 8, 8, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 0, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6], [3, 3, 3, 3, 8, 8, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6], [3, 3, 3, 3, 8, 3, 0, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 6, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 0, 6, 6], [3, 3, 3, 3, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 0, 0, 0, 6], [3, 3, 3, 3, 8, 8, 0, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 0, 0, 0, 6], [3, 3, 3, 3, 8, 0, 0, 0, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 0, 0, 0, 6], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 6, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 6, 6, 6, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 6, 6, 6, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 5, 2, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 2, 2, 0, 5, 2, 5, 5, 2, 5, 5, 2, 2, 2], [2, 2, 2, 2, 5, 2, 2, 2, 5, 2, 5, 2, 2, 2, 5, 2, 2, 2], [2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 5, 2, 4, 2, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 2, 2, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 0, 9, 0, 0, 2, 8, 8, 2, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 0, 2, 2, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 5, 0, 5, 5, 2, 4, 4, 4, 4, 4, 2, 2, 2], [2, 2, 2, 2, 5, 0, 0, 0, 5, 2, 5, 5, 4, 5, 5, 2, 2, 2], [2, 2, 2, 2, 5, 0, 0, 0, 5, 2, 5, 4, 4, 4, 5, 2, 2, 2], [2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 5, 4, 4, 4, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 4, 4, 4, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 9, 4, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 9, 9, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 9, 9, 9, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 9, 9, 9, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 9, 9, 9, 0, 2, 0, 0, 0, 0, 0, 2, 2], [2, 2, 2, 2, 2, 0, 0, 9, 0, 0, 2, 8, 8, 0, 8, 8, 2, 2], [2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 2, 8, 0, 0, 0, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [6, 6, 6, 6, 6, 2, 6, 2, 2, 2, 6, 2, 2, 2, 2, 2], [6, 2, 2, 2, 6, 2, 6, 6, 3, 6, 6, 2, 2, 2, 2, 2], [6, 2, 4, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 6, 2, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 2, 2, 2, 3, 2, 2, 2, 4, 4, 2, 4, 4, 2, 2], [2, 3, 2, 2, 0, 3, 2, 2, 2, 4, 2, 2, 6, 4, 2, 2], [2, 3, 3, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 2], [3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 3, 2, 4, 2], [3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2], [3, 2, 2, 6, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 6, 2, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2], [6, 6, 6, 6, 6, 2, 6, 3, 3, 3, 6, 2, 2, 2, 2, 2], [6, 4, 4, 4, 6, 2, 6, 6, 3, 6, 6, 2, 2, 2, 2, 2], [6, 4, 4, 4, 6, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2], [6, 6, 4, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 3, 0, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 0, 0, 0, 3, 2, 2, 2, 6, 6, 6, 6, 6, 2, 2], [2, 3, 0, 0, 0, 3, 2, 2, 2, 4, 4, 6, 4, 4, 2, 2], [2, 3, 0, 0, 0, 3, 2, 2, 2, 4, 6, 6, 6, 4, 2, 2], [2, 3, 3, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2], [3, 3, 6, 3, 3, 2, 2, 2, 2, 2, 4, 4, 3, 4, 4, 2], [3, 6, 6, 6, 3, 2, 2, 2, 2, 2, 4, 3, 3, 3, 4, 2], [3, 6, 6, 6, 3, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2], [3, 6, 6, 6, 3, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 2], [3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 4, 4, 6, 4, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2]]}], "input_grid": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 6, 8, 8], [1, 1, 1, 1, 1, 8, 1, 1, 1, 8, 1, 1, 1, 8, 1, 1, 1, 8], [1, 1, 1, 1, 1, 8, 4, 1, 1, 8, 1, 1, 1, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 8, 8, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "task_key": "444801d8"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 6, 8, 8, 6, 8, 4],\n[8, 2, 8, 8, 7, 4, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 2, 8, 8],\n[8, 8, 6, 8, 7, 6, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6],\n[8, 4, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 5, 8, 6, 8, 8, 6, 8, 6, 8, 5, 8, 5, 2, 8, 8, 8],\n[8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 7, 6],\n[8, 6, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 4, 8, 8, 7],\n[8, 7, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 8, 8, 8, 7, 8, 8, 2, 8, 8],\n[8, 8, 2, 7, 2, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 2, 8, 4],\n[8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 4, 4, 6, 8, 8, 8, 7, 8, 8, 8, 8, 8, 2, 8, 8],\n[8, 8, 6, 8, 8, 8, 8, 8, 2, 8, 8, 8, 4, 2, 2, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 4, 4, 8, 6, 8, 7, 6, 8],\n[8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 4, 4],\n[8, 8, 8, 8, 8, 8, 8, 7, 2, 8, 8, 8, 2, 8, 4, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[9, 3, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 5, 3, 5, 3, 9],\n[5, 9, 9, 9, 2, 9, 5, 3, 9, 3, 9, 9, 2, 2, 9, 2, 9],\n[9, 5, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[5, 9, 9, 5, 9, 9, 2, 9, 9, 9, 3, 9, 9, 9, 5, 9, 9],\n[3, 9, 9, 2, 5, 3, 9, 2, 9, 9, 9, 2, 5, 9, 2, 9, 2],\n[9, 2, 9, 2, 5, 3, 9, 9, 5, 5, 9, 3, 2, 2, 3, 9, 9],\n[2, 2, 9, 9, 9, 3, 2, 9, 5, 3, 9, 9, 9, 5, 9, 2, 9],\n[9, 9, 9, 9, 2, 3, 9, 3, 9, 3, 3, 9, 9, 2, 9, 9, 2],\n[3, 9, 9, 5, 9, 5, 5, 9, 3, 3, 2, 9, 2, 3, 2, 9, 9],\n[9, 3, 2, 3, 9, 3, 3, 3, 5, 9, 9, 9, 2, 9, 9, 9, 9],\n[5, 2, 9, 2, 9, 2, 3, 2, 3, 9, 9, 5, 9, 9, 9, 3, 5],\n[5, 2, 3, 9, 2, 2, 2, 2, 3, 9, 9, 9, 5, 3, 3, 9, 2],\n[3, 2, 5, 9, 5, 9, 5, 3, 3, 5, 9, 5, 3, 2, 2, 9, 2],\n[9, 9, 9, 9, 5, 2, 2, 9, 9, 5, 9, 3, 3, 9, 9, 5, 9],\n[9, 3, 9, 9, 9, 2, 9, 9, 5, 5, 9, 2, 3, 5, 5, 9, 9],\n[5, 3, 9, 2, 9, 2, 9, 3, 9, 9, 5, 9, 9, 3, 9, 5, 9],\n[5, 3, 5, 2, 9, 3, 9, 9, 9, 3, 2, 2, 9, 2, 9, 9, 3],\n[9, 9, 9, 9, 3, 9, 5, 9, 3, 9, 9, 2, 9, 2, 3, 5, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 1, 7, 7, 1, 1, 7, 1, 7, 7, 7, 7, 7, 1, 1],\n[7, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 7, 7, 7, 7],\n[7, 7, 7, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 1, 7],\n[1, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1],\n[7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 1, 1, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 1, 1, 1, 7, 7, 7, 7, 7, 7],\n[1, 7, 1, 1, 7, 7, 1, 7, 1, 1, 7, 7, 7, 7, 7],\n[1, 1, 7, 7, 7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 7],\n[7, 7, 1, 1, 1, 7, 1, 7, 7, 1, 7, 7, 1, 1, 7],\n[7, 7, 7, 7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7],\n[1, 7, 7, 1, 7, 7, 7, 7, 7, 1, 1, 7, 7, 7, 7],\n[1, 7, 7, 7, 7, 7, 7, 1, 1, 1, 7, 7, 1, 7, 1],\n[1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 1],\n[7, 1, 7, 7, 7, 7, 1, 7, 1, 7, 7, 7, 7, 7, 1],\n[1, 7, 7, 7, 7, 7, 1, 7, 1, 7, 7, 1, 7, 1, 7],\n[7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 1, 1, 7, 7],\n[1, 7, 7, 7, 7, 1, 7, 7, 1, 1, 7, 7, 1, 7, 7],\n[1, 7, 1, 1, 1, 7, 1, 1, 7, 7, 7, 1, 1, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 1, 7, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8],\n[8, 8, 8, 1, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 1],\n[8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 1, 8, 8, 1, 1],\n[1, 8, 8, 1, 1, 8, 1, 8, 8, 8, 1, 1, 1, 8, 8],\n[8, 8, 1, 8, 8, 8, 1, 8, 8, 1, 8, 8, 8, 8, 8],\n[1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 1, 1],\n[8, 1, 8, 8, 8, 8, 1, 1, 8, 8, 1, 8, 1, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 1, 8],\n[1, 1, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 1, 8, 8],\n[8, 8, 1, 1, 8, 8, 1, 1, 1, 8, 8, 1, 1, 1, 8],\n[8, 8, 8, 8, 1, 1, 8, 1, 8, 1, 8, 8, 1, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 6, 8, 8, 6, 8, 4], [8, 2, 8, 8, 7, 4, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 2, 8, 8], [8, 8, 6, 8, 7, 6, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6], [8, 4, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 5, 8, 6, 8, 8, 6, 8, 6, 8, 5, 8, 5, 2, 8, 8, 8], [8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 7, 6], [8, 6, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 4, 8, 8, 7], [8, 7, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 7, 8, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 6, 2, 8, 8, 8, 7, 8, 8, 2, 8, 8], [8, 8, 2, 7, 2, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 2, 8, 4], [8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 4, 4, 4, 6, 8, 8, 8, 7, 8, 8, 8, 8, 8, 2, 8, 8], [8, 8, 6, 8, 8, 8, 8, 8, 2, 8, 8, 8, 4, 2, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 4, 4, 8, 6, 8, 7, 6, 8], [8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 4, 4], [8, 8, 8, 8, 8, 8, 8, 7, 2, 8, 8, 8, 2, 8, 4, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[9, 3, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 5, 3, 5, 3, 9], [5, 9, 9, 9, 2, 9, 5, 3, 9, 3, 9, 9, 2, 2, 9, 2, 9], [9, 5, 9, 2, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [5, 9, 9, 5, 9, 9, 2, 9, 9, 9, 3, 9, 9, 9, 5, 9, 9], [3, 9, 9, 2, 5, 3, 9, 2, 9, 9, 9, 2, 5, 9, 2, 9, 2], [9, 2, 9, 2, 5, 3, 9, 9, 5, 5, 9, 3, 2, 2, 3, 9, 9], [2, 2, 9, 9, 9, 3, 2, 9, 5, 3, 9, 9, 9, 5, 9, 2, 9], [9, 9, 9, 9, 2, 3, 9, 3, 9, 3, 3, 9, 9, 2, 9, 9, 2], [3, 9, 9, 5, 9, 5, 5, 9, 3, 3, 2, 9, 2, 3, 2, 9, 9], [9, 3, 2, 3, 9, 3, 3, 3, 5, 9, 9, 9, 2, 9, 9, 9, 9], [5, 2, 9, 2, 9, 2, 3, 2, 3, 9, 9, 5, 9, 9, 9, 3, 5], [5, 2, 3, 9, 2, 2, 2, 2, 3, 9, 9, 9, 5, 3, 3, 9, 2], [3, 2, 5, 9, 5, 9, 5, 3, 3, 5, 9, 5, 3, 2, 2, 9, 2], [9, 9, 9, 9, 5, 2, 2, 9, 9, 5, 9, 3, 3, 9, 9, 5, 9], [9, 3, 9, 9, 9, 2, 9, 9, 5, 5, 9, 2, 3, 5, 5, 9, 9], [5, 3, 9, 2, 9, 2, 9, 3, 9, 9, 5, 9, 9, 3, 9, 5, 9], [5, 3, 5, 2, 9, 3, 9, 9, 9, 3, 2, 2, 9, 2, 9, 9, 3], [9, 9, 9, 9, 3, 9, 5, 9, 3, 9, 9, 2, 9, 2, 3, 5, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[7, 1, 7, 7, 1, 1, 7, 1, 7, 7, 7, 7, 7, 1, 1], [7, 1, 1, 7, 7, 7, 7, 7, 1, 1, 1, 7, 7, 7, 7], [7, 7, 7, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 1, 7], [1, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1], [7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 1, 1, 7, 7, 7], [7, 7, 7, 7, 7, 7, 1, 1, 1, 7, 7, 7, 7, 7, 7], [1, 7, 1, 1, 7, 7, 1, 7, 1, 1, 7, 7, 7, 7, 7], [1, 1, 7, 7, 7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 7], [7, 7, 1, 1, 1, 7, 1, 7, 7, 1, 7, 7, 1, 1, 7], [7, 7, 7, 7, 1, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7], [1, 7, 7, 1, 7, 7, 7, 7, 7, 1, 1, 7, 7, 7, 7], [1, 7, 7, 7, 7, 7, 7, 1, 1, 1, 7, 7, 1, 7, 1], [1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 1], [7, 1, 7, 7, 7, 7, 1, 7, 1, 7, 7, 7, 7, 7, 1], [1, 7, 7, 7, 7, 7, 1, 7, 1, 7, 7, 1, 7, 1, 7], [7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 1, 1, 7, 7], [1, 7, 7, 7, 7, 1, 7, 7, 1, 1, 7, 7, 1, 7, 7], [1, 7, 1, 1, 1, 7, 1, 1, 7, 7, 7, 1, 1, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 1, 7, 1]], "output": [[7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 7]]}], "input_grid": [[8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 8, 1, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 1], [8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 1, 8, 8, 1, 1], [1, 8, 8, 1, 1, 8, 1, 8, 8, 8, 1, 1, 1, 8, 8], [8, 8, 1, 8, 8, 8, 1, 8, 8, 1, 8, 8, 8, 8, 8], [1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 1, 1], [8, 1, 8, 8, 8, 8, 1, 1, 8, 8, 1, 8, 1, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 1, 8], [1, 1, 8, 8, 1, 8, 8, 8, 1, 8, 8, 8, 1, 8, 8], [8, 8, 1, 1, 8, 8, 1, 1, 1, 8, 8, 1, 1, 1, 8], [8, 8, 8, 8, 1, 1, 8, 1, 8, 1, 8, 8, 1, 8, 8]], "task_key": "d23f8c26"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 6, 6, 6, 6, 8, 8, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 6, 6, 6, 6, 8, 8, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8],\n[8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 1, 1, 1, 8, 8],\n[8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8],\n[8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8],\n[8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8],\n[8, 8, 8, 6, 6, 6, 6, 8, 8, 9, 8, 8, 8, 9, 8, 8],\n[8, 8, 8, 6, 8, 8, 6, 8, 8, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8],\n[8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 1, 1, 1, 8, 8],\n[8, 8, 0, 8, 8, 0, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8],\n[8, 8, 0, 8, 8, 0, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8],\n[8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 8, 8, 6, 8, 8, 8, 8, 8, 2, 8, 8, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 6, 8, 8, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 6, 8, 8, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 8, 8, 6, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 5, 8, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 6, 6, 6, 6, 8, 8, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 6, 6, 6, 6, 8, 8, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8], [8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 1, 1, 1, 8, 8], [8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8], [8, 8, 8, 6, 6, 6, 6, 8, 8, 9, 8, 8, 8, 9, 8, 8], [8, 8, 8, 6, 8, 8, 6, 8, 8, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 0, 0, 0, 0, 7, 7, 7, 7, 7, 1, 1, 1, 8, 8], [8, 8, 0, 8, 8, 0, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8], [8, 8, 0, 8, 8, 0, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 8, 8, 6, 8, 8, 8, 8, 8, 2, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 6, 8, 8, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8], [8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 6, 8, 8, 6, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 6, 8, 8, 6, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 5, 8, 3, 8, 8, 8, 8, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "task_key": "4347f46a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 0, 5, 2, 9, 5, 7, 5, 3],\n[7, 9, 3, 7, 7, 2, 5, 5, 9],\n[6, 5, 2, 4, 5, 9, 9, 2, 2],\n[8, 9, 7, 8, 6, 0, 3, 9, 1],\n[7, 8, 8, 6, 8, 2, 5, 3, 4],\n[9, 1, 9, 3, 2, 1, 5, 8, 3],\n[2, 3, 2, 1, 9, 7, 0, 4, 3],\n[9, 9, 2, 5, 9, 9, 1, 3, 5],\n[9, 2, 5, 1, 6, 6, 2, 4, 1],\n[9, 3, 2, 7, 8, 9, 1, 5, 1],\n[8, 0, 6, 6, 5, 6, 5, 8, 8],\n[5, 0, 2, 3, 2, 9, 7, 1, 7],\n[3, 5, 6, 3, 1, 4, 7, 2, 1],\n[2, 7, 2, 9, 6, 6, 4, 1, 4],\n[2, 3, 4, 4, 8, 1, 8, 9, 6],\n[6, 6, 2, 3, 1, 2, 4, 7, 2],\n[4, 5, 4, 3, 6, 6, 6, 6, 8],\n[9, 7, 0, 6, 5, 3, 1, 0, 3],\n[9, 9, 1, 6, 8, 4, 8, 7, 1],\n[5, 6, 5, 3, 5, 5, 0, 0, 3],\n[4, 4, 1, 3, 9, 6, 3, 7, 1],\n[2, 1, 4, 1, 9, 0, 5, 0, 6],\n[8, 4, 8, 9, 6, 9, 5, 0, 8],\n[3, 8, 9, 1, 2, 5, 3, 1, 9],\n[7, 3, 4, 6, 5, 1, 6, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 0, 5, 2, 9, 5, 7, 5, 3],\n[7, 9, 3, 7, 7, 2, 5, 5, 9],\n[2, 5, 2, 4, 5, 9, 9, 2, 2],\n[8, 9, 7, 8, 2, 0, 3, 9, 1],\n[7, 8, 8, 2, 8, 2, 5, 3, 4],\n[9, 1, 9, 3, 2, 1, 5, 8, 3],\n[2, 3, 2, 1, 9, 7, 0, 4, 3],\n[9, 9, 2, 5, 9, 9, 1, 3, 5],\n[9, 2, 5, 1, 2, 2, 2, 4, 1],\n[9, 3, 2, 7, 8, 9, 1, 5, 1],\n[8, 0, 2, 2, 5, 2, 5, 8, 8],\n[5, 0, 2, 3, 2, 9, 7, 1, 7],\n[3, 5, 2, 3, 1, 4, 7, 2, 1],\n[2, 7, 2, 9, 2, 2, 4, 1, 4],\n[2, 3, 4, 4, 8, 1, 8, 9, 2],\n[2, 2, 2, 3, 1, 2, 4, 7, 2],\n[4, 5, 4, 3, 2, 2, 2, 2, 8],\n[9, 7, 0, 2, 5, 3, 1, 0, 3],\n[9, 9, 1, 2, 8, 4, 8, 7, 1],\n[5, 2, 5, 3, 5, 5, 0, 0, 3],\n[4, 4, 1, 3, 9, 2, 3, 7, 1],\n[2, 1, 4, 1, 9, 0, 5, 0, 2],\n[8, 4, 8, 9, 2, 9, 5, 0, 8],\n[3, 8, 9, 1, 2, 5, 3, 1, 9],\n[7, 3, 4, 2, 5, 1, 2, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 9, 9, 6, 5, 2, 5, 7, 0, 2, 7, 4, 9, 2, 3],\n[5, 5, 7, 9, 4, 0, 5, 5, 2, 8, 9, 5, 7, 6, 9],\n[5, 6, 5, 2, 9, 3, 2, 6, 2, 4, 5, 7, 9, 3, 8],\n[3, 4, 7, 9, 5, 7, 6, 4, 4, 2, 0, 9, 5, 7, 6],\n[0, 3, 7, 7, 3, 0, 6, 2, 4, 7, 5, 9, 6, 1, 8],\n[4, 9, 9, 9, 6, 5, 4, 9, 4, 2, 6, 8, 7, 7, 1],\n[2, 5, 0, 3, 6, 8, 3, 3, 5, 5, 3, 2, 7, 5, 4],\n[5, 5, 5, 8, 0, 1, 3, 3, 3, 6, 9, 3, 4, 3, 5],\n[1, 1, 4, 8, 2, 2, 7, 3, 7, 8, 8, 7, 3, 0, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 9, 9, 2, 5, 2, 5, 7, 0, 2, 7, 4, 9, 2, 3],\n[5, 5, 7, 9, 4, 0, 5, 5, 2, 8, 9, 5, 7, 2, 9],\n[5, 2, 5, 2, 9, 3, 2, 2, 2, 4, 5, 7, 9, 3, 8],\n[3, 4, 7, 9, 5, 7, 2, 4, 4, 2, 0, 9, 5, 7, 2],\n[0, 3, 7, 7, 3, 0, 2, 2, 4, 7, 5, 9, 2, 1, 8],\n[4, 9, 9, 9, 2, 5, 4, 9, 4, 2, 2, 8, 7, 7, 1],\n[2, 5, 0, 3, 2, 8, 3, 3, 5, 5, 3, 2, 7, 5, 4],\n[5, 5, 5, 8, 0, 1, 3, 3, 3, 2, 9, 3, 4, 3, 5],\n[1, 1, 4, 8, 2, 2, 7, 3, 7, 8, 8, 7, 3, 0, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 0, 7, 2, 9, 4, 0, 3],\n[1, 7, 4, 5, 3, 7, 9, 8],\n[1, 0, 0, 3, 8, 4, 8, 4],\n[5, 3, 3, 9, 2, 2, 9, 2],\n[8, 8, 3, 1, 4, 3, 1, 9],\n[9, 1, 2, 4, 8, 2, 8, 0],\n[3, 8, 7, 5, 9, 8, 0, 3],\n[8, 2, 5, 3, 9, 0, 1, 5],\n[8, 4, 4, 8, 1, 3, 4, 4],\n[7, 0, 3, 1, 1, 5, 5, 9],\n[1, 8, 1, 8, 2, 3, 9, 0],\n[0, 3, 3, 3, 8, 7, 8, 0],\n[3, 9, 2, 5, 0, 4, 2, 9],\n[8, 0, 0, 4, 8, 7, 4, 3],\n[8, 5, 1, 3, 9, 4, 5, 4],\n[7, 9, 2, 9, 4, 9, 2, 8],\n[2, 3, 3, 0, 3, 0, 5, 0],\n[2, 8, 7, 3, 3, 3, 1, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 0, 7, 2, 9, 4, 0, 3],\n[1, 7, 4, 5, 3, 7, 9, 8],\n[1, 0, 0, 3, 8, 4, 8, 4],\n[5, 3, 3, 9, 2, 2, 9, 2],\n[8, 8, 3, 1, 4, 3, 1, 9],\n[9, 1, 2, 4, 8, 2, 8, 0],\n[3, 8, 7, 5, 9, 8, 0, 3],\n[8, 2, 5, 3, 9, 0, 1, 5],\n[8, 4, 4, 8, 1, 3, 4, 4],\n[7, 0, 3, 1, 1, 5, 5, 9],\n[1, 8, 1, 8, 2, 3, 9, 0],\n[0, 3, 3, 3, 8, 7, 8, 0],\n[3, 9, 2, 5, 0, 4, 2, 9],\n[8, 0, 0, 4, 8, 7, 4, 3],\n[8, 5, 1, 3, 9, 4, 5, 4],\n[7, 9, 2, 9, 4, 9, 2, 8],\n[2, 3, 3, 0, 3, 0, 5, 0],\n[2, 8, 7, 3, 3, 3, 1, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 4, 7, 3, 5, 0, 2, 1, 2, 2, 2, 9, 3, 5, 3, 7, 7, 0, 8, 0, 9, 8, 2, 0, 0, 6, 5, 7],\n[1, 3, 5, 2, 4, 7, 5, 0, 1, 0, 3, 9, 1, 5, 5, 8, 3, 4, 9, 2, 4, 9, 2, 7, 1, 3, 4, 2],\n[8, 2, 2, 7, 5, 8, 9, 8, 5, 2, 2, 5, 5, 5, 8, 9, 0, 7, 1, 3, 7, 5, 3, 7, 1, 8, 3, 5],\n[6, 5, 6, 5, 0, 0, 3, 2, 5, 5, 3, 1, 2, 3, 5, 4, 9, 7, 1, 4, 2, 7, 3, 4, 6, 0, 9, 8],\n[7, 0, 1, 2, 8, 9, 0, 1, 4, 7, 7, 2, 0, 5, 4, 9, 2, 9, 0, 4, 3, 2, 0, 7, 2, 6, 4, 1],\n[0, 7, 9, 7, 3, 6, 0, 2, 5, 9, 5, 9, 0, 7, 6, 3, 0, 9, 4, 9, 4, 1, 6, 0, 3, 6, 0, 9],\n[4, 1, 4, 5, 0, 0, 8, 2, 8, 0, 1, 4, 6, 9, 5, 5, 3, 8, 5, 9, 5, 4, 1, 9, 2, 5, 4, 9],\n[8, 3, 2, 3, 4, 1, 1, 0, 9, 8, 0, 7, 9, 8, 9, 2, 0, 8, 5, 3, 1, 1, 1, 5, 2, 5, 7, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 0, 5, 2, 9, 5, 7, 5, 3], [7, 9, 3, 7, 7, 2, 5, 5, 9], [6, 5, 2, 4, 5, 9, 9, 2, 2], [8, 9, 7, 8, 6, 0, 3, 9, 1], [7, 8, 8, 6, 8, 2, 5, 3, 4], [9, 1, 9, 3, 2, 1, 5, 8, 3], [2, 3, 2, 1, 9, 7, 0, 4, 3], [9, 9, 2, 5, 9, 9, 1, 3, 5], [9, 2, 5, 1, 6, 6, 2, 4, 1], [9, 3, 2, 7, 8, 9, 1, 5, 1], [8, 0, 6, 6, 5, 6, 5, 8, 8], [5, 0, 2, 3, 2, 9, 7, 1, 7], [3, 5, 6, 3, 1, 4, 7, 2, 1], [2, 7, 2, 9, 6, 6, 4, 1, 4], [2, 3, 4, 4, 8, 1, 8, 9, 6], [6, 6, 2, 3, 1, 2, 4, 7, 2], [4, 5, 4, 3, 6, 6, 6, 6, 8], [9, 7, 0, 6, 5, 3, 1, 0, 3], [9, 9, 1, 6, 8, 4, 8, 7, 1], [5, 6, 5, 3, 5, 5, 0, 0, 3], [4, 4, 1, 3, 9, 6, 3, 7, 1], [2, 1, 4, 1, 9, 0, 5, 0, 6], [8, 4, 8, 9, 6, 9, 5, 0, 8], [3, 8, 9, 1, 2, 5, 3, 1, 9], [7, 3, 4, 6, 5, 1, 6, 8, 8]], "output": [[4, 0, 5, 2, 9, 5, 7, 5, 3], [7, 9, 3, 7, 7, 2, 5, 5, 9], [2, 5, 2, 4, 5, 9, 9, 2, 2], [8, 9, 7, 8, 2, 0, 3, 9, 1], [7, 8, 8, 2, 8, 2, 5, 3, 4], [9, 1, 9, 3, 2, 1, 5, 8, 3], [2, 3, 2, 1, 9, 7, 0, 4, 3], [9, 9, 2, 5, 9, 9, 1, 3, 5], [9, 2, 5, 1, 2, 2, 2, 4, 1], [9, 3, 2, 7, 8, 9, 1, 5, 1], [8, 0, 2, 2, 5, 2, 5, 8, 8], [5, 0, 2, 3, 2, 9, 7, 1, 7], [3, 5, 2, 3, 1, 4, 7, 2, 1], [2, 7, 2, 9, 2, 2, 4, 1, 4], [2, 3, 4, 4, 8, 1, 8, 9, 2], [2, 2, 2, 3, 1, 2, 4, 7, 2], [4, 5, 4, 3, 2, 2, 2, 2, 8], [9, 7, 0, 2, 5, 3, 1, 0, 3], [9, 9, 1, 2, 8, 4, 8, 7, 1], [5, 2, 5, 3, 5, 5, 0, 0, 3], [4, 4, 1, 3, 9, 2, 3, 7, 1], [2, 1, 4, 1, 9, 0, 5, 0, 2], [8, 4, 8, 9, 2, 9, 5, 0, 8], [3, 8, 9, 1, 2, 5, 3, 1, 9], [7, 3, 4, 2, 5, 1, 2, 8, 8]]}, {"input": [[6, 9, 9, 6, 5, 2, 5, 7, 0, 2, 7, 4, 9, 2, 3], [5, 5, 7, 9, 4, 0, 5, 5, 2, 8, 9, 5, 7, 6, 9], [5, 6, 5, 2, 9, 3, 2, 6, 2, 4, 5, 7, 9, 3, 8], [3, 4, 7, 9, 5, 7, 6, 4, 4, 2, 0, 9, 5, 7, 6], [0, 3, 7, 7, 3, 0, 6, 2, 4, 7, 5, 9, 6, 1, 8], [4, 9, 9, 9, 6, 5, 4, 9, 4, 2, 6, 8, 7, 7, 1], [2, 5, 0, 3, 6, 8, 3, 3, 5, 5, 3, 2, 7, 5, 4], [5, 5, 5, 8, 0, 1, 3, 3, 3, 6, 9, 3, 4, 3, 5], [1, 1, 4, 8, 2, 2, 7, 3, 7, 8, 8, 7, 3, 0, 9]], "output": [[2, 9, 9, 2, 5, 2, 5, 7, 0, 2, 7, 4, 9, 2, 3], [5, 5, 7, 9, 4, 0, 5, 5, 2, 8, 9, 5, 7, 2, 9], [5, 2, 5, 2, 9, 3, 2, 2, 2, 4, 5, 7, 9, 3, 8], [3, 4, 7, 9, 5, 7, 2, 4, 4, 2, 0, 9, 5, 7, 2], [0, 3, 7, 7, 3, 0, 2, 2, 4, 7, 5, 9, 2, 1, 8], [4, 9, 9, 9, 2, 5, 4, 9, 4, 2, 2, 8, 7, 7, 1], [2, 5, 0, 3, 2, 8, 3, 3, 5, 5, 3, 2, 7, 5, 4], [5, 5, 5, 8, 0, 1, 3, 3, 3, 2, 9, 3, 4, 3, 5], [1, 1, 4, 8, 2, 2, 7, 3, 7, 8, 8, 7, 3, 0, 9]]}, {"input": [[7, 0, 7, 2, 9, 4, 0, 3], [1, 7, 4, 5, 3, 7, 9, 8], [1, 0, 0, 3, 8, 4, 8, 4], [5, 3, 3, 9, 2, 2, 9, 2], [8, 8, 3, 1, 4, 3, 1, 9], [9, 1, 2, 4, 8, 2, 8, 0], [3, 8, 7, 5, 9, 8, 0, 3], [8, 2, 5, 3, 9, 0, 1, 5], [8, 4, 4, 8, 1, 3, 4, 4], [7, 0, 3, 1, 1, 5, 5, 9], [1, 8, 1, 8, 2, 3, 9, 0], [0, 3, 3, 3, 8, 7, 8, 0], [3, 9, 2, 5, 0, 4, 2, 9], [8, 0, 0, 4, 8, 7, 4, 3], [8, 5, 1, 3, 9, 4, 5, 4], [7, 9, 2, 9, 4, 9, 2, 8], [2, 3, 3, 0, 3, 0, 5, 0], [2, 8, 7, 3, 3, 3, 1, 7]], "output": [[7, 0, 7, 2, 9, 4, 0, 3], [1, 7, 4, 5, 3, 7, 9, 8], [1, 0, 0, 3, 8, 4, 8, 4], [5, 3, 3, 9, 2, 2, 9, 2], [8, 8, 3, 1, 4, 3, 1, 9], [9, 1, 2, 4, 8, 2, 8, 0], [3, 8, 7, 5, 9, 8, 0, 3], [8, 2, 5, 3, 9, 0, 1, 5], [8, 4, 4, 8, 1, 3, 4, 4], [7, 0, 3, 1, 1, 5, 5, 9], [1, 8, 1, 8, 2, 3, 9, 0], [0, 3, 3, 3, 8, 7, 8, 0], [3, 9, 2, 5, 0, 4, 2, 9], [8, 0, 0, 4, 8, 7, 4, 3], [8, 5, 1, 3, 9, 4, 5, 4], [7, 9, 2, 9, 4, 9, 2, 8], [2, 3, 3, 0, 3, 0, 5, 0], [2, 8, 7, 3, 3, 3, 1, 7]]}], "input_grid": [[0, 4, 7, 3, 5, 0, 2, 1, 2, 2, 2, 9, 3, 5, 3, 7, 7, 0, 8, 0, 9, 8, 2, 0, 0, 6, 5, 7], [1, 3, 5, 2, 4, 7, 5, 0, 1, 0, 3, 9, 1, 5, 5, 8, 3, 4, 9, 2, 4, 9, 2, 7, 1, 3, 4, 2], [8, 2, 2, 7, 5, 8, 9, 8, 5, 2, 2, 5, 5, 5, 8, 9, 0, 7, 1, 3, 7, 5, 3, 7, 1, 8, 3, 5], [6, 5, 6, 5, 0, 0, 3, 2, 5, 5, 3, 1, 2, 3, 5, 4, 9, 7, 1, 4, 2, 7, 3, 4, 6, 0, 9, 8], [7, 0, 1, 2, 8, 9, 0, 1, 4, 7, 7, 2, 0, 5, 4, 9, 2, 9, 0, 4, 3, 2, 0, 7, 2, 6, 4, 1], [0, 7, 9, 7, 3, 6, 0, 2, 5, 9, 5, 9, 0, 7, 6, 3, 0, 9, 4, 9, 4, 1, 6, 0, 3, 6, 0, 9], [4, 1, 4, 5, 0, 0, 8, 2, 8, 0, 1, 4, 6, 9, 5, 5, 3, 8, 5, 9, 5, 4, 1, 9, 2, 5, 4, 9], [8, 3, 2, 3, 4, 1, 1, 0, 9, 8, 0, 7, 9, 8, 9, 2, 0, 8, 5, 3, 1, 1, 1, 5, 2, 5, 7, 4]], "task_key": "b1948b0a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 9, 1],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4],\n[4, 6, 9, 1, 4],\n[4, 2, 2, 6, 4],\n[4, 4, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 4, 0, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 4, 4, 4, 0, 0, 0, 5, 5, 5, 6],\n[6, 4, 4, 4, 0, 0, 0, 5, 5, 5, 6],\n[6, 4, 4, 4, 0, 0, 0, 5, 5, 5, 6],\n[6, 9, 9, 9, 9, 9, 9, 0, 0, 0, 6],\n[6, 9, 9, 9, 9, 9, 9, 0, 0, 0, 6],\n[6, 9, 9, 9, 9, 9, 9, 0, 0, 0, 6],\n[6, 9, 9, 9, 9, 9, 9, 5, 5, 5, 6],\n[6, 9, 9, 9, 9, 9, 9, 5, 5, 5, 6],\n[6, 9, 9, 9, 9, 9, 9, 5, 5, 5, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3],\n[3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3],\n[3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3],\n[3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3],\n[3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3],\n[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3],\n[9, 7, 6, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[7, 9, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 9, 9, 7, 7, 6, 6, 5, 5, 1],\n[1, 9, 9, 7, 7, 6, 6, 5, 5, 1],\n[1, 7, 7, 9, 9, 5, 5, 3, 3, 1],\n[1, 7, 7, 9, 9, 5, 5, 3, 3, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 9, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 6, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 7, 7, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 9, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 9, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[4, 4, 4, 4, 4], [4, 6, 9, 1, 4], [4, 2, 2, 6, 4], [4, 4, 4, 4, 4]]}, {"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 4, 0, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 4, 4, 4, 0, 0, 0, 5, 5, 5, 6], [6, 4, 4, 4, 0, 0, 0, 5, 5, 5, 6], [6, 4, 4, 4, 0, 0, 0, 5, 5, 5, 6], [6, 9, 9, 9, 9, 9, 9, 0, 0, 0, 6], [6, 9, 9, 9, 9, 9, 9, 0, 0, 0, 6], [6, 9, 9, 9, 9, 9, 9, 0, 0, 0, 6], [6, 9, 9, 9, 9, 9, 9, 5, 5, 5, 6], [6, 9, 9, 9, 9, 9, 9, 5, 5, 5, 6], [6, 9, 9, 9, 9, 9, 9, 5, 5, 5, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3], [3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3], [3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3], [3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [9, 7, 6, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [7, 9, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 9, 9, 7, 7, 6, 6, 5, 5, 1], [1, 9, 9, 7, 7, 6, 6, 5, 5, 1], [1, 7, 7, 9, 9, 5, 5, 3, 3, 1], [1, 7, 7, 9, 9, 5, 5, 3, 3, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 7, 7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "6b9890af"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8],\n[1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1],\n[1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1],\n[1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1],\n[1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1],\n[1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1],\n[0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 7],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 7, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 2],\n[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0],\n[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 7],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 2, 0, 7, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 2, 0, 7, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 7, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7],\n[0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0],\n[3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 4, 1, 1, 1, 1, 2, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 4, 2, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[7, 1, 1, 1, 1, 1, 1, 1],\n[3, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 5],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 8, 1, 3, 7],\n[1, 1, 1, 1, 1, 1, 1, 9],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[8, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 0],\n[1, 1, 9, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1],\n[0, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8], [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1], [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1], [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1], [1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1], [1, 0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 8, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 7, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 2, 0, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 2, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 7, 0, 0, 0]]}, {"input": [[6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0]], "output": [[6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[5, 4, 1, 1, 1, 1, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 4, 2, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [7, 1, 1, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 8, 1, 3, 7], [1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 0], [1, 1, 9, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 1, 1, 1]], "task_key": "1f876c06"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8],\n[8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 7, 7, 8, 8, 0, 8, 9, 8, 7, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8],\n[8, 8, 8, 9, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 0, 8, 8, 7, 8, 0, 0, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 9, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8, 8, 9, 0, 8, 0, 8, 8, 8],\n[9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 0, 0, 8, 7, 7, 8, 9, 8, 8, 8, 7, 0, 8, 8, 8, 8],\n[8, 8, 3, 3, 3, 7, 8, 8, 8, 7, 0, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 0, 7, 8, 8, 8, 8, 8, 0, 0, 8, 7, 7, 8],\n[7, 8, 3, 3, 3, 8, 7, 8, 9, 0, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 9, 7, 8, 8, 7, 8, 8, 8, 8],\n[8, 8, 3, 3, 3, 8, 7, 0, 9, 8, 7, 8, 8, 8, 0, 8, 8, 8, 8, 0, 8, 8, 0, 8, 9, 8, 8, 8, 8],\n[8, 8, 3, 3, 3, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 9, 8, 8, 8, 8, 0, 9, 0, 0],\n[7, 9, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 9, 0, 8, 0, 8, 8, 8],\n[8, 8, 8, 3, 3, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8],\n[0, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 8, 0, 8, 8, 0, 8, 8],\n[9, 7, 8, 8, 0, 8, 0, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 9, 8, 8, 8, 0, 8, 8, 8, 8],\n[8, 8, 8, 9, 8, 0, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 0, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 9, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3],\n[3, 3, 3],\n[3, 3, 3],\n[3, 3, 3],\n[3, 3, 3],\n[8, 3, 3],\n[8, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 9, 0, 0, 3, 0, 0],\n[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8],\n[0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 0],\n[0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 3, 5, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7],\n[7, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 9],\n[1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 0, 1, 1, 1, 6, 2, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 7, 3, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 8, 1, 1, 1, 1, 7, 1],\n[1, 9, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1],\n[6, 5, 1, 7, 1, 1, 0, 9, 6, 1, 1, 1, 5, 1, 1, 1, 9, 1, 9],\n[1, 1, 7, 8, 9, 1, 7, 7, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1],\n[1, 8, 5, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 9, 1, 3, 1, 1],\n[3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 1, 1, 1, 1, 1, 7],\n[1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 3, 1, 1, 8, 2, 1, 6, 1, 1, 1, 2, 1, 1],\n[8, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 3, 1],\n[1, 1, 6, 1, 4, 4, 4, 4, 4, 4, 4, 8, 5, 1, 1, 1, 1, 1, 1],\n[8, 9, 1, 1, 4, 1, 4, 4, 4, 4, 4, 1, 3, 9, 1, 1, 1, 1, 1],\n[1, 7, 1, 2, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 7, 1, 1, 1, 7],\n[1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 5, 8, 1, 1, 1, 1, 0, 1],\n[1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 7, 1, 1, 1, 2, 7, 1, 1],\n[1, 1, 9, 8, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 3, 1, 1],\n[5, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 8, 3, 1, 1, 1, 4, 4, 4, 4, 4, 1, 1, 1, 5, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4],\n[4, 1, 4, 4, 4, 4, 4],\n[1, 1, 1, 1, 4, 4, 4],\n[1, 1, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4],\n[1, 1, 4, 4, 4, 4, 4],\n[1, 1, 4, 4, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 0, 4, 4, 0, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 0, 4, 4],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 5, 5, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 5, 5, 4, 4, 4, 9, 4, 0, 4, 4, 9, 4, 5, 4, 0, 4, 4, 4, 4, 4, 5, 4, 4],\n[4, 4, 4, 0, 5, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 0, 4],\n[4, 4, 4, 4, 9, 4, 4, 4, 4, 9, 4, 4, 8, 8, 8, 9, 4, 4, 4, 4, 4, 4, 4, 0, 9, 4, 4],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 9, 9, 9, 9, 4, 4, 8, 8, 8, 8, 8, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 0, 4, 4, 4, 9, 4, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 9, 4],\n[0, 4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 0, 4, 4, 4, 4, 4, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 9],\n[4, 9, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 0, 0, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8], [8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 7, 7, 8, 8, 0, 8, 9, 8, 7, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8], [8, 8, 8, 9, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 0, 8, 8, 7, 8, 0, 0, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 9, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 9, 8, 8, 8, 9, 0, 8, 0, 8, 8, 8], [9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 0, 0, 8, 7, 7, 8, 9, 8, 8, 8, 7, 0, 8, 8, 8, 8], [8, 8, 3, 3, 3, 7, 8, 8, 8, 7, 0, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 0, 7, 8, 8, 8, 8, 8, 0, 0, 8, 7, 7, 8], [7, 8, 3, 3, 3, 8, 7, 8, 9, 0, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 9, 7, 8, 8, 7, 8, 8, 8, 8], [8, 8, 3, 3, 3, 8, 7, 0, 9, 8, 7, 8, 8, 8, 0, 8, 8, 8, 8, 0, 8, 8, 0, 8, 9, 8, 8, 8, 8], [8, 8, 3, 3, 3, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 9, 8, 8, 8, 8, 0, 9, 0, 0], [7, 9, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 9, 0, 8, 0, 8, 8, 8], [8, 8, 8, 3, 3, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8], [0, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 8, 0, 8, 8, 0, 8, 8], [9, 7, 8, 8, 0, 8, 0, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 9, 8, 8, 8, 0, 8, 8, 8, 8], [8, 8, 8, 9, 8, 0, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 0, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8], [8, 8, 8, 8, 8, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 9, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[3, 3, 3], [3, 3, 3], [3, 3, 3], [3, 3, 3], [3, 3, 3], [8, 3, 3], [8, 3, 3]]}, {"input": [[0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 9, 0, 0, 3, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8], [0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 0], [0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 3, 5, 0, 0, 0]], "output": [[7, 7, 7], [7, 7, 7]]}, {"input": [[1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 9], [1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 0, 1, 1, 1, 6, 2, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1], [1, 1, 1, 7, 3, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6, 1], [1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 8, 1, 1, 1, 1, 7, 1], [1, 9, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 1, 7, 1], [6, 5, 1, 7, 1, 1, 0, 9, 6, 1, 1, 1, 5, 1, 1, 1, 9, 1, 9], [1, 1, 7, 8, 9, 1, 7, 7, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1], [1, 8, 5, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 9, 1, 3, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 1, 1, 1, 1, 1, 7], [1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 3, 1, 1, 8, 2, 1, 6, 1, 1, 1, 2, 1, 1], [8, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 3, 1], [1, 1, 6, 1, 4, 4, 4, 4, 4, 4, 4, 8, 5, 1, 1, 1, 1, 1, 1], [8, 9, 1, 1, 4, 1, 4, 4, 4, 4, 4, 1, 3, 9, 1, 1, 1, 1, 1], [1, 7, 1, 2, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 7, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 5, 8, 1, 1, 1, 1, 0, 1], [1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 7, 1, 1, 1, 2, 7, 1, 1], [1, 1, 9, 8, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 3, 1, 1], [5, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1], [1, 8, 3, 1, 1, 1, 4, 4, 4, 4, 4, 1, 1, 1, 5, 1, 1, 1, 1]], "output": [[4, 4, 4, 4, 4, 4, 4], [4, 1, 4, 4, 4, 4, 4], [1, 1, 1, 1, 4, 4, 4], [1, 1, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4], [1, 1, 4, 4, 4, 4, 4], [1, 1, 4, 4, 4, 4, 4]]}], "input_grid": [[4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 9, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 0, 4, 4, 0, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 0, 4, 4], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 5, 5, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 5, 5, 4, 4, 4, 9, 4, 0, 4, 4, 9, 4, 5, 4, 0, 4, 4, 4, 4, 4, 5, 4, 4], [4, 4, 4, 0, 5, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 0, 4], [4, 4, 4, 4, 9, 4, 4, 4, 4, 9, 4, 4, 8, 8, 8, 9, 4, 4, 4, 4, 4, 4, 4, 0, 9, 4, 4], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 8, 8, 8, 8, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 9, 9, 9, 9, 4, 4, 8, 8, 8, 8, 8, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 4, 4, 4, 9, 4, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 9, 4], [0, 4, 9, 4, 4, 4, 9, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 0, 4, 4, 4, 4, 4, 9, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 9], [4, 9, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 0, 0, 4, 4, 4]], "task_key": "1f85a75f"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[0, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[0, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 6, 6, 6, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[0, 6, 8, 6, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 5, 8, 8, 8, 5, 0, 0, 0, 0],\n[0, 6, 8, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 8, 8, 8, 5, 0, 0, 0, 0],\n[0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 4, 8, 8, 8, 8, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 4, 8, 8, 8, 8, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0],\n[0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0],\n[0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0],\n[0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0],\n[0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 3, 8, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0],\n[0, 0, 3, 8, 3, 0, 0, 2, 8, 8, 8, 2, 0, 0],\n[0, 0, 3, 8, 3, 0, 0, 2, 8, 8, 8, 2, 0, 0],\n[0, 0, 3, 8, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0],\n[0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 8, 8, 8, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 8, 8, 8, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 8, 8, 8, 3, 0],\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 3, 8, 8, 8, 8, 3, 0],\n[0, 0, 0, 0, 0, 0, 5, 8, 5, 0, 3, 3, 3, 3, 3, 3, 0],\n[0, 0, 0, 0, 0, 0, 5, 8, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2],\n[0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2],\n[0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2],\n[0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2],\n[0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2],\n[2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2],\n[2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2],\n[2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 2],\n[2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 2],\n[2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 2],\n[2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2],\n[2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2],\n[2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2],\n[2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2],\n[2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [0, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [0, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 7, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [0, 6, 8, 6, 4, 8, 8, 8, 8, 8, 4, 0, 0, 0, 0, 0, 0, 0, 5, 8, 8, 8, 5, 0, 0, 0, 0], [0, 6, 8, 6, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 8, 8, 8, 5, 0, 0, 0, 0], [0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 3, 3, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 4, 8, 8, 8, 8, 4, 0, 0, 0], [0, 0, 0, 0, 0, 4, 8, 8, 8, 8, 4, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0], [0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0], [0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0], [0, 0, 9, 8, 8, 9, 0, 0, 5, 8, 8, 8, 5, 0], [0, 0, 9, 9, 9, 9, 0, 0, 5, 5, 5, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 8, 8, 8, 8, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 8, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 3, 8, 3, 0, 0, 2, 8, 8, 8, 2, 0, 0], [0, 0, 3, 8, 3, 0, 0, 2, 8, 8, 8, 2, 0, 0], [0, 0, 3, 8, 3, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 8, 8, 8, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 8, 8, 8, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 8, 8, 8, 3, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 3, 8, 8, 8, 8, 3, 0], [0, 0, 0, 0, 0, 0, 5, 8, 5, 0, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 5, 8, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2], [0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2], [0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2], [0, 0, 0, 7, 7, 7, 2, 2, 2, 2, 2], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2], [2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2], [2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2], [2, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 2], [2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 2], [2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 2], [2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2], [2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2], [2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2], [2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2], [2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "task_key": "50cb2852"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0],\n[0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0],\n[0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0],\n[0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 1],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 1, 0, 0],\n[0, 1, 0, 0, 1, 0, 0],\n[1, 0, 0, 0, 0, 0, 0],\n[1, 1, 0, 0, 0, 1, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 1, 0, 0],\n[0, 0, 0, 0, 1, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[0, 1, 0, 0, 0, 0, 1],\n[1, 0, 0, 0, 0, 0, 0],\n[1, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0],\n[1, 0, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[2, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 2],\n[2, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 2, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0],\n[0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5],\n[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5],\n[0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 7, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}, {"input": [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [2, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 2], [2, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 2, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]], "output": [[2, 2, 2, 2]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5], [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "d631b094"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 1, 9, 1, 1, 1, 1, 0, 1, 0, 5, 1, 0, 1, 1, 1, 1],\n[1, 9, 9, 1, 0, 5, 1, 8, 0, 1, 9, 5, 3, 1, 8, 3, 8],\n[1, 1, 1, 1, 1, 3, 5, 3, 3, 9, 1, 1, 0, 1, 1, 1, 1],\n[1, 1, 1, 1, 9, 1, 1, 1, 0, 9, 9, 1, 1, 1, 9, 1, 1],\n[0, 5, 8, 5, 8, 1, 1, 1, 5, 1, 1, 3, 1, 1, 8, 9, 1],\n[1, 1, 0, 1, 8, 5, 1, 9, 5, 1, 1, 1, 1, 1, 3, 1, 1],\n[1, 8, 3, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 0, 8, 1],\n[9, 1, 1, 9, 1, 3, 5, 9, 1, 1, 1, 1, 9, 5, 1, 9, 1],\n[0, 9, 1, 1, 0, 5, 1, 1, 0, 5, 3, 8, 1, 1, 1, 1, 1],\n[1, 3, 1, 0, 1, 1, 1, 1, 3, 8, 9, 1, 8, 9, 8, 8, 1],\n[3, 8, 1, 5, 0, 5, 1, 0, 5, 1, 8, 3, 1, 3, 3, 9, 1],\n[0, 0, 3, 5, 3, 0, 1, 1, 9, 8, 9, 1, 1, 1, 1, 1, 5],\n[1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 8, 8, 5, 1, 3, 8, 1],\n[1, 1, 1, 8, 8, 5, 5, 1, 1, 8, 5, 1, 3, 1, 1, 0, 1],\n[3, 1, 1, 8, 8, 0, 1, 0, 0, 9, 3, 9, 1, 8, 1, 5, 1],\n[3, 1, 3, 1, 9, 1, 1, 0, 5, 1, 1, 1, 0, 0, 8, 3, 3],\n[1, 3, 1, 3, 1, 1, 3, 9, 1, 1, 9, 1, 9, 5, 1, 1, 0],\n[1, 8, 3, 3, 9, 0, 1, 1, 1, 9, 1, 9, 1, 8, 5, 3, 1],\n[3, 1, 5, 3, 1, 5, 1, 8, 9, 0, 1, 1, 1, 5, 0, 1, 1],\n[5, 1, 1, 1, 8, 1, 5, 1, 0, 3, 1, 3, 5, 8, 3, 5, 1],\n[1, 3, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 1, 1, 1],\n[9, 1, 1, 9, 1, 9, 5, 5, 1, 0, 1, 3, 3, 1, 0, 9, 1],\n[1, 5, 5, 5, 1, 9, 1, 1, 1, 3, 0, 1, 1, 9, 8, 1, 9],\n[1, 1, 8, 1, 3, 0, 3, 5, 1, 3, 1, 1, 8, 1, 1, 0, 3],\n[1, 1, 9, 5, 0, 1, 1, 1, 5, 1, 3, 1, 5, 1, 1, 0, 9],\n[3, 1, 3, 0, 1, 1, 9, 5, 1, 5, 1, 9, 1, 3, 1, 8, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 9, 9, 4, 4, 4, 4],\n[4, 5, 4, 1, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 1, 4, 4, 4, 5],\n[4, 7, 4, 4, 4, 4, 4, 8, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 3, 4, 4, 4, 4, 1, 0, 1],\n[4, 4, 4, 4, 7, 4, 1, 8, 4],\n[0, 4, 4, 4, 4, 4, 3, 0, 4],\n[8, 8, 4, 4, 4, 4, 4, 4, 9],\n[8, 3, 9, 4, 4, 4, 1, 4, 4],\n[4, 4, 4, 9, 8, 4, 9, 4, 4],\n[4, 4, 4, 4, 6, 3, 4, 3, 6],\n[4, 5, 4, 7, 4, 6, 4, 4, 4],\n[4, 5, 4, 0, 3, 4, 6, 4, 4],\n[4, 4, 6, 4, 0, 1, 4, 4, 5],\n[4, 8, 1, 4, 4, 4, 8, 4, 4],\n[4, 4, 4, 1, 4, 4, 4, 4, 4],\n[4, 4, 9, 4, 4, 4, 4, 1, 3],\n[4, 4, 4, 3, 4, 4, 4, 4, 9],\n[4, 4, 3, 4, 4, 4, 4, 5, 4],\n[3, 1, 4, 8, 6, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 8, 4, 4, 4],\n[0, 4, 4, 4, 4, 4, 8, 4, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 9, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 1, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 7, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 4, 4, 4, 4],\n[4, 4, 4, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 3, 4, 4, 4, 4],\n[4, 4, 4, 4, 0, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 9, 3, 9, 9, 5, 2, 6, 3, 6, 6, 6, 6],\n[6, 6, 5, 6, 6, 6, 6, 6, 6, 2, 6, 6, 4],\n[5, 6, 5, 6, 9, 6, 6, 3, 5, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 2, 3, 2, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 2, 5, 6, 6, 6, 5, 3, 6, 6],\n[6, 6, 6, 6, 2, 2, 5, 5, 6, 2, 3, 6, 6],\n[3, 6, 6, 6, 4, 6, 2, 6, 3, 3, 6, 3, 6],\n[5, 6, 4, 5, 6, 6, 6, 6, 6, 6, 5, 5, 6],\n[6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 5, 9],\n[6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 3, 3, 6],\n[6, 4, 6, 3, 6, 6, 6, 9, 3, 6, 6, 9, 5],\n[6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 4],\n[9, 6, 6, 2, 6, 6, 6, 6, 9, 6, 6, 6, 3],\n[6, 6, 6, 2, 6, 5, 6, 5, 6, 6, 6, 2, 6],\n[6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 5, 6],\n[6, 6, 4, 2, 6, 3, 4, 6, 2, 4, 6, 9, 6],\n[2, 9, 6, 4, 6, 2, 9, 5, 6, 6, 6, 9, 5],\n[6, 3, 6, 9, 6, 2, 9, 6, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 2, 6, 6, 3, 6, 6, 6, 9, 6],\n[9, 9, 5, 6, 6, 5, 3, 6, 6, 2, 6, 6, 6],\n[6, 6, 9, 6, 5, 6, 6, 6, 4, 6, 9, 6, 6],\n[9, 6, 5, 6, 3, 4, 6, 6, 6, 6, 6, 6, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4],\n[4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 9, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 1, 9, 1, 1, 1, 1, 0, 1, 0, 5, 1, 0, 1, 1, 1, 1], [1, 9, 9, 1, 0, 5, 1, 8, 0, 1, 9, 5, 3, 1, 8, 3, 8], [1, 1, 1, 1, 1, 3, 5, 3, 3, 9, 1, 1, 0, 1, 1, 1, 1], [1, 1, 1, 1, 9, 1, 1, 1, 0, 9, 9, 1, 1, 1, 9, 1, 1], [0, 5, 8, 5, 8, 1, 1, 1, 5, 1, 1, 3, 1, 1, 8, 9, 1], [1, 1, 0, 1, 8, 5, 1, 9, 5, 1, 1, 1, 1, 1, 3, 1, 1], [1, 8, 3, 1, 1, 0, 9, 1, 1, 1, 1, 1, 1, 1, 0, 8, 1], [9, 1, 1, 9, 1, 3, 5, 9, 1, 1, 1, 1, 9, 5, 1, 9, 1], [0, 9, 1, 1, 0, 5, 1, 1, 0, 5, 3, 8, 1, 1, 1, 1, 1], [1, 3, 1, 0, 1, 1, 1, 1, 3, 8, 9, 1, 8, 9, 8, 8, 1], [3, 8, 1, 5, 0, 5, 1, 0, 5, 1, 8, 3, 1, 3, 3, 9, 1], [0, 0, 3, 5, 3, 0, 1, 1, 9, 8, 9, 1, 1, 1, 1, 1, 5], [1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 8, 8, 5, 1, 3, 8, 1], [1, 1, 1, 8, 8, 5, 5, 1, 1, 8, 5, 1, 3, 1, 1, 0, 1], [3, 1, 1, 8, 8, 0, 1, 0, 0, 9, 3, 9, 1, 8, 1, 5, 1], [3, 1, 3, 1, 9, 1, 1, 0, 5, 1, 1, 1, 0, 0, 8, 3, 3], [1, 3, 1, 3, 1, 1, 3, 9, 1, 1, 9, 1, 9, 5, 1, 1, 0], [1, 8, 3, 3, 9, 0, 1, 1, 1, 9, 1, 9, 1, 8, 5, 3, 1], [3, 1, 5, 3, 1, 5, 1, 8, 9, 0, 1, 1, 1, 5, 0, 1, 1], [5, 1, 1, 1, 8, 1, 5, 1, 0, 3, 1, 3, 5, 8, 3, 5, 1], [1, 3, 1, 1, 1, 1, 1, 0, 1, 3, 1, 1, 0, 1, 1, 1, 1], [9, 1, 1, 9, 1, 9, 5, 5, 1, 0, 1, 3, 3, 1, 0, 9, 1], [1, 5, 5, 5, 1, 9, 1, 1, 1, 3, 0, 1, 1, 9, 8, 1, 9], [1, 1, 8, 1, 3, 0, 3, 5, 1, 3, 1, 1, 8, 1, 1, 0, 3], [1, 1, 9, 5, 0, 1, 1, 1, 5, 1, 3, 1, 5, 1, 1, 0, 9], [3, 1, 3, 0, 1, 1, 9, 5, 1, 5, 1, 9, 1, 3, 1, 8, 1]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}, {"input": [[4, 4, 4, 9, 9, 4, 4, 4, 4], [4, 5, 4, 1, 4, 4, 4, 4, 4], [4, 4, 4, 4, 1, 4, 4, 4, 5], [4, 7, 4, 4, 4, 4, 4, 8, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 3, 4, 4, 4, 4, 1, 0, 1], [4, 4, 4, 4, 7, 4, 1, 8, 4], [0, 4, 4, 4, 4, 4, 3, 0, 4], [8, 8, 4, 4, 4, 4, 4, 4, 9], [8, 3, 9, 4, 4, 4, 1, 4, 4], [4, 4, 4, 9, 8, 4, 9, 4, 4], [4, 4, 4, 4, 6, 3, 4, 3, 6], [4, 5, 4, 7, 4, 6, 4, 4, 4], [4, 5, 4, 0, 3, 4, 6, 4, 4], [4, 4, 6, 4, 0, 1, 4, 4, 5], [4, 8, 1, 4, 4, 4, 8, 4, 4], [4, 4, 4, 1, 4, 4, 4, 4, 4], [4, 4, 9, 4, 4, 4, 4, 1, 3], [4, 4, 4, 3, 4, 4, 4, 4, 9], [4, 4, 3, 4, 4, 4, 4, 5, 4], [3, 1, 4, 8, 6, 4, 4, 4, 4], [4, 4, 4, 4, 4, 8, 4, 4, 4], [0, 4, 4, 4, 4, 4, 8, 4, 9]], "output": [[4, 4, 4, 4, 9, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 1, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 7, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 4, 4, 4, 4], [4, 4, 4, 4, 6, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 3, 4, 4, 4, 4], [4, 4, 4, 4, 0, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 6, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[6, 9, 3, 9, 9, 5, 2, 6, 3, 6, 6, 6, 6], [6, 6, 5, 6, 6, 6, 6, 6, 6, 2, 6, 6, 4], [5, 6, 5, 6, 9, 6, 6, 3, 5, 4, 6, 6, 6], [6, 6, 6, 6, 6, 2, 3, 2, 6, 6, 6, 6, 6], [6, 6, 6, 6, 2, 5, 6, 6, 6, 5, 3, 6, 6], [6, 6, 6, 6, 2, 2, 5, 5, 6, 2, 3, 6, 6], [3, 6, 6, 6, 4, 6, 2, 6, 3, 3, 6, 3, 6], [5, 6, 4, 5, 6, 6, 6, 6, 6, 6, 5, 5, 6], [6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 5, 9], [6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 3, 3, 6], [6, 4, 6, 3, 6, 6, 6, 9, 3, 6, 6, 9, 5], [6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 4], [9, 6, 6, 2, 6, 6, 6, 6, 9, 6, 6, 6, 3], [6, 6, 6, 2, 6, 5, 6, 5, 6, 6, 6, 2, 6], [6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 5, 6], [6, 6, 4, 2, 6, 3, 4, 6, 2, 4, 6, 9, 6], [2, 9, 6, 4, 6, 2, 9, 5, 6, 6, 6, 9, 5], [6, 3, 6, 9, 6, 2, 9, 6, 6, 6, 6, 6, 6], [6, 3, 6, 6, 2, 6, 6, 3, 6, 6, 6, 9, 6], [9, 9, 5, 6, 6, 5, 3, 6, 6, 2, 6, 6, 6], [6, 6, 9, 6, 5, 6, 6, 6, 4, 6, 9, 6, 6], [9, 6, 5, 6, 3, 4, 6, 6, 6, 6, 6, 6, 3]], "output": [[6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}], "input_grid": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4], [4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 9, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "task_key": "d23f8c26"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 5, 3, 3, 3, 5, 3, 3],\n[3, 5, 3, 3, 5, 5, 5, 5, 3, 3, 5, 3, 3, 3, 5, 3, 5, 3],\n[3, 3, 5, 3, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 3, 5, 3, 5],\n[5, 3, 3, 5, 5, 5, 5, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3],\n[3, 5, 3, 3, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 5, 3, 3, 3],\n[3, 3, 5, 3, 5, 5, 5, 3, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3],\n[5, 3, 3, 5, 3, 3, 3, 5, 3, 5, 3, 5, 3, 3, 3, 3, 3, 5],\n[3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 5, 3, 5, 3, 5, 3, 3, 3],\n[5, 5, 5, 3, 3, 3, 3, 5, 3, 5, 3, 5, 3, 3, 3, 5, 3, 3],\n[5, 5, 5, 3, 3, 5, 3, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 5],\n[3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 3, 3, 3, 3, 5, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 6, 1, 1, 1, 1],\n[6, 6, 6, 6, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1],\n[6, 6, 6, 6, 1, 6, 1, 1, 1, 6, 1, 1, 6, 6, 6, 6, 6, 1, 1, 1],\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 1, 1, 6, 1],\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 6, 1, 6, 1, 1],\n[1, 1, 1, 1, 6, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 6],\n[6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 1, 1, 6, 1, 1],\n[1, 1, 1, 1, 6, 1, 1, 6, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 6, 1, 1, 6, 1, 1, 1, 6, 1, 1, 1, 6, 6, 6, 1, 1, 6, 1, 1],\n[1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 1, 1, 1, 1, 6],\n[6, 1, 6, 1, 6, 1, 6, 1, 1, 1, 6, 1, 6, 6, 6, 1, 1, 1, 6, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1],\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1],\n[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 7, 5, 5, 7, 7, 5, 5, 5, 5, 7, 5, 5],\n[7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 5, 7, 5, 7, 5, 7, 5],\n[5, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7],\n[5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 7, 5, 5, 7, 7, 7, 5, 5, 5, 7, 5, 5],\n[5, 7, 5, 5, 5, 7, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 7, 5, 5, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 7, 5],\n[5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 5],\n[7, 5, 7, 5, 5, 5, 5, 7, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 7],\n[5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5],\n[7, 5, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 7],\n[5, 7, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 5],\n[5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7],\n[7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 0, 8, 8, 8, 8, 0, 8, 0, 0, 0, 8, 0, 8, 0],\n[0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8],\n[0, 8, 8, 8, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0],\n[0, 0, 8, 8, 8, 0, 8, 0, 8, 0, 8, 0, 0, 8, 0],\n[0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0],\n[0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8],\n[0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0],\n[0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0],\n[8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 5, 3, 3, 3, 5, 3, 3], [3, 5, 3, 3, 5, 5, 5, 5, 3, 3, 5, 3, 3, 3, 5, 3, 5, 3], [3, 3, 5, 3, 5, 5, 5, 3, 3, 5, 3, 5, 3, 3, 3, 5, 3, 5], [5, 3, 3, 5, 5, 5, 5, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3], [3, 5, 3, 3, 5, 5, 5, 5, 3, 5, 3, 3, 5, 3, 5, 3, 3, 3], [3, 3, 5, 3, 5, 5, 5, 3, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3], [5, 3, 3, 5, 3, 3, 3, 5, 3, 5, 3, 5, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 5, 3, 5, 3, 5, 3, 3, 3], [5, 5, 5, 3, 3, 3, 3, 5, 3, 5, 3, 5, 3, 3, 3, 5, 3, 3], [5, 5, 5, 3, 3, 5, 3, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 5], [3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 3, 3, 3, 3, 5, 3, 3, 3]], "output": [[3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 6, 1, 1, 1, 1], [6, 6, 6, 6, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1], [6, 6, 6, 6, 1, 6, 1, 1, 1, 6, 1, 1, 6, 6, 6, 6, 6, 1, 1, 1], [6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 1, 1, 6, 1], [6, 6, 6, 6, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 6, 1, 6, 1, 1], [1, 1, 1, 1, 6, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 6], [6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 1, 1, 6, 1, 1], [1, 1, 1, 1, 6, 1, 1, 6, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 6, 1, 1, 6, 1, 1, 1, 6, 1, 1, 1, 6, 6, 6, 1, 1, 6, 1, 1], [1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 1, 1, 1, 1, 6], [6, 1, 6, 1, 6, 1, 6, 1, 1, 1, 6, 1, 6, 6, 6, 1, 1, 1, 6, 1]], "output": [[6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1], [6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1], [6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 1, 1, 1, 1, 1]]}, {"input": [[5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 7, 5, 5, 7, 7, 5, 5, 5, 5, 7, 5, 5], [7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 5, 7, 5, 7, 5, 7, 5], [5, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7], [5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 7, 5, 5, 7, 7, 7, 5, 5, 5, 7, 5, 5], [5, 7, 5, 5, 5, 7, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 7, 5, 5, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 7, 5], [5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 5], [7, 5, 7, 5, 5, 5, 5, 7, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 7], [5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5], [7, 5, 5, 7, 5, 5, 5, 5, 5, 7, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 7], [5, 7, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 5], [5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 7, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7], [7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}], "input_grid": [[8, 0, 8, 8, 8, 8, 0, 8, 0, 0, 0, 8, 0, 8, 0], [0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8], [0, 8, 8, 8, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0], [0, 0, 8, 8, 8, 0, 8, 0, 8, 0, 8, 0, 0, 8, 0], [0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8], [0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0], [8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0]], "task_key": "7f4411dc"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 0, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 4],\n[4, 4, 4, 7, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 2, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7],\n[7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 4, 7, 7, 7],\n[7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4, 7, 7],\n[4, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 7],\n[4, 4, 7, 7, 7, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7],\n[4, 4, 4, 7, 7, 7, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7, 7],\n[7, 4, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7, 7, 4],\n[7, 7, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4],\n[7, 7, 7, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7, 4, 4, 4, 4],\n[7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 4],\n[7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 7, 4, 4, 7, 7, 7, 7],\n[4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 4, 7, 7, 7, 7, 7],\n[4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 7, 7, 4, 4, 7],\n[4, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4],\n[4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7, 7, 4, 4, 4],\n[4, 4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 4, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 2, 9, 7, 7, 7],\n[7, 9, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 9, 9, 7, 7, 7, 7, 7, 2, 9, 7, 7, 7],\n[7, 7, 7, 7, 7, 9, 2, 7, 2, 2, 7, 9, 9],\n[7, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7, 2, 9],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 9, 2, 7, 7, 7],\n[7, 7, 2, 9, 7, 7, 9, 2, 7, 7, 7, 7, 7],\n[7, 7, 2, 2, 7, 7, 2, 9, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 9, 2, 7, 7, 7, 7],\n[7, 7, 2, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 9, 9, 7, 7, 9, 9, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 7, 7, 7, 7, 7, 7, 9, 9, 9, 7, 7],\n[9, 9, 9, 7, 7, 7, 7, 9, 9, 9, 9, 9, 7],\n[7, 9, 9, 9, 7, 7, 9, 9, 9, 9, 9, 9, 9],\n[7, 7, 9, 9, 9, 9, 9, 9, 9, 7, 7, 9, 9],\n[7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 9, 9, 9],\n[7, 7, 7, 9, 9, 9, 9, 7, 9, 9, 9, 9, 7],\n[7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7],\n[7, 9, 9, 9, 9, 7, 9, 9, 9, 9, 7, 7, 7],\n[7, 9, 9, 9, 7, 9, 9, 9, 9, 9, 7, 7, 9],\n[9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 7, 9],\n[9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 9, 9, 9],\n[9, 9, 7, 9, 9, 9, 9, 7, 7, 9, 9, 9, 9],\n[9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7],\n[9, 9, 9, 9, 7, 7, 9, 9, 9, 9, 7, 7, 7],\n[9, 9, 9, 7, 7, 7, 7, 9, 9, 9, 7, 7, 7],\n[9, 9, 9, 9, 7, 7, 7, 7, 9, 9, 9, 7, 7],\n[9, 7, 9, 9, 7, 7, 9, 9, 7, 9, 9, 9, 7],\n[7, 7, 7, 7, 7, 9, 9, 9, 9, 7, 9, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 8, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 2, 2, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 8, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 8, 8],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 2, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 0, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 8, 8]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 4], [4, 4, 4, 7, 2, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 2, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7], [7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 4, 7, 7, 7], [7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4, 7, 7], [4, 7, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 7], [4, 4, 7, 7, 7, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7], [4, 4, 4, 7, 7, 7, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7, 7], [7, 4, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7, 7, 4], [7, 7, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4], [7, 7, 7, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 7, 7, 7, 4, 4, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7, 4, 4, 4, 4], [7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 7, 7, 4], [7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 7, 4, 4, 7, 7, 7, 7], [4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 4, 7, 7, 7, 7, 7], [4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 7, 7, 4, 4, 7], [4, 4, 4, 7, 7, 7, 7, 7, 7, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4], [4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7, 7, 4, 4, 4], [4, 4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 4, 4]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 2, 9, 7, 7, 7], [7, 9, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 9, 9, 7, 7, 7, 7, 7, 2, 9, 7, 7, 7], [7, 7, 7, 7, 7, 9, 2, 7, 2, 2, 7, 9, 9], [7, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7, 2, 9], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 9, 2, 7, 7, 7], [7, 7, 2, 9, 7, 7, 9, 2, 7, 7, 7, 7, 7], [7, 7, 2, 2, 7, 7, 2, 9, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 9, 2, 7, 7, 7, 7], [7, 7, 2, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 9, 9, 7, 7, 9, 9, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 2, 2, 7, 7, 7, 7, 7]], "output": [[9, 9, 7, 7, 7, 7, 7, 7, 9, 9, 9, 7, 7], [9, 9, 9, 7, 7, 7, 7, 9, 9, 9, 9, 9, 7], [7, 9, 9, 9, 7, 7, 9, 9, 9, 9, 9, 9, 9], [7, 7, 9, 9, 9, 9, 9, 9, 9, 7, 7, 9, 9], [7, 7, 7, 9, 9, 9, 9, 9, 7, 7, 9, 9, 9], [7, 7, 7, 9, 9, 9, 9, 7, 9, 9, 9, 9, 7], [7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7], [7, 9, 9, 9, 9, 7, 9, 9, 9, 9, 7, 7, 7], [7, 9, 9, 9, 7, 9, 9, 9, 9, 9, 7, 7, 9], [9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 7, 9], [9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 9, 9, 9], [9, 9, 7, 9, 9, 9, 9, 7, 7, 9, 9, 9, 9], [9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7], [9, 9, 9, 9, 7, 7, 9, 9, 9, 9, 7, 7, 7], [9, 9, 9, 7, 7, 7, 7, 9, 9, 9, 7, 7, 7], [9, 9, 9, 9, 7, 7, 7, 7, 9, 9, 9, 7, 7], [9, 7, 9, 9, 7, 7, 9, 9, 7, 9, 9, 9, 7], [7, 7, 7, 7, 7, 9, 9, 9, 9, 7, 9, 9, 9]]}], "input_grid": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 2, 2, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 8, 2], [3, 3, 3, 3, 3, 3, 3, 3, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "task_key": "1f0c79e5"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 5, 4, 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0],\n[4, 4, 5, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0],\n[4, 4, 5, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4],\n[4, 4, 5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[9, 9, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[6, 8, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 9, 4, 4, 9, 9, 4, 4, 9, 9, 9, 9, 4, 9],\n[9, 9, 9, 9, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 4, 4, 6, 4, 8, 8, 8, 8, 8, 4],\n[6, 6, 6, 6, 4, 6, 6, 8, 8, 4, 8, 4, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 1, 1],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 1, 1],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 9, 4, 4, 4, 4, 2, 9, 9],\n[4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 2, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 9, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[3, 3, 5, 4, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 3],\n[3, 3, 5, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4],\n[3, 3, 5, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 5, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4],\n[3, 3, 5, 4, 4, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3],\n[3, 3, 5, 3, 3, 4, 3, 4, 4, 3, 4, 3, 4, 3, 3],\n[3, 3, 5, 3, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 3],\n[3, 3, 5, 4, 3, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3],\n[3, 3, 5, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3],\n[3, 3, 5, 3, 4, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[6, 9, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[6, 6, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 3, 6, 3, 6, 3, 9, 9, 3, 3, 3],\n[6, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 9],\n[3, 6, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 6, 3, 9, 3, 9, 9, 9],\n[6, 6, 6, 6, 3, 6, 3, 3, 3, 9, 3, 3],\n[3, 3, 6, 3, 6, 6, 3, 6, 3, 6, 3, 3],\n[3, 3, 6, 6, 3, 3, 6, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 6, 3, 3, 3, 6, 3, 3],\n[3, 3, 3, 6, 3, 3, 6, 3, 3, 6, 3, 3],\n[3, 6, 3, 3, 3, 3, 6, 3, 3, 6, 6, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 0, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[7, 7, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[3, 3, 6, 3, 9, 9, 3, 9, 3, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 3, 9, 9, 9],\n[3, 3, 6, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 3, 9, 3, 9],\n[3, 3, 6, 3, 9, 3, 9, 9, 9, 9, 9, 3, 9, 3, 9, 9, 3, 9, 9, 9, 9, 3, 9],\n[3, 3, 6, 3, 9, 9, 9, 3, 9, 9, 9, 3, 9, 3, 3, 9, 9, 9, 3, 9, 9, 9, 9],\n[3, 3, 6, 3, 3, 3, 3, 9, 9, 3, 9, 9, 9, 3, 9, 3, 3, 3, 9, 3, 9, 9, 9],\n[3, 3, 6, 9, 9, 9, 3, 9, 3, 3, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 9],\n[3, 3, 6, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 9, 3, 9, 9, 9, 9],\n[3, 3, 6, 9, 9, 9, 9, 3, 9, 9, 9, 3, 9, 9, 3, 9, 9, 9, 3, 9, 9, 3, 9],\n[3, 3, 6, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 3, 3, 9, 3, 9, 3, 3, 3],\n[3, 3, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 3, 9, 3, 9, 3, 3, 3],\n[3, 3, 6, 3, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9],\n[3, 3, 6, 9, 9, 9, 9, 9, 3, 9, 3, 3, 3, 9, 9, 9, 3, 3, 9, 3, 3, 9, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 5, 4, 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0], [4, 4, 5, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 5, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4], [4, 4, 5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [9, 9, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [6, 8, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 9, 4, 4, 9, 9, 4, 4, 9, 9, 9, 9, 4, 9], [9, 9, 9, 9, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 4, 4, 6, 4, 8, 8, 8, 8, 8, 4], [6, 6, 6, 6, 4, 6, 6, 8, 8, 4, 8, 4, 8, 8]]}, {"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 1, 1], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 9, 4, 4, 4, 4, 2, 9, 9], [4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 2, 9, 9]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 9, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1]]}, {"input": [[3, 3, 5, 4, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 3], [3, 3, 5, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4], [3, 3, 5, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3], [3, 3, 5, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4], [3, 3, 5, 4, 4, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3], [3, 3, 5, 3, 3, 4, 3, 4, 4, 3, 4, 3, 4, 3, 3], [3, 3, 5, 3, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 3], [3, 3, 5, 4, 3, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3], [3, 3, 5, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3], [3, 3, 5, 3, 4, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [6, 9, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [6, 6, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[6, 6, 3, 6, 3, 6, 3, 9, 9, 3, 3, 3], [6, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 9], [3, 6, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 6, 3, 9, 3, 9, 9, 9], [6, 6, 6, 6, 3, 6, 3, 3, 3, 9, 3, 3], [3, 3, 6, 3, 6, 6, 3, 6, 3, 6, 3, 3], [3, 3, 6, 6, 3, 3, 6, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 6, 3, 3, 3, 6, 3, 3], [3, 3, 3, 6, 3, 3, 6, 3, 3, 6, 3, 3], [3, 6, 3, 3, 3, 3, 6, 3, 3, 6, 6, 3]]}], "input_grid": [[1, 0, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [7, 7, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [3, 3, 6, 3, 9, 9, 3, 9, 3, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 3, 9, 9, 9], [3, 3, 6, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 3, 9, 3, 9], [3, 3, 6, 3, 9, 3, 9, 9, 9, 9, 9, 3, 9, 3, 9, 9, 3, 9, 9, 9, 9, 3, 9], [3, 3, 6, 3, 9, 9, 9, 3, 9, 9, 9, 3, 9, 3, 3, 9, 9, 9, 3, 9, 9, 9, 9], [3, 3, 6, 3, 3, 3, 3, 9, 9, 3, 9, 9, 9, 3, 9, 3, 3, 3, 9, 3, 9, 9, 9], [3, 3, 6, 9, 9, 9, 3, 9, 3, 3, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 9], [3, 3, 6, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 9, 3, 9, 9, 9, 9], [3, 3, 6, 9, 9, 9, 9, 3, 9, 9, 9, 3, 9, 9, 3, 9, 9, 9, 3, 9, 9, 3, 9], [3, 3, 6, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 3, 3, 9, 3, 9, 3, 3, 3], [3, 3, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 3, 9, 3, 9, 3, 3, 3], [3, 3, 6, 3, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9], [3, 3, 6, 9, 9, 9, 9, 9, 3, 9, 3, 3, 3, 9, 9, 9, 3, 3, 9, 3, 3, 9, 3]], "task_key": "7c008303"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7],\n[6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8],\n[9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7],\n[3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7],\n[6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7],\n[0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7],\n[6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7],\n[8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7],\n[6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8],\n[9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7],\n[3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7],\n[6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7],\n[0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7],\n[6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7],\n[8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 8, 2, 8, 3, 8, 2, 8],\n[8, 8, 4, 8, 8, 8, 4, 8],\n[8, 8, 2, 3, 8, 8, 2, 3],\n[5, 6, 5, 8, 5, 6, 5, 8],\n[2, 6, 7, 8, 2, 6, 7, 8],\n[8, 7, 6, 6, 8, 7, 6, 6],\n[8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 8, 2, 8, 3, 8, 2, 8, 3, 8, 2, 8, 3, 8, 2, 8],\n[8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8],\n[8, 8, 2, 3, 8, 8, 2, 3, 8, 8, 2, 3, 8, 8, 2, 3],\n[5, 6, 5, 8, 5, 6, 5, 8, 5, 6, 5, 8, 5, 6, 5, 8],\n[2, 6, 7, 8, 2, 6, 7, 8, 2, 6, 7, 8, 2, 6, 7, 8],\n[8, 7, 6, 6, 8, 7, 6, 6, 8, 7, 6, 6, 8, 7, 6, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 0, 4, 4, 0, 4, 4],\n[4, 4, 4, 4, 4, 4, 4],\n[4, 0, 4, 4, 0, 4, 4],\n[4, 6, 4, 4, 6, 4, 4],\n[4, 3, 4, 4, 3, 4, 4],\n[1, 4, 4, 1, 4, 4, 1],\n[4, 0, 4, 4, 0, 4, 4],\n[4, 4, 4, 4, 4, 4, 4],\n[0, 1, 4, 0, 1, 4, 0],\n[6, 7, 5, 6, 7, 5, 6],\n[2, 2, 4, 2, 2, 4, 2],\n[1, 4, 9, 1, 4, 9, 1],\n[4, 4, 1, 4, 4, 1, 4],\n[4, 4, 7, 4, 4, 7, 4],\n[4, 4, 1, 4, 4, 1, 4],\n[4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0],\n[4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6],\n[4, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3],\n[1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4],\n[4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1],\n[6, 7, 5, 6, 7, 5, 6, 7, 5, 6, 7, 5, 6, 7],\n[2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2],\n[1, 4, 9, 1, 4, 9, 1, 4, 9, 1, 4, 9, 1, 4],\n[4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4],\n[4, 4, 7, 4, 4, 7, 4, 4, 7, 4, 4, 7, 4, 4],\n[4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 8, 8, 8, 8, 9, 8, 8, 8, 8, 9, 8, 8],\n[0, 8, 8, 8, 7, 0, 8, 8, 8, 7, 0, 8, 8],\n[8, 8, 7, 8, 8, 8, 8, 7, 8, 8, 8, 8, 7],\n[8, 7, 4, 8, 7, 8, 7, 4, 8, 7, 8, 7, 4],\n[7, 2, 8, 8, 8, 7, 2, 8, 8, 8, 7, 2, 8],\n[8, 9, 8, 0, 8, 8, 9, 8, 0, 8, 8, 9, 8],\n[4, 0, 8, 8, 5, 4, 0, 8, 8, 5, 4, 0, 8],\n[8, 0, 8, 8, 8, 8, 0, 8, 8, 8, 8, 0, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 4, 8, 0, 0, 8, 4, 8, 0, 0, 8, 4, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 7, 8, 8, 8, 8, 7, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7], [6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8], [9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7], [3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7], [6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7], [0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7], [6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7], [8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7], [6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8, 6, 3, 8], [9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7, 9, 9, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7], [3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7, 3, 7, 7], [6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7], [0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7, 0, 7, 7], [6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7], [8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7, 8, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[3, 8, 2, 8, 3, 8, 2, 8], [8, 8, 4, 8, 8, 8, 4, 8], [8, 8, 2, 3, 8, 8, 2, 3], [5, 6, 5, 8, 5, 6, 5, 8], [2, 6, 7, 8, 2, 6, 7, 8], [8, 7, 6, 6, 8, 7, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8]], "output": [[3, 8, 2, 8, 3, 8, 2, 8, 3, 8, 2, 8, 3, 8, 2, 8], [8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 4, 8], [8, 8, 2, 3, 8, 8, 2, 3, 8, 8, 2, 3, 8, 8, 2, 3], [5, 6, 5, 8, 5, 6, 5, 8, 5, 6, 5, 8, 5, 6, 5, 8], [2, 6, 7, 8, 2, 6, 7, 8, 2, 6, 7, 8, 2, 6, 7, 8], [8, 7, 6, 6, 8, 7, 6, 6, 8, 7, 6, 6, 8, 7, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[4, 0, 4, 4, 0, 4, 4], [4, 4, 4, 4, 4, 4, 4], [4, 0, 4, 4, 0, 4, 4], [4, 6, 4, 4, 6, 4, 4], [4, 3, 4, 4, 3, 4, 4], [1, 4, 4, 1, 4, 4, 1], [4, 0, 4, 4, 0, 4, 4], [4, 4, 4, 4, 4, 4, 4], [0, 1, 4, 0, 1, 4, 0], [6, 7, 5, 6, 7, 5, 6], [2, 2, 4, 2, 2, 4, 2], [1, 4, 9, 1, 4, 9, 1], [4, 4, 1, 4, 4, 1, 4], [4, 4, 7, 4, 4, 7, 4], [4, 4, 1, 4, 4, 1, 4], [4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4]], "output": [[4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0], [4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6], [4, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3], [1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4], [4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1], [6, 7, 5, 6, 7, 5, 6, 7, 5, 6, 7, 5, 6, 7], [2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2], [1, 4, 9, 1, 4, 9, 1, 4, 9, 1, 4, 9, 1, 4], [4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4], [4, 4, 7, 4, 4, 7, 4, 4, 7, 4, 4, 7, 4, 4], [4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}], "input_grid": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 8, 8, 8, 8, 9, 8, 8, 8, 8, 9, 8, 8], [0, 8, 8, 8, 7, 0, 8, 8, 8, 7, 0, 8, 8], [8, 8, 7, 8, 8, 8, 8, 7, 8, 8, 8, 8, 7], [8, 7, 4, 8, 7, 8, 7, 4, 8, 7, 8, 7, 4], [7, 2, 8, 8, 8, 7, 2, 8, 8, 8, 7, 2, 8], [8, 9, 8, 0, 8, 8, 9, 8, 0, 8, 8, 9, 8], [4, 0, 8, 8, 5, 4, 0, 8, 8, 5, 4, 0, 8], [8, 0, 8, 8, 8, 8, 0, 8, 8, 8, 8, 0, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 8, 0, 0, 8, 4, 8, 0, 0, 8, 4, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 7, 8, 8, 8, 8, 7, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 2, 8, 8, 8, 8, 2, 8, 8, 8, 8]], "task_key": "963e52fc"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 9, 9, 9, 9, 3, 3, 3, 9, 9, 9, 9, 6, 9, 9],\n[9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 5, 5, 3, 3],\n[5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 5, 5, 5, 1],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9], [6, 9, 9, 9, 9, 3, 3, 3, 9, 9, 9, 9, 6, 9, 9], [9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 5, 5, 3, 3], [5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 5, 5, 5, 1], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8]]}], "input_grid": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "task_key": "e9614598"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9],\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9],\n[0, 9, 0, 0, 9, 9, 0, 0, 0, 0, 9, 0, 0, 9],\n[0, 0, 0, 0, 9, 0, 9, 0, 9, 0, 0, 9, 0, 0],\n[9, 9, 0, 0, 0, 0, 9, 0, 0, 9, 9, 9, 9, 9],\n[0, 9, 0, 0, 0, 0, 0, 0, 3, 3, 0, 9, 0, 0],\n[0, 0, 0, 0, 0, 0, 9, 0, 9, 9, 0, 0, 9, 9],\n[0, 9, 0, 0, 9, 9, 0, 0, 9, 0, 0, 0, 9, 0],\n[9, 0, 0, 0, 0, 0, 0, 0, 2, 2, 9, 0, 9, 0],\n[0, 0, 9, 0, 9, 9, 0, 9, 9, 0, 0, 0, 0, 0],\n[0, 9, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9],\n[0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9],\n[0, 9, 0, 0, 9, 9, 0, 0, 0, 0, 9, 0, 0, 9],\n[0, 0, 0, 0, 9, 0, 9, 0, 9, 0, 0, 9, 0, 0],\n[9, 9, 0, 0, 0, 0, 9, 0, 0, 9, 9, 9, 9, 9],\n[0, 9, 3, 3, 3, 3, 3, 3, 3, 3, 0, 9, 0, 0],\n[0, 0, 3, 0, 0, 0, 9, 0, 9, 9, 0, 0, 9, 9],\n[0, 9, 3, 0, 9, 9, 0, 0, 9, 0, 0, 0, 9, 0],\n[9, 0, 3, 3, 3, 3, 3, 3, 2, 2, 9, 0, 9, 0],\n[0, 0, 9, 0, 9, 9, 0, 9, 9, 0, 0, 0, 0, 0],\n[0, 9, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6],\n[6, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 6, 0, 0, 6, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0],\n[0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0],\n[0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0],\n[0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0],\n[0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6],\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0],\n[0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6],\n[6, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 6, 6, 0, 6, 0, 0, 6, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0],\n[0, 3, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0],\n[0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0],\n[0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0],\n[0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6],\n[0, 3, 3, 3, 3, 3, 3, 3, 2, 2, 0, 0, 0, 0, 0],\n[0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 4, 5, 5, 5, 5, 5, 4, 5, 5],\n[5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5],\n[5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5],\n[5, 5, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 2, 5, 5, 4, 5, 3, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5],\n[5, 5, 2, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5],\n[5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 4, 5, 5, 5, 5, 5, 4, 5, 5],\n[5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5],\n[5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5],\n[5, 5, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 2, 5, 5, 4, 5, 3, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5],\n[5, 5, 2, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5],\n[5, 4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 4, 4, 8],\n[8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 4, 8, 4, 8, 8, 3, 3, 8, 4, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 4, 8, 4, 8, 8, 8],\n[8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4],\n[4, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8],\n[8, 4, 4, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8],\n[8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 8, 4],\n[8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4],\n[8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[8, 8, 8, 4, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], [0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9], [0, 9, 0, 0, 9, 9, 0, 0, 0, 0, 9, 0, 0, 9], [0, 0, 0, 0, 9, 0, 9, 0, 9, 0, 0, 9, 0, 0], [9, 9, 0, 0, 0, 0, 9, 0, 0, 9, 9, 9, 9, 9], [0, 9, 0, 0, 0, 0, 0, 0, 3, 3, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 9, 0, 9, 9, 0, 0, 9, 9], [0, 9, 0, 0, 9, 9, 0, 0, 9, 0, 0, 0, 9, 0], [9, 0, 0, 0, 0, 0, 0, 0, 2, 2, 9, 0, 9, 0], [0, 0, 9, 0, 9, 9, 0, 9, 9, 0, 0, 0, 0, 0], [0, 9, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9]], "output": [[0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], [0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 9], [0, 9, 0, 0, 9, 9, 0, 0, 0, 0, 9, 0, 0, 9], [0, 0, 0, 0, 9, 0, 9, 0, 9, 0, 0, 9, 0, 0], [9, 9, 0, 0, 0, 0, 9, 0, 0, 9, 9, 9, 9, 9], [0, 9, 3, 3, 3, 3, 3, 3, 3, 3, 0, 9, 0, 0], [0, 0, 3, 0, 0, 0, 9, 0, 9, 9, 0, 0, 9, 9], [0, 9, 3, 0, 9, 9, 0, 0, 9, 0, 0, 0, 9, 0], [9, 0, 3, 3, 3, 3, 3, 3, 2, 2, 9, 0, 9, 0], [0, 0, 9, 0, 9, 9, 0, 9, 9, 0, 0, 0, 0, 0], [0, 9, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 9]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6], [6, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 6, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0], [0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6], [6, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 6, 6, 0, 6, 0, 0, 6, 0], [0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0], [0, 3, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0], [0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6], [0, 3, 3, 3, 3, 3, 3, 3, 2, 2, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 4, 5, 5, 5, 5, 5, 4, 5, 5], [5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5], [5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5], [5, 5, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 2, 5, 5, 4, 5, 3, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5], [5, 5, 2, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5], [5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 4, 5, 5, 5, 5, 5, 4, 5, 5], [5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5], [5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5], [5, 5, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 2, 5, 5, 4, 5, 3, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5], [5, 5, 2, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5], [5, 4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}], "input_grid": [[8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 4, 4, 8], [8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 8, 4, 8, 8, 3, 3, 8, 4, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 4, 8, 4, 8, 8, 8], [8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4], [4, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8], [8, 4, 4, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8], [8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 8, 4], [8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4], [8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [8, 8, 8, 4, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8]], "task_key": "2dd70a9a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 0, 0],\n[7, 2, 6],\n[0, 7, 4],\n[2, 2, 2],\n[0, 7, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 0, 0, 0, 0, 0, 0, 0, 0],\n[7, 2, 6, 0, 0, 0, 0, 0, 0],\n[0, 7, 4, 0, 0, 0, 0, 0, 0],\n[2, 2, 2, 0, 0, 0, 0, 0, 0],\n[0, 7, 2, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 7, 2, 6, 0, 0, 0],\n[0, 0, 0, 0, 7, 4, 0, 0, 0],\n[0, 0, 0, 2, 2, 2, 0, 0, 0],\n[0, 0, 0, 0, 7, 2, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[2, 0, 0, 2, 0, 0, 2, 0, 0],\n[7, 2, 6, 7, 2, 6, 7, 2, 6],\n[0, 7, 4, 0, 7, 4, 0, 7, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[0, 7, 2, 0, 7, 2, 0, 7, 2],\n[0, 0, 0, 0, 0, 0, 2, 0, 0],\n[0, 0, 0, 0, 0, 0, 7, 2, 6],\n[0, 0, 0, 0, 0, 0, 0, 7, 4],\n[0, 0, 0, 0, 0, 0, 2, 2, 2],\n[0, 0, 0, 0, 0, 0, 0, 7, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 7, 2, 2],\n[2, 0, 0, 2],\n[0, 2, 0, 2],\n[0, 2, 5, 2],\n[2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 7, 2, 2, 0, 0, 0, 0, 2, 7, 2, 2, 2, 7, 2, 2],\n[2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2],\n[0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2],\n[0, 2, 5, 2, 0, 0, 0, 0, 0, 2, 5, 2, 0, 2, 5, 2],\n[2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 7, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 2, 2],\n[2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2],\n[0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2],\n[0, 2, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 2],\n[2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2],\n[0, 0, 0, 0, 2, 7, 2, 2, 0, 0, 0, 0, 2, 7, 2, 2],\n[0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2],\n[0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2],\n[0, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 0, 2, 5, 2],\n[0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2],\n[0, 0, 0, 0, 2, 7, 2, 2, 0, 0, 0, 0, 2, 7, 2, 2],\n[0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2],\n[0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2],\n[0, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 0, 2, 5, 2],\n[0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2],\n[2, 7, 2, 2, 2, 7, 2, 2, 2, 7, 2, 2, 2, 7, 2, 2],\n[2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2],\n[0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2],\n[0, 2, 5, 2, 0, 2, 5, 2, 0, 2, 5, 2, 0, 2, 5, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 6],\n[2, 2, 0],\n[2, 0, 0],\n[5, 6, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 6, 0, 0, 6, 0, 0, 0],\n[2, 2, 0, 2, 2, 0, 0, 0, 0],\n[2, 0, 0, 2, 0, 0, 0, 0, 0],\n[5, 6, 2, 5, 6, 2, 0, 0, 0],\n[0, 0, 6, 0, 0, 0, 0, 0, 0],\n[2, 2, 0, 0, 0, 0, 0, 0, 0],\n[2, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 6, 2, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 6],\n[0, 0, 0, 0, 0, 0, 2, 2, 0],\n[0, 0, 0, 0, 0, 0, 2, 0, 0],\n[0, 0, 0, 0, 0, 0, 5, 6, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 2, 2, 2],\n[2, 0, 2, 2, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 0, 0], [7, 2, 6], [0, 7, 4], [2, 2, 2], [0, 7, 2]], "output": [[2, 0, 0, 0, 0, 0, 0, 0, 0], [7, 2, 6, 0, 0, 0, 0, 0, 0], [0, 7, 4, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 7, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 7, 2, 6, 0, 0, 0], [0, 0, 0, 0, 7, 4, 0, 0, 0], [0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 7, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 2, 0, 0], [7, 2, 6, 7, 2, 6, 7, 2, 6], [0, 7, 4, 0, 7, 4, 0, 7, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 7, 2, 0, 7, 2, 0, 7, 2], [0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 7, 2, 6], [0, 0, 0, 0, 0, 0, 0, 7, 4], [0, 0, 0, 0, 0, 0, 2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 7, 2]]}, {"input": [[2, 7, 2, 2], [2, 0, 0, 2], [0, 2, 0, 2], [0, 2, 5, 2], [2, 2, 2, 2]], "output": [[2, 7, 2, 2, 0, 0, 0, 0, 2, 7, 2, 2, 2, 7, 2, 2], [2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2], [0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2], [0, 2, 5, 2, 0, 0, 0, 0, 0, 2, 5, 2, 0, 2, 5, 2], [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 7, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 2, 2], [2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2], [0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2], [0, 2, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 2], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], [0, 0, 0, 0, 2, 7, 2, 2, 0, 0, 0, 0, 2, 7, 2, 2], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2], [0, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 0, 2, 5, 2], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2], [0, 0, 0, 0, 2, 7, 2, 2, 0, 0, 0, 0, 2, 7, 2, 2], [0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2], [0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2], [0, 0, 0, 0, 0, 2, 5, 2, 0, 0, 0, 0, 0, 2, 5, 2], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2], [2, 7, 2, 2, 2, 7, 2, 2, 2, 7, 2, 2, 2, 7, 2, 2], [2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2], [0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2], [0, 2, 5, 2, 0, 2, 5, 2, 0, 2, 5, 2, 0, 2, 5, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[0, 0, 6], [2, 2, 0], [2, 0, 0], [5, 6, 2]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 6, 0, 0, 0], [2, 2, 0, 2, 2, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0, 0], [5, 6, 2, 5, 6, 2, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0], [5, 6, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 5, 6, 2]]}], "input_grid": [[1, 1, 2, 2, 2], [2, 0, 2, 2, 0]], "task_key": "cce03e0d"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 8, 2, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 8, 8, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 8, 2, 8, 8, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 8, 8, 2, 8, 2, 8, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 8, 8, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 8, 2, 8, 8, 2, 2, 2, 2],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2],\n[2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2],\n[2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2],\n[2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2],\n[2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 1, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 1, 1, 5, 1, 1, 1, 1, 1],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 1, 1, 5, 1, 5, 1, 1, 1],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1],\n[1, 5, 1, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1],\n[1, 1, 5, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 1, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 1, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 1, 1, 7, 7, 7, 7, 5, 1, 1, 1, 1, 5, 1, 5, 5, 1],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5],\n[5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 8, 5, 5, 8, 8, 8, 8, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[8, 8, 5, 8, 8, 8, 5, 8, 8, 8, 1, 1, 5, 5, 8, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 8, 5, 5, 5, 5, 5, 5, 5],\n[8, 5, 8, 8, 5, 5, 5, 8, 5, 5, 1, 1, 5, 8, 8, 8, 8, 8, 8, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[8, 5, 8, 8, 5, 5, 5, 8, 8, 8, 1, 1, 8, 8, 8, 5, 8, 8, 5, 8],\n[8, 8, 5, 5, 8, 5, 8, 8, 8, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 8, 8, 5, 5, 8, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 8, 8, 8, 8, 8, 8, 8],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5],\n[5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 4, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[8, 4, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[8, 4, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8],\n[8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8],\n[8, 4, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[8, 4, 8, 8, 8, 4, 4, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4],\n[8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 4, 8, 4, 8, 8, 8, 8, 8, 4, 4, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8],\n[8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 8, 2, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 8, 8, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 2, 2, 2], [2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 8, 2, 8, 8, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 8, 8, 2, 8, 2, 8, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 8, 8, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 8, 2, 8, 8, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2], [2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2], [2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2], [2, 2, 2, 2, 2, 8, 2, 8, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2], [2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2], [2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2], [2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[5, 5, 1, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 1, 1, 5, 1, 1, 1, 1, 1], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 1, 1, 5, 1, 5, 1, 1, 1], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1], [1, 5, 1, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1], [1, 1, 5, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 1, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 1, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 7, 7, 7, 7, 5, 1, 1, 1, 1, 5, 1, 5, 5, 1], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5], [5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5], [5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 8, 5, 5, 8, 8, 8, 8, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [8, 8, 5, 8, 8, 8, 5, 8, 8, 8, 1, 1, 5, 5, 8, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 8, 5, 5, 5, 5, 5, 5, 5], [8, 5, 8, 8, 5, 5, 5, 8, 5, 5, 1, 1, 5, 8, 8, 8, 8, 8, 8, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [8, 5, 8, 8, 5, 5, 5, 8, 8, 8, 1, 1, 8, 8, 8, 5, 8, 8, 5, 8], [8, 8, 5, 5, 8, 5, 8, 8, 8, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 8, 8, 5, 5, 8, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5]]}], "input_grid": [[8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [8, 4, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [8, 4, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8], [8, 8, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8], [8, 4, 8, 8, 8, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 4, 8, 8, 8, 4, 4, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4], [8, 8, 8, 8, 8, 8, 4, 8, 8, 4, 4, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 8, 4, 8, 8, 8, 8, 8, 4, 4, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8], [8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 4]], "task_key": "4093f84a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7],\n[8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7],\n[8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[8, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 5, 3],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 5, 3],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 4, 9, 9, 9, 9, 5, 3],\n[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 4, 9, 9, 9, 9, 5, 3],\n[8, 1, 9, 6, 9, 9, 9, 9, 9, 7, 9, 9, 9, 4, 9, 9, 9, 9, 9, 3],\n[8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3],\n[8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3],\n[8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3],\n[8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 5, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 5, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 7, 3, 6, 2, 1, 5, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[5, 5, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7], [8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7], [8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7]], "output": [[8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [8, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 5, 3], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 5, 3], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 4, 9, 9, 9, 9, 5, 3], [8, 9, 9, 6, 9, 9, 9, 2, 9, 7, 9, 9, 9, 4, 9, 9, 9, 9, 5, 3], [8, 1, 9, 6, 9, 9, 9, 9, 9, 7, 9, 9, 9, 4, 9, 9, 9, 9, 9, 3], [8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3], [8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3], [8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3], [8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 1, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 5, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 5, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 7, 3, 6, 2, 1, 5, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8]], "task_key": "beb8660c"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 8, 8, 8, 8, 8],\n[6, 8, 6, 6, 6, 8],\n[6, 8, 6, 4, 6, 8],\n[6, 8, 6, 4, 6, 8],\n[6, 8, 6, 4, 6, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6],\n[4, 6, 6, 6, 6, 6],\n[6, 8, 8, 8, 8, 8],\n[6, 8, 6, 6, 6, 8],\n[6, 8, 6, 4, 6, 8],\n[6, 8, 6, 4, 6, 8],\n[6, 8, 6, 4, 6, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 6, 4, 2, 2, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 6, 4, 2, 2, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4],\n[4, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4],\n[4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0],\n[5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 8, 8, 8, 8, 8], [6, 8, 6, 6, 6, 8], [6, 8, 6, 4, 6, 8], [6, 8, 6, 4, 6, 8], [6, 8, 6, 4, 6, 8]], "output": [[6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [4, 6, 6, 6, 6, 6], [6, 8, 8, 8, 8, 8], [6, 8, 6, 6, 6, 8], [6, 8, 6, 4, 6, 8], [6, 8, 6, 4, 6, 8], [6, 8, 6, 4, 6, 8]]}, {"input": [[4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4], [4, 4, 4, 6, 4, 2, 2, 4, 6, 4, 4, 4, 4], [4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4], [4, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4], [4, 4, 4, 6, 4, 2, 2, 4, 6, 4, 4, 4, 4], [4, 4, 4, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4], [4, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4], [4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 9, 9, 9, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}], "input_grid": [[5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "ec883f72"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 3, 8, 8, 3, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0],\n[0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7],\n[7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7],\n[5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7],\n[5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 5, 5, 7, 7, 7, 7, 7, 7],\n[7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 5, 5, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7],\n[7, 7, 3, 3, 3, 3, 3, 5, 5, 3, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7],\n[7, 7, 3, 5, 5, 3, 3, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7],\n[3, 3, 3, 5, 5, 3, 3, 3, 3, 3, 7, 1, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7],\n[5, 5, 3, 3, 3, 3, 7, 1, 1, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7],\n[5, 5, 3, 1, 1, 7, 7, 1, 1, 7, 7, 3, 5, 5, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 5, 5, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7],\n[1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7],\n[1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7],\n[1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7],\n[1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7],\n[1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7],\n[1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7],\n[3, 5, 5, 3, 1, 1, 1, 1, 1, 7, 3, 5, 5, 3, 3, 5, 5, 3, 5, 5, 3, 7, 7, 7, 7, 7],\n[3, 5, 5, 3, 1, 1, 1, 1, 1, 7, 3, 5, 5, 3, 3, 5, 5, 3, 5, 5, 3, 7, 7, 7, 7, 7],\n[3, 3, 3, 3, 1, 1, 1, 1, 1, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 4, 4, 4, 4, 4],\n[3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 4],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 4],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 1, 1, 4, 4],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 1, 1, 4, 4],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 9, 9, 3],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 9, 9, 3],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 3, 3, 3],\n[3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 1, 1, 1, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 1, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 1, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 1, 4],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3],\n[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 3, 9, 9, 3],\n[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 3, 9, 9, 3],\n[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 3, 3, 3, 3],\n[4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 8, 8, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2],\n[2, 8, 8, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 8, 8, 3, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0], [0, 0, 0, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 5, 5, 7, 7, 7, 7, 7, 7], [7, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 5, 5, 7, 5, 5, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [7, 7, 3, 3, 3, 3, 3, 5, 5, 3, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [7, 7, 3, 5, 5, 3, 3, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7], [3, 3, 3, 5, 5, 3, 3, 3, 3, 3, 7, 1, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7], [5, 5, 3, 3, 3, 3, 7, 1, 1, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7], [5, 5, 3, 1, 1, 7, 7, 1, 1, 7, 7, 3, 5, 5, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 5, 5, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7], [1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 3, 3, 7, 7], [1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [1, 1, 3, 3, 5, 5, 5, 5, 3, 3, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7], [1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7], [3, 5, 5, 3, 1, 1, 1, 1, 1, 7, 3, 5, 5, 3, 3, 5, 5, 3, 5, 5, 3, 7, 7, 7, 7, 7], [3, 5, 5, 3, 1, 1, 1, 1, 1, 7, 3, 5, 5, 3, 3, 5, 5, 3, 5, 5, 3, 7, 7, 7, 7, 7], [3, 3, 3, 3, 1, 1, 1, 1, 1, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7]]}, {"input": [[4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 9, 9, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 4, 4, 4, 4, 4], [3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 4], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 4], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 1, 1, 4, 4], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 1, 1, 4, 4], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 9, 9, 3], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 9, 9, 3], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 3, 3, 3, 3], [3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 3, 3, 3, 3, 4, 1, 1, 1, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 1, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 1, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 1, 1, 1, 4], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3], [4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 3, 9, 9, 3], [4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 3, 9, 9, 3], [4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 3, 3, 3, 3], [4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 4]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8, 8, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2], [2, 8, 8, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 2, 2, 2, 8, 8, 2, 2, 2, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "task_key": "db93a21d"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 5, 7, 7, 3, 7, 7, 7, 7],\n[7, 3, 7, 3, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 3, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7],\n[3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[3, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7],\n[7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 3, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 3, 7, 7, 7, 7],\n[7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 5],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 5, 7, 7, 3, 5, 7, 5, 7],\n[7, 3, 5, 3, 5, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 5, 7],\n[7, 5, 7, 5, 7, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 3, 5],\n[7, 5, 7, 5, 7, 7, 7, 7, 7, 7, 7, 3, 3, 5, 5, 7, 5, 7],\n[3, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 5, 5, 7, 5, 7],\n[5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7],\n[5, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 3, 3, 5, 5],\n[7, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 3, 3, 5, 5],\n[7, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 7],\n[3, 5, 7, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 5, 5, 7, 7],\n[5, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 3, 5],\n[5, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 7],\n[7, 5, 7, 5, 5, 5, 5, 3, 5, 7, 7, 3, 5, 7, 7, 7, 5, 7],\n[7, 5, 7, 5, 5, 5, 5, 5, 7, 7, 7, 5, 7, 7, 3, 5, 7, 7],\n[7, 7, 7, 5, 5, 5, 5, 5, 7, 3, 5, 5, 7, 7, 5, 7, 3, 5],\n[7, 7, 7, 5, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 5, 7, 5, 7],\n[7, 7, 7, 5, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 7, 7, 5, 7],\n[7, 7, 7, 5, 5, 5, 5, 7, 3, 5, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 3, 5, 7, 3, 5, 7, 7, 7],\n[7, 7, 3, 5, 7, 7, 7, 7, 5, 7, 5, 7, 7, 5, 7, 7, 7, 7],\n[7, 7, 5, 7, 7, 3, 5, 7, 7, 7, 5, 7, 7, 5, 7, 7, 7, 7],\n[7, 7, 5, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 8, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 8, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 8, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 1, 1, 1, 1, 5, 5, 1, 1, 5, 5, 8, 1, 1, 5, 5, 5],\n[5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 8, 1, 1, 5, 5, 5, 5, 1, 1, 5],\n[5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1],\n[5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 5, 8, 1, 1, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 5, 5, 1, 1, 5, 5, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 8, 1, 1, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 5],\n[5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 8, 1, 1, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 8, 1, 1, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 1, 1, 5, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 8, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5],\n[5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 8, 8, 1, 1, 1, 1, 1, 1, 5],\n[5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 8, 8, 1, 1, 1, 1, 8, 1, 1],\n[5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 5, 1, 1, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 8, 1, 1, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5],\n[5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5],\n[5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5],\n[5, 7, 7, 5, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5],\n[4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5],\n[4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5],\n[5, 7, 7, 4, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 5, 5, 7, 7, 7, 7, 4, 4, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 7, 7, 5, 5, 7, 7, 7, 7, 4, 4, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 5, 7, 7, 3, 7, 7, 7, 7], [7, 3, 7, 3, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 3, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7], [3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [3, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7], [7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 3, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 3, 7, 7, 7, 7], [7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 5], [7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 5, 7, 7, 3, 5, 7, 5, 7], [7, 3, 5, 3, 5, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 5, 7], [7, 5, 7, 5, 7, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 7, 3, 5], [7, 5, 7, 5, 7, 7, 7, 7, 7, 7, 7, 3, 3, 5, 5, 7, 5, 7], [3, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 5, 5, 7, 5, 7], [5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7], [5, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 3, 3, 5, 5], [7, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 3, 3, 5, 5], [7, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 5, 5, 7, 7], [3, 5, 7, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 5, 5, 7, 7], [5, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 3, 5], [5, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 7], [7, 5, 7, 5, 5, 5, 5, 3, 5, 7, 7, 3, 5, 7, 7, 7, 5, 7], [7, 5, 7, 5, 5, 5, 5, 5, 7, 7, 7, 5, 7, 7, 3, 5, 7, 7], [7, 7, 7, 5, 5, 5, 5, 5, 7, 3, 5, 5, 7, 7, 5, 7, 3, 5], [7, 7, 7, 5, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 5, 7, 5, 7], [7, 7, 7, 5, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 7, 7, 5, 7], [7, 7, 7, 5, 5, 5, 5, 7, 3, 5, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 3, 5, 7, 3, 5, 7, 7, 7], [7, 7, 3, 5, 7, 7, 7, 7, 5, 7, 5, 7, 7, 5, 7, 7, 7, 7], [7, 7, 5, 7, 7, 3, 5, 7, 7, 7, 5, 7, 7, 5, 7, 7, 7, 7], [7, 7, 5, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 8, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 5, 5, 5, 5, 8, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 5, 5, 8, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 1, 1, 1, 1, 5, 5, 1, 1, 5, 5, 8, 1, 1, 5, 5, 5], [5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 8, 1, 1, 5, 5, 5, 5, 1, 1, 5], [5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1], [5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 5, 8, 1, 1, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 5, 5, 1, 1, 5, 5, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 8, 1, 1, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 5], [5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 8, 1, 1, 5, 5, 5], [5, 5, 5, 8, 8, 8, 1, 1, 1, 1, 1, 1, 5, 8, 8, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 8, 1, 1, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 1, 1, 5, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 8, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5], [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5], [5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 5, 5, 5], [5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 8, 8, 1, 1, 1, 1, 1, 1, 5], [5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 8, 8, 1, 1, 1, 1, 8, 1, 1], [5, 5, 5, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 5, 1, 1, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 1, 1, 5, 8, 1, 1, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 7, 5, 5, 5, 5, 5], [5, 7, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5], [5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5], [5, 7, 7, 5, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5], [4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5], [4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5], [5, 7, 7, 4, 5, 4, 7, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5], [4, 4, 4, 5, 5, 4, 4, 4, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 7, 7, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 7, 7, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 7, 7, 4, 4, 7, 7, 5, 5, 7, 7, 7, 7, 4, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 7, 7, 5, 5, 7, 7, 7, 7, 4, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 7, 7, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}], "input_grid": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "task_key": "447fd412"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5],\n[5, 5, 0, 0, 5, 5],\n[5, 0, 5, 5, 0, 5],\n[5, 0, 5, 5, 0, 5],\n[5, 5, 0, 3, 5, 5],\n[5, 5, 5, 3, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0],\n[5]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 3, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 3, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 9, 8, 8, 9, 3, 8, 8, 9, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 3, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 9, 5, 9, 8, 5, 9, 3, 5, 8, 9, 5, 9, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 9, 5, 8, 9, 8, 8, 8, 9, 3, 8, 8, 8, 9, 8, 5, 9, 5, 5, 5, 5],\n[5, 5, 5, 5, 9, 9, 8, 9, 5, 8, 8, 9, 3, 8, 8, 5, 9, 8, 9, 9, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 9, 9, 8, 9, 9, 9, 8, 3, 9, 9, 9, 8, 9, 9, 8, 5, 5, 5, 5],\n[5, 5, 5, 5, 8, 9, 9, 8, 9, 9, 9, 8, 3, 9, 9, 9, 8, 9, 9, 8, 5, 5, 5, 5],\n[5, 5, 5, 5, 9, 9, 8, 9, 5, 8, 8, 9, 3, 8, 8, 5, 9, 8, 9, 9, 5, 5, 5, 5],\n[5, 5, 5, 5, 9, 5, 8, 9, 8, 8, 8, 9, 3, 8, 8, 8, 9, 8, 5, 9, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 9, 5, 9, 8, 5, 9, 3, 5, 8, 9, 5, 9, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 3, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 9, 8, 8, 9, 3, 8, 8, 9, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 3, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 8, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5],\n[5],\n[8],\n[9],\n[9],\n[8],\n[9],\n[9],\n[9],\n[8],\n[8],\n[9],\n[9],\n[9],\n[8],\n[9],\n[9]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8],\n[8, 8],\n[8, 8],\n[8, 8],\n[8, 8],\n[5, 8],\n[8, 1]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 5, 0, 7, 7, 0, 5, 5],\n[5, 7, 7, 7, 7, 7, 7, 5],\n[0, 7, 7, 7, 7, 7, 7, 0],\n[7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7],\n[0, 7, 7, 7, 7, 7, 7, 0],\n[3, 3, 3, 3, 3, 3, 3, 5],\n[5, 5, 0, 7, 7, 0, 5, 5]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[5, 5, 5, 5, 5, 5], [5, 5, 0, 0, 5, 5], [5, 0, 5, 5, 0, 5], [5, 0, 5, 5, 0, 5], [5, 5, 0, 3, 5, 5], [5, 5, 5, 3, 5, 5]], "output": [[0], [5]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 3, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 3, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 9, 8, 8, 9, 3, 8, 8, 9, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 3, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 9, 5, 9, 8, 5, 9, 3, 5, 8, 9, 5, 9, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 9, 5, 8, 9, 8, 8, 8, 9, 3, 8, 8, 8, 9, 8, 5, 9, 5, 5, 5, 5], [5, 5, 5, 5, 9, 9, 8, 9, 5, 8, 8, 9, 3, 8, 8, 5, 9, 8, 9, 9, 5, 5, 5, 5], [5, 5, 5, 5, 8, 9, 9, 8, 9, 9, 9, 8, 3, 9, 9, 9, 8, 9, 9, 8, 5, 5, 5, 5], [5, 5, 5, 5, 8, 9, 9, 8, 9, 9, 9, 8, 3, 9, 9, 9, 8, 9, 9, 8, 5, 5, 5, 5], [5, 5, 5, 5, 9, 9, 8, 9, 5, 8, 8, 9, 3, 8, 8, 5, 9, 8, 9, 9, 5, 5, 5, 5], [5, 5, 5, 5, 9, 5, 8, 9, 8, 8, 8, 9, 3, 8, 8, 8, 9, 8, 5, 9, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 9, 5, 9, 8, 5, 9, 3, 5, 8, 9, 5, 9, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 3, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 9, 8, 8, 9, 3, 8, 8, 9, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 3, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 8, 8, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5], [5], [8], [9], [9], [8], [9], [9], [9], [8], [8], [9], [9], [9], [8], [9], [9]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8], [8, 8], [8, 8], [8, 8], [8, 8], [5, 8], [8, 1]]}], "input_grid": [[5, 5, 0, 7, 7, 0, 5, 5], [5, 7, 7, 7, 7, 7, 7, 5], [0, 7, 7, 7, 7, 7, 7, 0], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [0, 7, 7, 7, 7, 7, 7, 0], [3, 3, 3, 3, 3, 3, 3, 5], [5, 5, 0, 7, 7, 0, 5, 5]], "task_key": "dc0a314f"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 1, 1, 1, 1, 1, 4, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 7, 7, 7, 7, 7, 7, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 7, 4, 4, 4, 4, 7, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 7, 4, 4, 4, 4, 7, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 7, 7, 7, 7, 7, 7, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 9, 4],\n[4, 1, 1, 1, 1, 1, 4, 9, 9, 9, 9, 9, 9, 9, 4],\n[4, 1, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 9, 9, 9, 7, 9, 9, 9, 9, 0, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 5, 9, 5, 2, 9, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 5, 9, 5, 2, 9, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 5, 5, 5, 2, 9, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9],\n[9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4], [4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4], [4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4], [4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4], [4, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 4], [4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4], [4, 1, 1, 1, 1, 1, 4, 9, 9, 9, 9, 9, 9, 9, 4], [4, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 4], [4, 7, 7, 7, 7, 7, 7, 9, 4, 4, 4, 4, 4, 9, 4], [4, 7, 4, 4, 4, 4, 7, 9, 4, 4, 4, 4, 4, 9, 4], [4, 7, 4, 4, 4, 4, 7, 9, 4, 4, 4, 4, 4, 9, 4], [4, 7, 7, 7, 7, 7, 7, 9, 4, 4, 4, 4, 4, 9, 4], [4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 9, 4], [4, 1, 1, 1, 1, 1, 4, 9, 9, 9, 9, 9, 9, 9, 4], [4, 1, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 9, 9, 9, 7, 9, 9, 9, 9, 0, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9], [9, 7, 7, 7, 7, 7, 9, 9, 9, 9, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 5, 5, 5, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 5, 9, 5, 2, 9, 2, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 5, 9, 5, 2, 9, 2, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 5, 5, 5, 2, 9, 2, 9, 9, 9, 9], [9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9], [9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 2, 9, 2, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}], "input_grid": [[7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "task_key": "4347f46a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 2, 2, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[1, 6, 6, 6, 6, 2, 6, 2, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 2, 2, 6, 6],\n[6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6],\n[6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6],\n[6, 6, 6, 3, 3, 6, 0, 6, 6, 6, 6, 7, 6, 6, 4, 4, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 0, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 6],\n[6, 6, 2, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 9, 9],\n[6, 2, 2, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 6, 9, 6, 9],\n[6, 2, 2, 2, 6, 5, 6, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 2, 2, 6, 5, 5, 6, 6, 3, 3, 6, 3, 6, 6, 6, 6, 6, 6],\n[7, 6, 6, 2, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 5, 5, 6, 6],\n[7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6],\n[6, 7, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 6, 0, 6, 6],\n[6, 7, 7, 6, 6, 6, 6, 9, 6, 9, 6, 6, 8, 6, 6, 6, 0, 0, 0],\n[6, 7, 6, 7, 6, 6, 6, 9, 9, 9, 6, 8, 8, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 6, 6, 6, 6, 6, 0, 0, 0, 6],\n[1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 0, 0, 6],\n[1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6],\n[6, 1, 1, 1, 6, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[1, 6, 1, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 5, 5, 6, 5, 5, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 5, 5, 5, 6, 6, 6, 6, 4],\n[6, 6, 6, 9, 9, 6, 6, 6, 2, 9, 6, 5, 5, 6, 6, 6, 6, 4, 6],\n[6, 6, 6, 9, 9, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 4, 6],\n[4, 4, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6],\n[4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9],\n[6, 9],\n[9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 6, 6, 6, 6, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 6, 5, 6, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 5, 1, 5, 1, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 5, 1, 1, 5, 5, 5],\n[5, 5, 5, 8, 5, 5, 4, 4, 5, 2, 2, 2, 2, 5, 5, 5, 1, 1, 5, 5, 5],\n[5, 5, 8, 8, 5, 5, 5, 4, 5, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 0, 5, 5],\n[3, 3, 5, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 0, 5, 0, 0, 5, 5, 5],\n[3, 3, 3, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 3, 3, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 9, 9, 9],\n[3, 3, 3, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 9, 9, 9, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 5, 6, 5, 6, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5],\n[5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 7, 7, 5, 5, 5],\n[5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 6, 5, 7, 7, 5, 6, 6],\n[5, 5, 5, 2, 5, 0, 5, 7, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6],\n[5, 5, 2, 2, 5, 5, 7, 7, 5, 4, 4, 5, 5, 5, 5, 2, 2, 5, 5, 6, 6],\n[5, 5, 5, 2, 5, 7, 5, 5, 5, 4, 5, 5, 5, 5, 2, 5, 2, 2, 5, 6, 6],\n[3, 3, 5, 2, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 2, 2, 2, 2, 5, 6, 6],\n[3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[3, 3, 5, 9, 9, 9, 9, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5],\n[3, 3, 5, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 5],\n[5, 5, 7],\n[5, 7, 7],\n[7, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 4, 4, 4, 4, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 7, 8, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 7, 0, 0, 0, 0],\n[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7],\n[0, 7],\n[7, 0],\n[0, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 8, 8, 4, 6, 4, 4, 4, 4, 7, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4],\n[8, 8, 4, 8, 4, 6, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 4, 0, 0, 4, 1, 1, 4, 4, 3, 3, 4, 4, 7, 7, 4, 4, 4],\n[4, 4, 4, 4, 0, 0, 0, 4, 2, 2, 2, 2, 4, 4, 0, 0, 4, 1, 4, 1, 4, 3, 3, 4, 4, 7, 7, 4, 4, 4],\n[4, 4, 4, 4, 0, 0, 0, 4, 2, 2, 2, 3, 4, 4, 4, 4, 4, 1, 1, 4, 4, 3, 3, 4, 4, 4, 7, 4, 5, 4],\n[4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 2, 2, 4, 4, 4, 4, 4, 1, 1, 1, 4, 3, 3, 4, 4, 7, 4, 4, 5, 5],\n[4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 3, 3, 4, 4, 4, 8, 4, 4, 2, 2, 4, 4, 4, 4],\n[5, 4, 5, 4, 4, 4, 4, 4, 1, 1, 1, 4, 4, 4, 4, 4, 3, 3, 4, 4, 8, 8, 4, 4, 2, 2, 4, 4, 4, 4],\n[5, 5, 5, 4, 4, 4, 4, 4, 1, 1, 1, 4, 4, 4, 4, 4, 3, 3, 4, 8, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4],\n[4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 1],\n[5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 1, 1],\n[5, 4, 5, 5, 4, 1, 1, 1, 1, 4, 4, 4, 4, 7, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 1, 1],\n[4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 1, 1],\n[4, 4, 4, 4, 4, 1, 4, 4, 1, 1, 4, 7, 7, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 1, 4],\n[4, 8, 8, 8, 4, 1, 4, 4, 4, 4, 4, 4, 7, 4, 9, 4, 4, 4, 8, 8, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4],\n[4, 8, 8, 8, 4, 4, 4, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 8, 8, 4, 4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 6, 6, 2, 2, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [1, 6, 6, 6, 6, 2, 6, 2, 6, 6, 0, 0, 6, 6, 6, 6, 6, 6, 6], [1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 2, 2, 6, 6], [6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6], [6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6], [6, 6, 6, 3, 3, 6, 0, 6, 6, 6, 6, 7, 6, 6, 4, 4, 6, 6, 6], [6, 6, 6, 6, 6, 6, 0, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 6], [6, 6, 2, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 9, 9], [6, 2, 2, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 6, 9, 6, 9], [6, 2, 2, 2, 6, 5, 6, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6], [6, 6, 2, 2, 6, 5, 5, 6, 6, 3, 3, 6, 3, 6, 6, 6, 6, 6, 6], [7, 6, 6, 2, 6, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 5, 5, 6, 6], [7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6], [6, 7, 6, 6, 6, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 6, 0, 6, 6], [6, 7, 7, 6, 6, 6, 6, 9, 6, 9, 6, 6, 8, 6, 6, 6, 0, 0, 0], [6, 7, 6, 7, 6, 6, 6, 9, 9, 9, 6, 8, 8, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 6, 6, 6, 6, 6, 0, 0, 0, 6], [1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 0, 0, 6], [1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 6], [6, 1, 1, 1, 6, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [1, 6, 1, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 5, 5, 6, 5, 5, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 6, 5, 5, 5, 6, 6, 6, 6, 4], [6, 6, 6, 9, 9, 6, 6, 6, 2, 9, 6, 5, 5, 6, 6, 6, 6, 4, 6], [6, 6, 6, 9, 9, 6, 6, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 4, 6], [4, 4, 6, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6], [4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 6, 6]], "output": [[9, 9], [6, 9], [9, 9]]}, {"input": [[5, 5, 6, 6, 6, 6, 5, 5, 5, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 6, 5, 6, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 5, 1, 5, 1, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 5, 1, 1, 5, 5, 5], [5, 5, 5, 8, 5, 5, 4, 4, 5, 2, 2, 2, 2, 5, 5, 5, 1, 1, 5, 5, 5], [5, 5, 8, 8, 5, 5, 5, 4, 5, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 0, 5, 5], [3, 3, 5, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 0, 5, 0, 0, 5, 5, 5], [3, 3, 3, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 3, 3, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 9, 9, 9], [3, 3, 3, 3, 3, 3, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5, 9, 9, 9, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 7, 7, 7, 5, 5, 5, 6, 5, 6, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5], [5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 7, 7, 5, 5, 5], [5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 6, 5, 7, 7, 5, 6, 6], [5, 5, 5, 2, 5, 0, 5, 7, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6], [5, 5, 2, 2, 5, 5, 7, 7, 5, 4, 4, 5, 5, 5, 5, 2, 2, 5, 5, 6, 6], [5, 5, 5, 2, 5, 7, 5, 5, 5, 4, 5, 5, 5, 5, 2, 5, 2, 2, 5, 6, 6], [3, 3, 5, 2, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 2, 2, 2, 2, 5, 6, 6], [3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [3, 3, 5, 9, 9, 9, 9, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5, 5], [3, 3, 5, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 1, 1, 5, 5, 5, 5, 5, 5]], "output": [[7, 7, 5], [5, 5, 7], [5, 7, 7], [7, 5, 5]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 7, 8, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[7, 7], [0, 7], [7, 0], [0, 7]]}], "input_grid": [[4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 8, 8, 4, 6, 4, 4, 4, 4, 7, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4], [8, 8, 4, 8, 4, 6, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 4, 0, 0, 4, 1, 1, 4, 4, 3, 3, 4, 4, 7, 7, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 4, 2, 2, 2, 2, 4, 4, 0, 0, 4, 1, 4, 1, 4, 3, 3, 4, 4, 7, 7, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 4, 2, 2, 2, 3, 4, 4, 4, 4, 4, 1, 1, 4, 4, 3, 3, 4, 4, 4, 7, 4, 5, 4], [4, 4, 4, 4, 4, 4, 0, 4, 4, 2, 2, 2, 4, 4, 4, 4, 4, 1, 1, 1, 4, 3, 3, 4, 4, 7, 4, 4, 5, 5], [4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 4, 4, 3, 3, 4, 4, 4, 8, 4, 4, 2, 2, 4, 4, 4, 4], [5, 4, 5, 4, 4, 4, 4, 4, 1, 1, 1, 4, 4, 4, 4, 4, 3, 3, 4, 4, 8, 8, 4, 4, 2, 2, 4, 4, 4, 4], [5, 5, 5, 4, 4, 4, 4, 4, 1, 1, 1, 4, 4, 4, 4, 4, 3, 3, 4, 8, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4], [4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 1], [5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 1, 1], [5, 4, 5, 5, 4, 1, 1, 1, 1, 4, 4, 4, 4, 7, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 1, 1], [4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 4, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 1, 1], [4, 4, 4, 4, 4, 1, 4, 4, 1, 1, 4, 7, 7, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 1, 4], [4, 8, 8, 8, 4, 1, 4, 4, 4, 4, 4, 4, 7, 4, 9, 4, 4, 4, 8, 8, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4], [4, 8, 8, 8, 4, 4, 4, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 8, 8, 4, 4, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "task_key": "48d8fb45"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0],\n[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0],\n[2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0],\n[2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0],\n[2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0],\n[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 1, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 0, 2],\n[2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0],\n[2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0],\n[2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0],\n[0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 5, 2, 2, 2, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 2, 5, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 5, 5, 5],\n[2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 5, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 2, 2, 2, 2, 5, 2, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 2, 2, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 2, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5],\n[2, 2, 5, 5, 5, 5, 5, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 5, 1, 1, 1, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 2, 2, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 2, 2, 2],\n[2, 2, 2, 2, 5, 1, 5, 1, 1, 5, 2, 2, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 5, 5, 5],\n[2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 5, 1, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 1, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 1, 1, 1, 1, 5, 1, 1, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 1, 1, 5],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 1, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5],\n[2, 2, 5, 5, 5, 5, 5, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 7, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 6, 6, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 7, 7, 7, 6, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 7, 6, 7, 6, 6, 7, 6, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6],\n[7, 7, 7, 6, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6],\n[7, 7, 7, 6, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 7, 6],\n[6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 1, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 1, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 6, 6, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 1, 6, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 1, 1, 6, 6, 6, 7, 6, 1, 1, 6, 1, 1, 6, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 1, 6, 1, 6, 6, 7, 6, 1, 1, 6, 1, 6, 6, 7, 7, 7, 6],\n[7, 7, 7, 7, 7, 6, 6, 1, 6, 1, 6, 7, 6, 1, 1, 6, 1, 1, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 1, 1, 1, 6, 6, 7, 6, 1, 1, 6, 1, 1, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 1, 6, 1, 6, 6, 7, 6, 1, 1, 6, 6, 1, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 6, 6, 1, 6, 6, 7, 6, 1, 1, 6, 6, 6, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 1, 1, 1, 1, 6, 6],\n[7, 7, 7, 6, 6, 6, 1, 1, 6, 6, 7, 7, 7, 7, 7, 7, 6, 1, 1, 1, 1, 6, 6],\n[7, 7, 7, 6, 1, 1, 6, 6, 1, 6, 7, 7, 7, 7, 7, 7, 6, 1, 1, 1, 1, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 7, 6],\n[6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 4, 4, 4, 4, 4, 4, 2],\n[2, 2, 2, 4, 2, 2, 2, 2, 4, 2],\n[2, 2, 2, 4, 4, 4, 4, 4, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 4, 4, 4, 4, 4, 4, 2, 2, 2],\n[2, 4, 2, 2, 2, 4, 4, 2, 2, 2],\n[2, 4, 4, 4, 4, 4, 4, 2, 2, 2],\n[4, 4, 4, 4, 4, 2, 2, 2, 4, 4],\n[4, 4, 2, 2, 4, 2, 2, 2, 4, 2],\n[4, 4, 4, 4, 4, 2, 2, 2, 4, 2],\n[2, 2, 2, 4, 4, 4, 2, 2, 4, 4],\n[2, 2, 2, 4, 4, 4, 2, 2, 4, 2],\n[2, 2, 2, 4, 2, 4, 2, 2, 4, 4],\n[2, 2, 2, 4, 2, 4, 2, 2, 2, 2],\n[2, 2, 2, 4, 4, 4, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 4, 4, 4, 4, 4],\n[2, 2, 2, 2, 2, 4, 2, 2, 4, 2],\n[2, 2, 2, 2, 2, 4, 4, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2], [2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 1, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 0, 2], [2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0], [2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 5, 2, 2, 2, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2], [2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 2], [2, 2, 2, 2, 5, 2, 5, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 5, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 5, 5, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 2, 2, 2, 2, 5, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 2, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 5, 5, 5, 5, 5, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 5]], "output": [[2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 5, 1, 1, 1, 5, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 2, 2, 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2], [2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 2, 2, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 2, 2, 2], [2, 2, 2, 2, 5, 1, 5, 1, 1, 5, 2, 2, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 5, 5, 5], [2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 5, 5, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 5, 5, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 1, 1, 1, 1, 5, 1, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 1, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 5, 1, 1, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 1, 5, 5, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 5, 5, 5, 5, 5, 5, 2, 5, 2, 5, 2, 2, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 5]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 7, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 6, 6, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 7, 7, 7, 6, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 7, 6, 7, 6, 6, 7, 6, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6], [7, 7, 7, 6, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6], [7, 7, 7, 6, 7, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6], [6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 7, 6], [6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 1, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 1, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 6, 6, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 1, 1, 6, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 1, 1, 6, 6, 6, 7, 6, 1, 1, 6, 1, 1, 6, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 1, 6, 1, 6, 6, 7, 6, 1, 1, 6, 1, 6, 6, 7, 7, 7, 6], [7, 7, 7, 7, 7, 6, 6, 1, 6, 1, 6, 7, 6, 1, 1, 6, 1, 1, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 1, 1, 1, 6, 6, 7, 6, 1, 1, 6, 1, 1, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 1, 6, 1, 6, 6, 7, 6, 1, 1, 6, 6, 1, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 6, 6, 1, 6, 6, 7, 6, 1, 1, 6, 6, 6, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 1, 1, 1, 1, 6, 6], [7, 7, 7, 6, 6, 6, 1, 1, 6, 6, 7, 7, 7, 7, 7, 7, 6, 1, 1, 1, 1, 6, 6], [7, 7, 7, 6, 1, 1, 6, 6, 1, 6, 7, 7, 7, 7, 7, 7, 6, 1, 1, 1, 1, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6], [6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 7, 7, 6], [6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 7, 7, 7]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 4, 4, 4, 4, 4, 4, 2], [2, 2, 2, 4, 2, 2, 2, 2, 4, 2], [2, 2, 2, 4, 4, 4, 4, 4, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 4, 4, 4, 4, 4, 4, 2, 2, 2], [2, 4, 2, 2, 2, 4, 4, 2, 2, 2], [2, 4, 4, 4, 4, 4, 4, 2, 2, 2], [4, 4, 4, 4, 4, 2, 2, 2, 4, 4], [4, 4, 2, 2, 4, 2, 2, 2, 4, 2], [4, 4, 4, 4, 4, 2, 2, 2, 4, 2], [2, 2, 2, 4, 4, 4, 2, 2, 4, 4], [2, 2, 2, 4, 4, 4, 2, 2, 4, 2], [2, 2, 2, 4, 2, 4, 2, 2, 4, 4], [2, 2, 2, 4, 2, 4, 2, 2, 2, 2], [2, 2, 2, 4, 4, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 4, 4, 4, 4], [2, 2, 2, 2, 2, 4, 2, 2, 4, 2], [2, 2, 2, 2, 2, 4, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "task_key": "a5313dff"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2],\n[2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2],\n[2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2],\n[2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0],\n[2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2],\n[2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 1, 1, 0, 2, 2, 0, 8, 0, 2, 2, 0, 2, 2, 2],\n[1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2],\n[1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2],\n[1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0],\n[1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2],\n[1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 3, 6, 6, 3, 6, 6, 3, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 3, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 3, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 3, 3, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 3, 6, 6, 3, 8, 8, 3, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 3, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 3, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 1, 1, 1, 1, 1],\n[6, 3, 3, 3, 3, 1, 1, 1, 1, 1],\n[6, 3, 6, 6, 3, 1, 1, 1, 1, 1],\n[6, 3, 6, 6, 3, 1, 1, 1, 1, 1],\n[6, 3, 6, 6, 3, 1, 1, 1, 1, 1],\n[6, 3, 6, 6, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 3, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 7, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7],\n[6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 7, 7, 7],\n[6, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 6, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 8, 7, 6, 6, 6, 6, 7, 6],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 6, 7, 6, 6, 7, 1, 1, 7, 6, 7, 7, 7, 7, 7, 7, 7],\n[6, 7, 6, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 6, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 7, 7, 7],\n[6, 7, 7, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6],\n[6, 7, 8, 7, 6, 6, 7, 1, 1, 7, 7, 7, 6, 6, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6],\n[8, 7, 8, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6],\n[3, 3, 3, 3, 3, 3, 3],\n[6, 3, 6, 3, 6, 6, 6],\n[6, 3, 6, 3, 6, 6, 6],\n[6, 3, 6, 3, 6, 6, 6],\n[6, 3, 6, 3, 6, 6, 6],\n[6, 3, 6, 3, 6, 6, 6],\n[6, 3, 6, 3, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2], [2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2]], "output": [[1, 1, 1, 1, 0, 2, 2, 0, 8, 0, 2, 2, 0, 2, 2, 2], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2], [1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2], [1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2], [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2]]}, {"input": [[6, 3, 6, 6, 3, 6, 6, 3, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 6, 6], [6, 3, 6, 6, 3, 6, 6, 3, 6, 6], [6, 3, 6, 6, 3, 6, 6, 3, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 3, 3, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6]], "output": [[6, 3, 6, 6, 3, 8, 8, 3, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 6, 6], [6, 3, 6, 6, 3, 6, 6, 3, 6, 6], [6, 3, 6, 6, 3, 6, 6, 3, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 1, 1, 1, 1, 1], [6, 3, 3, 3, 3, 1, 1, 1, 1, 1], [6, 3, 6, 6, 3, 1, 1, 1, 1, 1], [6, 3, 6, 6, 3, 1, 1, 1, 1, 1], [6, 3, 6, 6, 3, 1, 1, 1, 1, 1], [6, 3, 6, 6, 3, 3, 3, 3, 3, 3], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [6, 3, 6, 6, 3, 6, 6, 6, 6, 6]]}, {"input": [[6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 6, 7, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 6], [6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7], [6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6], [6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 7, 7, 7], [6, 7, 7, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6], [6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 7, 7, 6, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6], [6, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 6, 6]], "output": [[6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 8, 7, 6, 6, 6, 6, 7, 6], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 6, 6, 6], [6, 7, 6, 7, 6, 6, 7, 1, 1, 7, 6, 7, 7, 7, 7, 7, 7, 7], [6, 7, 6, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6], [6, 7, 6, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 7, 7, 7], [6, 7, 7, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6], [6, 7, 8, 7, 6, 6, 7, 1, 1, 7, 7, 7, 6, 6, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6], [8, 7, 8, 7, 6, 6, 7, 1, 1, 7, 6, 7, 6, 6, 7, 6, 6, 6]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3], [6, 3, 6, 3, 6, 6, 6], [6, 3, 6, 3, 6, 6, 6], [6, 3, 6, 3, 6, 6, 6], [6, 3, 6, 3, 6, 6, 6], [6, 3, 6, 3, 6, 6, 6], [6, 3, 6, 3, 6, 6, 6]], "task_key": "6455b5f5"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 5, 5, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 5, 5, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 0, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 0, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 0, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7],\n[7, 8, 7, 5, 7, 7, 7, 7, 7, 7, 5, 7, 8],\n[7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7],\n[7, 7, 7, 5, 7, 8, 7, 7, 8, 7, 5, 7, 7],\n[7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 7, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 7, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 7, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7],\n[7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7],\n[7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 5, 5, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 5, 5, 9, 9, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 0, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 0, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 9, 3, 0, 0, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 3, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 0, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 3, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 3, 3, 3, 0, 0, 3, 9, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7], [7, 8, 7, 5, 7, 7, 7, 7, 7, 7, 5, 7, 8], [7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7], [7, 7, 7, 5, 7, 8, 7, 7, 8, 7, 5, 7, 7], [7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}], "input_grid": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 7, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 7, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 7, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 1, 1, 7], [7, 1, 1, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7], [7, 7, 7, 7, 3, 3, 7, 7, 7, 7, 7, 7, 7, 3, 3, 7, 7, 7, 7]], "task_key": "6855a6e4"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5],\n[5, 5, 5],\n[0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 6, 6],\n[6, 6, 6],\n[6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 8, 2, 2, 2, 2, 2, 8, 2, 2],\n[2, 2, 2, 8, 5, 5, 5, 5, 5, 8, 2, 2],\n[2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 2, 2],\n[2, 2, 2],\n[2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9],\n[9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9],\n[9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9],\n[9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9],\n[9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9],\n[9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9],\n[9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9],\n[9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9],\n[9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[5, 5, 5], [5, 5, 5], [0, 0, 0]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[5, 6, 6], [6, 6, 6], [6, 6, 6]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 8, 2, 2, 2, 2, 2, 8, 2, 2], [2, 2, 2, 8, 5, 5, 5, 5, 5, 8, 2, 2], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[5, 2, 2], [2, 2, 2], [2, 2, 2]]}], "input_grid": [[9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9], [9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9], [9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9], [9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9], [9, 9, 9, 3, 7, 7, 7, 7, 7, 7, 7, 3, 9], [9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9], [9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9], [9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9], [9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 3, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "task_key": "b0c4d837"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 0, 0, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 0, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 0, 0, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 0, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 0, 0, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 0, 0, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 0, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 5, 5, 0, 0, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 0, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 0, 0, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]}], "input_grid": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "task_key": "b7249182"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 1, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 8, 9, 2, 2, 2, 2, 2, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6],\n[6, 5, 6, 5, 6, 6],\n[6, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6],\n[6, 5, 6, 5, 6, 6],\n[6, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 2, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6],\n[5, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[1, 5, 8, 5, 8],\n[1, 5, 8, 5, 8],\n[1, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 2, 5, 8],\n[8, 5, 2, 5, 8],\n[8, 5, 2, 5, 8],\n[8, 5, 2, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 8],\n[8, 5, 8, 5, 8],\n[5, 5, 5, 5, 5],\n[8, 5, 8, 5, 3]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4],\n[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[1, 1, 9, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 9, 2, 2, 2, 2, 2, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 9, 8, 8, 8, 8, 8, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[6, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6], [6, 5, 6, 5, 6, 6], [6, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6]], "output": [[1, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6], [6, 5, 6, 5, 6, 6], [6, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 2, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6], [5, 5, 5, 5, 5, 5], [6, 5, 6, 5, 3, 3]]}, {"input": [[8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 8]], "output": [[1, 5, 8, 5, 8], [1, 5, 8, 5, 8], [1, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 2, 5, 8], [8, 5, 2, 5, 8], [8, 5, 2, 5, 8], [8, 5, 2, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 8], [8, 5, 8, 5, 8], [5, 5, 5, 5, 5], [8, 5, 8, 5, 3]]}], "input_grid": [[4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4], [4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4]], "task_key": "941d9a10"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 0, 9, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 0],\n[0, 0, 0, 0, 0, 0, 0, 8, 0, 9],\n[0, 0, 0, 0, 0, 0, 8, 0, 9, 0],\n[0, 0, 0, 0, 0, 8, 0, 9, 0, 0],\n[0, 0, 0, 0, 8, 0, 9, 0, 0, 0],\n[0, 0, 0, 8, 0, 9, 0, 0, 0, 0],\n[0, 0, 8, 0, 9, 0, 0, 0, 0, 0],\n[0, 8, 0, 9, 0, 0, 0, 0, 0, 0],\n[8, 0, 9, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 7, 5, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 7],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 5, 0],\n[0, 0, 0, 0, 0, 0, 0, 8, 7, 5, 0, 0],\n[0, 0, 0, 0, 0, 0, 8, 7, 5, 0, 0, 0],\n[0, 0, 0, 0, 0, 8, 7, 5, 0, 0, 0, 0],\n[0, 0, 0, 0, 8, 7, 5, 0, 0, 0, 0, 0],\n[0, 0, 0, 8, 7, 5, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 7, 5, 0, 0, 0, 0, 0, 0, 0],\n[0, 8, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[8, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 0, 9, 2, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 0, 9, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 8, 0, 9], [0, 0, 0, 0, 0, 0, 8, 0, 9, 0], [0, 0, 0, 0, 0, 8, 0, 9, 0, 0], [0, 0, 0, 0, 8, 0, 9, 0, 0, 0], [0, 0, 0, 8, 0, 9, 0, 0, 0, 0], [0, 0, 8, 0, 9, 0, 0, 0, 0, 0], [0, 8, 0, 9, 0, 0, 0, 0, 0, 0], [8, 0, 9, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[8, 7, 5, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 5], [0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 5, 0], [0, 0, 0, 0, 0, 0, 0, 8, 7, 5, 0, 0], [0, 0, 0, 0, 0, 0, 8, 7, 5, 0, 0, 0], [0, 0, 0, 0, 0, 8, 7, 5, 0, 0, 0, 0], [0, 0, 0, 0, 8, 7, 5, 0, 0, 0, 0, 0], [0, 0, 0, 8, 7, 5, 0, 0, 0, 0, 0, 0], [0, 0, 8, 7, 5, 0, 0, 0, 0, 0, 0, 0], [0, 8, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0], [8, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[7, 0, 9, 2, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[6, 3]], "task_key": "feca6190"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 4, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 8, 8, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 8, 8, 3, 4, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 4, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 8, 8, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 8, 4, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3],\n[3, 8, 3, 3, 3, 3, 3, 3],\n[3, 4, 3, 4, 3, 3, 3, 3],\n[8, 8, 4, 4, 3, 3, 3, 3],\n[8, 8, 3, 4, 8, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 9, 2, 9, 9, 2, 1, 9, 1, 1, 1, 1, 1, 1, 2, 1, 9, 1, 1],\n[1, 1, 2, 9, 9, 2, 2, 2, 9, 1, 1, 1, 1, 9, 2, 2, 2, 1, 1],\n[1, 2, 2, 9, 2, 9, 2, 9, 9, 1, 1, 1, 2, 1, 9, 9, 9, 1, 1],\n[1, 1, 9, 1, 9, 2, 1, 1, 1, 9, 1, 1, 9, 9, 2, 9, 9, 1, 1],\n[1, 1, 1, 2, 9, 2, 9, 1, 1, 1, 9, 1, 2, 2, 9, 2, 2, 1, 1],\n[1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 9, 1, 2, 2, 1, 1, 1],\n[1, 1, 1, 1, 1, 9, 1, 9, 1, 1, 9, 1, 1, 1, 9, 2, 9, 1, 1],\n[1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 1, 1, 1],\n[1, 1, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1],\n[1, 9, 2, 9, 1, 1, 1, 9, 1, 1, 9, 1, 9, 1, 1, 1, 1, 1, 1],\n[1, 1, 2, 2, 1, 9, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1],\n[1, 2, 2, 9, 2, 2, 1, 9, 1, 1, 1, 9, 2, 9, 2, 1, 1, 1, 1],\n[1, 9, 9, 2, 9, 9, 1, 1, 9, 1, 1, 1, 2, 9, 1, 9, 1, 1, 1],\n[1, 9, 9, 9, 1, 2, 1, 1, 1, 9, 9, 2, 9, 2, 9, 2, 2, 1, 1],\n[1, 2, 2, 2, 9, 1, 1, 1, 1, 9, 2, 2, 2, 9, 9, 2, 1, 1, 1],\n[1, 9, 1, 2, 1, 1, 1, 1, 1, 1, 9, 1, 2, 9, 9, 2, 9, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 2, 9, 9, 2, 1, 9, 1],\n[1, 2, 9, 9, 2, 2, 2, 9],\n[2, 2, 9, 2, 9, 2, 9, 9],\n[1, 9, 1, 9, 2, 1, 1, 1],\n[1, 1, 2, 9, 2, 9, 1, 1],\n[1, 1, 1, 1, 1, 2, 1, 1],\n[1, 1, 1, 1, 9, 1, 9, 1],\n[1, 1, 1, 9, 1, 1, 1, 1]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 3, 7, 5, 1, 7, 7, 7, 2, 7, 3],\n[7, 7, 3, 9, 7, 1, 7, 7, 7, 3, 7],\n[7, 2, 7, 9, 7, 7, 7, 3, 9, 9, 5],\n[7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 1],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 7],\n[7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 1, 7, 7, 7, 7, 7, 7, 3, 7, 7],\n[7, 5, 9, 9, 3, 7, 7, 7, 9, 7, 2],\n[7, 7, 3, 7, 7, 7, 1, 7, 9, 3, 7],\n[7, 3, 7, 2, 7, 7, 7, 1, 5, 7, 3],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 7, 5, 1, 7],\n[7, 3, 9, 7, 1],\n[2, 7, 9, 7, 7],\n[7, 7, 3, 7, 7],\n[7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 6, 7, 5, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 5, 2, 8, 5, 6, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 8, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 8, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 9, 6, 5, 8, 2, 5, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 5, 7, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 4, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 8, 8, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 8, 8, 3, 4, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 4, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 8, 8, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 8, 4, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3], [3, 8, 3, 3, 3, 3, 3, 3], [3, 4, 3, 4, 3, 3, 3, 3], [8, 8, 4, 4, 3, 3, 3, 3], [8, 8, 3, 4, 8, 3, 3, 3]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 9, 2, 9, 9, 2, 1, 9, 1, 1, 1, 1, 1, 1, 2, 1, 9, 1, 1], [1, 1, 2, 9, 9, 2, 2, 2, 9, 1, 1, 1, 1, 9, 2, 2, 2, 1, 1], [1, 2, 2, 9, 2, 9, 2, 9, 9, 1, 1, 1, 2, 1, 9, 9, 9, 1, 1], [1, 1, 9, 1, 9, 2, 1, 1, 1, 9, 1, 1, 9, 9, 2, 9, 9, 1, 1], [1, 1, 1, 2, 9, 2, 9, 1, 1, 1, 9, 1, 2, 2, 9, 2, 2, 1, 1], [1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 9, 1, 2, 2, 1, 1, 1], [1, 1, 1, 1, 1, 9, 1, 9, 1, 1, 9, 1, 1, 1, 9, 2, 9, 1, 1], [1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 1, 1, 1], [1, 1, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1], [1, 9, 2, 9, 1, 1, 1, 9, 1, 1, 9, 1, 9, 1, 1, 1, 1, 1, 1], [1, 1, 2, 2, 1, 9, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 9, 2, 2, 1, 9, 1, 1, 1, 9, 2, 9, 2, 1, 1, 1, 1], [1, 9, 9, 2, 9, 9, 1, 1, 9, 1, 1, 1, 2, 9, 1, 9, 1, 1, 1], [1, 9, 9, 9, 1, 2, 1, 1, 1, 9, 9, 2, 9, 2, 9, 2, 2, 1, 1], [1, 2, 2, 2, 9, 1, 1, 1, 1, 9, 2, 2, 2, 9, 9, 2, 1, 1, 1], [1, 9, 1, 2, 1, 1, 1, 1, 1, 1, 9, 1, 2, 9, 9, 2, 9, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[9, 2, 9, 9, 2, 1, 9, 1], [1, 2, 9, 9, 2, 2, 2, 9], [2, 2, 9, 2, 9, 2, 9, 9], [1, 9, 1, 9, 2, 1, 1, 1], [1, 1, 2, 9, 2, 9, 1, 1], [1, 1, 1, 1, 1, 2, 1, 1], [1, 1, 1, 1, 9, 1, 9, 1], [1, 1, 1, 9, 1, 1, 1, 1]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 3, 7, 5, 1, 7, 7, 7, 2, 7, 3], [7, 7, 3, 9, 7, 1, 7, 7, 7, 3, 7], [7, 2, 7, 9, 7, 7, 7, 3, 9, 9, 5], [7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 1], [7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 7], [7, 7, 1, 7, 7, 7, 7, 7, 7, 7, 7], [7, 1, 7, 7, 7, 7, 7, 7, 3, 7, 7], [7, 5, 9, 9, 3, 7, 7, 7, 9, 7, 2], [7, 7, 3, 7, 7, 7, 1, 7, 9, 3, 7], [7, 3, 7, 2, 7, 7, 7, 1, 5, 7, 3], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[3, 7, 5, 1, 7], [7, 3, 9, 7, 1], [2, 7, 9, 7, 7], [7, 7, 3, 7, 7], [7, 7, 7, 7, 7]]}], "input_grid": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 6, 7, 5, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 5, 2, 8, 5, 6, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 8, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 8, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 9, 6, 5, 8, 2, 5, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 5, 7, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "task_key": "2013d3e2"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 2, 0, 2, 0, 2, 9, 2, 9, 2, 9],\n[2, 2, 0, 2, 0, 2, 9, 2, 9, 2, 2],\n[0, 0, 0, 2, 0, 2, 9, 2, 9, 9, 9],\n[2, 2, 2, 2, 0, 2, 9, 2, 2, 2, 2],\n[0, 0, 0, 0, 0, 2, 9, 9, 9, 9, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1],\n[2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2],\n[3, 3, 3, 2, 3, 2, 1, 2, 1, 1, 1],\n[2, 2, 3, 2, 3, 2, 1, 2, 1, 2, 2],\n[3, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 5],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[1, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 5, 3, 5, 3, 5, 3, 5],\n[3, 3, 5, 3, 5, 3, 5, 3, 3],\n[1, 1, 3, 3, 5, 3, 5, 5, 5],\n[3, 3, 3, 3, 5, 3, 3, 3, 3],\n[1, 1, 1, 1, 3, 5, 5, 5, 5],\n[3, 3, 3, 3, 1, 3, 3, 3, 3],\n[1, 1, 1, 3, 1, 3, 3, 5, 5],\n[3, 3, 1, 3, 1, 3, 1, 3, 3],\n[1, 3, 1, 3, 1, 3, 1, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 9],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 9, 6, 9, 6, 9, 6, 9],\n[6, 9, 6, 9, 6, 9, 6, 6],\n[6, 9, 6, 9, 6, 9, 9, 9],\n[6, 9, 6, 9, 6, 6, 6, 6],\n[6, 9, 6, 9, 9, 9, 9, 9],\n[6, 9, 6, 6, 6, 6, 6, 6],\n[6, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[6, 6, 6, 6, 6, 6, 6, 6],\n[6, 5, 5, 5, 5, 5, 5, 5],\n[6, 5, 6, 6, 6, 6, 6, 6],\n[6, 5, 6, 5, 5, 5, 5, 5],\n[6, 5, 6, 5, 6, 6, 6, 6],\n[6, 5, 6, 5, 6, 5, 5, 5],\n[6, 5, 6, 5, 6, 5, 6, 6],\n[6, 5, 6, 5, 6, 5, 6, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]], "output": [[0, 2, 0, 2, 0, 2, 9, 2, 9, 2, 9], [2, 2, 0, 2, 0, 2, 9, 2, 9, 2, 2], [0, 0, 0, 2, 0, 2, 9, 2, 9, 9, 9], [2, 2, 2, 2, 0, 2, 9, 2, 2, 2, 2], [0, 0, 0, 0, 0, 2, 9, 9, 9, 9, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1], [2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2], [3, 3, 3, 2, 3, 2, 1, 2, 1, 1, 1], [2, 2, 3, 2, 3, 2, 1, 2, 1, 2, 2], [3, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 5, 3, 5, 3, 5, 3, 5], [3, 3, 5, 3, 5, 3, 5, 3, 3], [1, 1, 3, 3, 5, 3, 5, 5, 5], [3, 3, 3, 3, 5, 3, 3, 3, 3], [1, 1, 1, 1, 3, 5, 5, 5, 5], [3, 3, 3, 3, 1, 3, 3, 3, 3], [1, 1, 1, 3, 1, 3, 3, 5, 5], [3, 3, 1, 3, 1, 3, 1, 3, 3], [1, 3, 1, 3, 1, 3, 1, 3, 3]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 5]], "output": [[6, 9, 6, 9, 6, 9, 6, 9], [6, 9, 6, 9, 6, 9, 6, 6], [6, 9, 6, 9, 6, 9, 9, 9], [6, 9, 6, 9, 6, 6, 6, 6], [6, 9, 6, 9, 9, 9, 9, 9], [6, 9, 6, 6, 6, 6, 6, 6], [6, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6], [9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6], [9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6], [9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6, 6, 6], [5, 5, 5, 5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6, 6, 6], [6, 5, 5, 5, 5, 5, 5, 5], [6, 5, 6, 6, 6, 6, 6, 6], [6, 5, 6, 5, 5, 5, 5, 5], [6, 5, 6, 5, 6, 6, 6, 6], [6, 5, 6, 5, 6, 5, 5, 5], [6, 5, 6, 5, 6, 5, 6, 6], [6, 5, 6, 5, 6, 5, 6, 5]]}], "input_grid": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1]], "task_key": "d22278a0"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6],\n[6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 4, 4, 4, 6, 6, 4, 6, 6],\n[4, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4],\n[6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4],\n[4, 6, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6],\n[6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 6],\n[4, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 4, 4, 4, 4],\n[6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 6, 6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 4, 4, 4],\n[4, 6, 6, 6, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 4, 6, 6],\n[6, 6, 4, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 4, 6, 6, 6, 6, 6, 6],\n[6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 6],\n[6, 6, 4, 4, 4, 4, 6, 4, 6, 6, 6, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4],\n[6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6],\n[6, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6],\n[6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 4],\n[4, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 4, 6, 4, 6, 6, 6, 4, 6, 4, 6, 6, 4, 6, 6, 6],\n[4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4],\n[4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 6, 6],\n[4, 4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 6, 4, 6],\n[4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 6, 4, 6, 6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 4, 6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 4],\n[6, 4, 6, 4, 6, 6, 6, 4, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6],\n[6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 4],\n[4, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 6],\n[6, 4, 6, 6, 6, 4, 6, 6, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6],\n[4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 4],\n[6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6, 6, 6],\n[6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 4, 6, 6, 6, 6, 4, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 4],\n[6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6],\n[6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 8, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3],\n[3, 3, 3, 8, 8, 8, 3, 8, 3, 8, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[8, 8, 8, 8, 3, 3, 8, 3, 3, 3, 8, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3],\n[8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 8, 3, 3, 3, 8, 8, 8, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 8],\n[8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 8, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3, 3, 3, 3, 8, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 3, 8, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3],\n[8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 6, 6],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 0, 6],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6],\n[6, 6, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 0, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 0, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0],\n[6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 0, 6, 6, 6, 0, 0, 0, 6, 6, 6, 0, 6],\n[0, 0, 0, 0, 0, 6, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 6, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6, 0, 6, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 2, 9, 9, 2, 9, 2, 2, 2, 2, 2, 9, 2, 9],\n[9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2, 9, 9, 9],\n[2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 9, 9],\n[9, 9, 2, 9, 2, 9, 9, 9, 2, 9, 2, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 2, 9, 9, 2, 9, 9, 2, 9, 2, 9, 2],\n[9, 2, 9, 9, 2, 9, 9, 9, 9, 9, 2, 9, 2, 9],\n[9, 9, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 2, 2, 9, 9, 9, 9, 9, 2, 9, 9],\n[9, 9, 9, 2, 2, 2, 9, 9, 2, 9, 2, 9, 9, 9],\n[9, 9, 2, 9, 2, 9, 9, 2, 9, 9, 9, 9, 9, 2],\n[9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 2, 9, 9, 9],\n[2, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 2],\n[9, 9, 2, 9, 9, 9, 2, 9, 2, 2, 2, 2, 2, 2],\n[2, 9, 9, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2],\n[9, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2],\n[2, 9, 9, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2],\n[9, 2, 9, 9, 9, 2, 9, 9, 2, 2, 2, 2, 2, 2],\n[2, 9, 2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6], [6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 4, 4, 4, 6, 6, 4, 6, 6], [4, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4], [6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4], [4, 6, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6], [6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 6], [4, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 4, 4, 4, 4], [6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 6, 6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 4, 4, 4], [4, 6, 6, 6, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 4, 6, 6], [6, 6, 4, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 4, 6, 6, 6, 6, 6, 6], [6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 6], [6, 6, 4, 4, 4, 4, 6, 4, 6, 6, 6, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4], [6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6], [6, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6], [6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 4], [4, 6, 6, 6, 4, 6, 4, 6, 4, 6, 6, 4, 6, 4, 6, 6, 6, 4, 6, 4, 6, 6, 4, 6, 6, 6], [4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4], [4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 6, 6], [4, 4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 6, 4, 6], [4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6], [4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 6, 4, 6, 6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6], [4, 4, 4, 4, 4, 6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 4], [6, 4, 6, 4, 6, 6, 6, 4, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6], [6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 4], [4, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 6], [6, 4, 6, 6, 6, 4, 6, 6, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6], [4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 4], [6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 4, 6, 6, 6], [6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 4, 6, 6, 6, 6, 4, 6]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 4], [6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 4, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6], [6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 4, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}, {"input": [[3, 8, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 8, 8, 8, 8, 8, 3, 3, 3], [3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3], [3, 3, 3, 8, 8, 8, 3, 8, 3, 8, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [8, 8, 8, 8, 3, 3, 8, 3, 3, 3, 8, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3], [8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 8, 3, 3, 3, 8, 8, 8, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 8, 3, 3, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3, 3, 3, 3, 8, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 3, 8, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3], [8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3], [8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6], [0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 6, 6], [6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 0, 6], [6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6], [6, 6, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 0, 6, 0, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 0, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0], [6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0], [0, 0, 0, 0, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0, 6, 6, 6, 0, 6, 6, 6, 0, 0, 0, 6, 6, 6, 0, 6], [0, 0, 0, 0, 0, 6, 0, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 0, 6, 0, 0, 0, 0, 6, 6, 6, 0, 6, 6, 6, 0, 6, 0]], "output": [[0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}], "input_grid": [[9, 2, 9, 9, 2, 9, 2, 2, 2, 2, 2, 9, 2, 9], [9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2, 9, 9, 9], [2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 9, 9], [9, 9, 2, 9, 2, 9, 9, 9, 2, 9, 2, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9], [9, 9, 9, 2, 9, 9, 2, 9, 9, 2, 9, 2, 9, 2], [9, 2, 9, 9, 2, 9, 9, 9, 9, 9, 2, 9, 2, 9], [9, 9, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 9, 9], [9, 9, 9, 9, 2, 2, 9, 9, 9, 9, 9, 2, 9, 9], [9, 9, 9, 2, 2, 2, 9, 9, 2, 9, 2, 9, 9, 9], [9, 9, 2, 9, 2, 9, 9, 2, 9, 9, 9, 9, 9, 2], [9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 2, 9, 9, 9], [2, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 2], [9, 9, 2, 9, 9, 9, 2, 9, 2, 2, 2, 2, 2, 2], [2, 9, 9, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2], [9, 2, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2], [2, 9, 9, 2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2], [9, 2, 9, 9, 9, 2, 9, 9, 2, 2, 2, 2, 2, 2], [2, 9, 2, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2]], "task_key": "7f4411dc"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 0, 7, 3, 9, 5, 9, 5, 7, 1, 6, 1, 3, 2, 1, 4, 3, 2, 2, 0, 4, 0, 6, 7, 2, 2, 7, 9],\n[2, 0, 2, 0, 6, 9, 1, 6, 9, 5, 1, 5, 6, 3, 5, 3, 7, 2, 4, 6, 0, 1, 2, 2, 2, 2, 7, 4, 1, 4],\n[2, 2, 6, 9, 7, 5, 6, 9, 1, 1, 6, 6, 8, 1, 8, 1, 4, 6, 7, 1, 4, 2, 5, 1, 3, 2, 4, 3, 4, 7],\n[0, 0, 9, 8, 5, 9, 9, 1, 1, 9, 1, 3, 1, 1, 5, 6, 2, 7, 2, 2, 0, 2, 1, 3, 0, 7, 1, 4, 9, 1],\n[7, 6, 7, 5, 2, 5, 5, 1, 9, 7, 3, 5, 8, 5, 7, 2, 6, 7, 2, 4, 6, 2, 3, 0, 0, 9, 4, 7, 1, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 1, 4, 3, 2],\n[3, 7, 2, 4, 6],\n[1, 4, 6, 7, 1],\n[6, 2, 7, 2, 2],\n[2, 6, 7, 2, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 7, 4, 4],\n[7, 7, 7, 7],\n[4, 7, 4, 4],\n[4, 7, 4, 7],\n[1, 1, 1, 6],\n[1, 1, 1, 1],\n[1, 1, 1, 6],\n[6, 1, 6, 6],\n[3, 5, 5, 5],\n[5, 5, 3, 5],\n[5, 3, 3, 5],\n[5, 5, 5, 5],\n[6, 6, 4, 6],\n[4, 6, 4, 6],\n[4, 4, 6, 4],\n[4, 4, 6, 4],\n[1, 0, 0, 0],\n[0, 0, 1, 0],\n[0, 1, 0, 0],\n[0, 0, 0, 0],\n[7, 7, 7, 0],\n[7, 7, 7, 7],\n[7, 7, 7, 0],\n[0, 7, 0, 7],\n[5, 9, 9, 9],\n[9, 5, 9, 9],\n[9, 9, 5, 9],\n[9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 4, 6],\n[4, 6, 4, 6],\n[4, 4, 6, 4],\n[4, 4, 6, 4]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[0, 9, 8, 0, 5, 6, 5, 5, 9, 4, 4, 9],\n[8, 8, 0, 9, 6, 2, 5, 2, 4, 1, 2, 1],\n[8, 0, 5, 2, 5, 5, 9, 2, 4, 2, 9, 2],\n[0, 2, 9, 9, 5, 2, 2, 2, 9, 1, 2, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 9, 8, 0],\n[8, 8, 0, 9],\n[8, 0, 5, 2],\n[0, 2, 9, 9]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 5, 6, 7, 7, 1, 5, 7, 5, 8, 7, 5, 5, 1, 1, 7, 5, 1],\n[5, 5, 7, 5, 1, 5, 6, 8, 1, 1, 1, 1, 1, 5, 3, 1, 9, 5],\n[6, 7, 7, 4, 1, 6, 5, 1, 5, 6, 8, 6, 1, 3, 9, 7, 7, 7],\n[7, 5, 4, 1, 1, 4, 8, 1, 6, 7, 1, 5, 7, 1, 7, 5, 3, 9],\n[7, 1, 1, 1, 7, 5, 1, 8, 1, 1, 8, 6, 5, 9, 7, 3, 7, 3],\n[1, 5, 6, 4, 5, 6, 5, 5, 7, 8, 8, 6, 1, 5, 7, 9, 3, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[2, 2, 2, 0, 7, 3, 9, 5, 9, 5, 7, 1, 6, 1, 3, 2, 1, 4, 3, 2, 2, 0, 4, 0, 6, 7, 2, 2, 7, 9], [2, 0, 2, 0, 6, 9, 1, 6, 9, 5, 1, 5, 6, 3, 5, 3, 7, 2, 4, 6, 0, 1, 2, 2, 2, 2, 7, 4, 1, 4], [2, 2, 6, 9, 7, 5, 6, 9, 1, 1, 6, 6, 8, 1, 8, 1, 4, 6, 7, 1, 4, 2, 5, 1, 3, 2, 4, 3, 4, 7], [0, 0, 9, 8, 5, 9, 9, 1, 1, 9, 1, 3, 1, 1, 5, 6, 2, 7, 2, 2, 0, 2, 1, 3, 0, 7, 1, 4, 9, 1], [7, 6, 7, 5, 2, 5, 5, 1, 9, 7, 3, 5, 8, 5, 7, 2, 6, 7, 2, 4, 6, 2, 3, 0, 0, 9, 4, 7, 1, 7]], "output": [[2, 1, 4, 3, 2], [3, 7, 2, 4, 6], [1, 4, 6, 7, 1], [6, 2, 7, 2, 2], [2, 6, 7, 2, 4]]}, {"input": [[4, 7, 4, 4], [7, 7, 7, 7], [4, 7, 4, 4], [4, 7, 4, 7], [1, 1, 1, 6], [1, 1, 1, 1], [1, 1, 1, 6], [6, 1, 6, 6], [3, 5, 5, 5], [5, 5, 3, 5], [5, 3, 3, 5], [5, 5, 5, 5], [6, 6, 4, 6], [4, 6, 4, 6], [4, 4, 6, 4], [4, 4, 6, 4], [1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0], [7, 7, 7, 0], [7, 7, 7, 7], [7, 7, 7, 0], [0, 7, 0, 7], [5, 9, 9, 9], [9, 5, 9, 9], [9, 9, 5, 9], [9, 9, 9, 9]], "output": [[6, 6, 4, 6], [4, 6, 4, 6], [4, 4, 6, 4], [4, 4, 6, 4]]}, {"input": [[0, 9, 8, 0, 5, 6, 5, 5, 9, 4, 4, 9], [8, 8, 0, 9, 6, 2, 5, 2, 4, 1, 2, 1], [8, 0, 5, 2, 5, 5, 9, 2, 4, 2, 9, 2], [0, 2, 9, 9, 5, 2, 2, 2, 9, 1, 2, 4]], "output": [[0, 9, 8, 0], [8, 8, 0, 9], [8, 0, 5, 2], [0, 2, 9, 9]]}], "input_grid": [[7, 5, 6, 7, 7, 1, 5, 7, 5, 8, 7, 5, 5, 1, 1, 7, 5, 1], [5, 5, 7, 5, 1, 5, 6, 8, 1, 1, 1, 1, 1, 5, 3, 1, 9, 5], [6, 7, 7, 4, 1, 6, 5, 1, 5, 6, 8, 6, 1, 3, 9, 7, 7, 7], [7, 5, 4, 1, 1, 4, 8, 1, 6, 7, 1, 5, 7, 1, 7, 5, 3, 9], [7, 1, 1, 1, 7, 5, 1, 8, 1, 1, 8, 6, 5, 9, 7, 3, 7, 3], [1, 5, 6, 4, 5, 6, 5, 5, 7, 8, 8, 6, 1, 5, 7, 9, 3, 1]], "task_key": "662c240a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 6, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 6, 3, 3],\n[3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 6, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6],\n[3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3],\n[3, 3, 3, 3, 3, 6, 6, 3, 3, 3, 6, 3, 3, 6, 3, 6, 6, 3, 3, 3, 3, 3, 6, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 6, 3, 3, 6, 6, 6, 3, 3, 3, 3, 3],\n[6, 6, 3, 3, 6, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[3, 3, 3, 5, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 6, 6, 5, 3, 3, 6, 5, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 6, 3, 3],\n[3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 6, 5],\n[3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6],\n[3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3],\n[3, 3, 3, 3, 3, 6, 6, 3, 3, 3, 6, 3, 3, 6, 3, 6, 6, 3, 3, 3, 3, 3, 6, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 6, 3, 3, 6, 6, 6, 5, 3, 3, 3, 3],\n[6, 6, 3, 3, 6, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 2, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 2, 2, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[7, 3, 3, 7, 3, 3, 3, 3, 3, 3],\n[3, 7, 7, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[7, 3, 7, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 2, 3, 3, 3, 3, 3, 3, 3, 3],\n[7, 3, 3, 7, 3, 3, 3, 3, 3, 3],\n[3, 7, 7, 3, 3, 2, 2, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[7, 3, 7, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5],\n[4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4],\n[5, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 5, 5, 5, 4],\n[5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5],\n[5, 4, 4, 5, 5, 5, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 4, 5, 4, 4, 5, 5, 5],\n[5, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5],\n[5, 5, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 4, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5],\n[4, 5, 6, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 5, 6, 4],\n[5, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 5, 5, 5, 4],\n[5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5],\n[5, 4, 4, 5, 5, 5, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 4, 5, 4, 4, 5, 5, 5],\n[5, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5],\n[5, 5, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 6, 4, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 4, 4, 4, 4, 6, 4, 1, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 1, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 5, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 5, 4, 4, 5, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 5, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[5, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 5, 4, 4, 6, 4, 4, 4, 4, 1],\n[4, 4, 4, 4, 4, 6, 4, 4, 1, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 1, 1, 4, 4],\n[4, 4, 4, 5, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 5, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 6, 4, 4, 1, 1, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 6, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 6, 3, 3], [3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 6, 3], [3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6], [3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3], [3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3], [3, 3, 3, 3, 3, 6, 6, 3, 3, 3, 6, 3, 3, 6, 3, 6, 6, 3, 3, 3, 3, 3, 6, 3, 3], [3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 6, 3, 3, 6, 6, 6, 3, 3, 3, 3, 3], [6, 6, 3, 3, 6, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 5, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 6, 6, 5, 3, 3, 6, 5, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 6, 3, 3], [3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 6, 5], [3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6], [3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3], [3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3], [3, 3, 3, 3, 3, 6, 6, 3, 3, 3, 6, 3, 3, 6, 3, 6, 6, 3, 3, 3, 3, 3, 6, 3, 3], [3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 6, 3, 3, 6, 6, 6, 5, 3, 3, 3, 3], [6, 6, 3, 3, 6, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 6, 3, 3, 3, 6, 3, 3, 3, 3]]}, {"input": [[3, 2, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 2, 2, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [7, 3, 3, 7, 3, 3, 3, 3, 3, 3], [3, 7, 7, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [7, 3, 7, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 2, 3, 3, 3, 3, 3, 3, 3, 3], [7, 3, 3, 7, 3, 3, 3, 3, 3, 3], [3, 7, 7, 3, 3, 2, 2, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [7, 3, 7, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5], [4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4], [5, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 5, 5, 5, 4], [5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5], [5, 4, 4, 5, 5, 5, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 4, 5, 4, 4, 5, 5, 5], [5, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5], [5, 5, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 4, 5]], "output": [[5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5], [4, 5, 6, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 5, 6, 4], [5, 5, 5, 4, 5, 4, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 4, 5, 5, 5, 4], [5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5], [5, 4, 4, 5, 5, 5, 5, 4, 5, 4, 4, 4, 5, 5, 5, 4, 4, 5, 4, 4, 5, 5, 5], [5, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 5, 5], [5, 5, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 6, 4, 5]]}], "input_grid": [[5, 4, 4, 4, 4, 6, 4, 1, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 1, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 5, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 5, 4, 4, 5, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 5, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [5, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 5, 4, 4, 6, 4, 4, 4, 4, 1], [4, 4, 4, 4, 4, 6, 4, 4, 1, 4, 4], [4, 4, 4, 4, 4, 6, 4, 1, 1, 4, 4], [4, 4, 4, 5, 4, 6, 4, 4, 4, 4, 4], [4, 4, 5, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 6, 4, 4, 1, 1, 4]], "task_key": "e98196ab"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 3, 4, 4, 4, 4, 2, 4, 4],\n[4, 4, 4, 4, 4, 4, 3, 4, 2, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[0, 0, 3, 6, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0],\n[0, 0, 3, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[3, 3, 3, 3, 3, 3, 3],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0],\n[0, 3, 0, 0, 0, 0, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[6, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 6, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 2, 1, 1],\n[1, 2, 1, 1],\n[1, 2, 3, 1],\n[1, 2, 1, 1],\n[2, 2, 2, 2],\n[1, 2, 1, 1],\n[1, 2, 1, 1],\n[1, 2, 1, 1],\n[1, 2, 1, 1],\n[1, 2, 1, 1],\n[1, 2, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 3, 4, 4, 4, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 3, 4, 2, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2]]}, {"input": [[0, 0, 3, 6, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0]], "output": [[0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0]]}, {"input": [[4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [6, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 6, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4]]}], "input_grid": [[1, 2, 1, 1], [1, 2, 1, 1], [1, 2, 3, 1], [1, 2, 1, 1], [2, 2, 2, 2], [1, 2, 1, 1], [1, 2, 1, 1], [1, 2, 1, 1], [1, 2, 1, 1], [1, 2, 1, 1], [1, 2, 1, 1]], "task_key": "e48d4e1a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 1],\n[1, 1, 4],\n[7, 1, 9],\n[1, 0, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 1, 1, 1, 1, 9, 9, 1],\n[1, 1, 7, 1, 1, 1, 1, 1, 9],\n[1, 1, 1, 0, 0, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 0, 1, 1, 1]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 2, 0],\n[3, 7, 3],\n[3, 3, 8],\n[3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 2, 3, 3, 0],\n[3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 7, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 2, 8],\n[8, 8, 8],\n[8, 8, 8],\n[2, 2, 2],\n[2, 5, 2],\n[2, 2, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 5, 2, 5, 2, 2, 2],\n[2, 2, 2, 5, 5, 5, 2, 2, 2],\n[2, 2, 2, 5, 5, 5, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 4, 2, 4],\n[2, 2, 2, 2, 2, 2, 4, 4, 4],\n[2, 2, 2, 2, 2, 2, 4, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[4, 4, 0, 4, 4, 3, 5, 6, 9, 4],\n[4, 4, 4, 0, 4, 9, 4, 7, 6, 4],\n[4, 4, 4, 4, 4, 1, 3, 5, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 1], [1, 1, 4], [7, 1, 9], [1, 0, 1]], "output": [[7, 7, 1, 1, 1, 1, 9, 9, 1], [1, 1, 7, 1, 1, 1, 1, 1, 9], [1, 1, 1, 0, 0, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 1, 1, 1]]}, {"input": [[3, 2, 0], [3, 7, 3], [3, 3, 8], [3, 3, 3]], "output": [[3, 3, 3, 3, 3, 2, 3, 3, 0], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 7, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3]]}, {"input": [[8, 2, 8], [8, 8, 8], [8, 8, 8], [2, 2, 2], [2, 5, 2], [2, 2, 4]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 5, 2, 5, 2, 2, 2], [2, 2, 2, 5, 5, 5, 2, 2, 2], [2, 2, 2, 5, 5, 5, 2, 2, 2], [2, 2, 2, 2, 2, 2, 4, 2, 4], [2, 2, 2, 2, 2, 2, 4, 4, 4], [2, 2, 2, 2, 2, 2, 4, 4, 4]]}], "input_grid": [[4, 4, 0, 4, 4, 3, 5, 6, 9, 4], [4, 4, 4, 0, 4, 9, 4, 7, 6, 4], [4, 4, 4, 4, 4, 1, 3, 5, 4, 4]], "task_key": "b190f7f5"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 0, 0, 0, 7, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 7, 0, 0, 7, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4],\n[0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 0, 0, 0, 0, 4],\n[0, 0, 0, 0, 7, 0, 0, 7, 0, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 7],\n[7, 0, 0, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 0, 0, 7]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 6, 6, 6, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 6, 6, 6, 6, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6],\n[2, 6, 6, 6, 2],\n[6, 6, 6, 6, 6],\n[2, 6, 6, 6, 6]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 8, 4, 8, 8, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 4, 4],\n[8, 4, 8, 8, 4, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 9, 9, 4, 8, 8, 8, 8, 8, 8, 8],\n[8, 9, 9, 4, 4, 4, 8, 8, 8, 8, 8, 8],\n[8, 8, 9, 4, 4, 4, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8],\n[8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 7, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 7, 0, 0, 7, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4], [0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 0, 0, 0, 0, 4], [0, 0, 0, 0, 7, 7, 7, 7, 4, 4, 0, 0, 0, 0, 4], [0, 0, 0, 0, 7, 0, 0, 7, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 7], [7, 0, 0, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 0, 0, 7]]}, {"input": [[2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 6, 6, 6, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 6, 6, 6, 6, 6, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 6, 6, 6, 6, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[6, 6, 6, 6, 6], [2, 6, 6, 6, 2], [6, 6, 6, 6, 6], [2, 6, 6, 6, 6]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 8, 4, 8, 8, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 4, 4], [8, 4, 8, 8, 4, 4]]}], "input_grid": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 9, 9, 9, 4, 8, 8, 8, 8, 8, 8, 8], [8, 9, 9, 4, 4, 4, 8, 8, 8, 8, 8, 8], [8, 8, 9, 4, 4, 4, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8]], "task_key": "ce602527"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[9, 5, 3, 9, 5, 3, 9, 5, 5, 8, 3, 8, 1, 8, 9, 3, 3, 8, 1, 8, 1, 1, 9, 1, 8, 5, 9],\n[5, 3, 5, 3, 3, 5, 1, 5, 8, 1, 8, 5, 3, 1, 9, 9, 9, 9, 1, 3, 8, 5, 9, 9, 5, 9, 9],\n[1, 8, 8, 3, 5, 3, 8, 3, 5, 3, 8, 8, 8, 5, 8, 1, 1, 5, 3, 5, 8, 3, 1, 5, 8, 8, 9],\n[8, 3, 9, 8, 5, 1, 5, 3, 3, 9, 8, 8, 3, 3, 1, 3, 8, 3, 8, 3, 1, 3, 9, 3, 9, 9, 3],\n[8, 3, 5, 1, 3, 3, 9, 5, 5, 1, 9, 9, 8, 3, 3, 9, 3, 3, 1, 1, 5, 5, 1, 1, 1, 1, 9],\n[5, 9, 1, 9, 9, 8, 8, 8, 8, 8, 5, 3, 3, 5, 9, 1, 5, 5, 1, 5, 8, 8, 1, 5, 8, 1, 9],\n[5, 5, 8, 8, 3, 3, 1, 9, 3, 5, 1, 5, 3, 5, 5, 9, 1, 9, 1, 9, 8, 1, 8, 3, 1, 9, 5],\n[5, 1, 8, 5, 8, 1, 8, 3, 8, 3, 3, 5, 5, 9, 8, 5, 3, 3, 3, 9, 3, 3, 1, 3, 3, 8, 1],\n[1, 8, 3, 5, 8, 5, 1, 9, 5, 5, 3, 1, 5, 8, 9, 9, 5, 1, 5, 3, 8, 5, 3, 8, 5, 5, 5],\n[1, 3, 8, 8, 9, 9, 8, 9, 8, 5, 9, 3, 9, 3, 9, 8, 1, 5, 3, 3, 1, 1, 8, 1, 3, 9, 8],\n[5, 1, 1, 5, 5, 3, 5, 1, 3, 9, 9, 3, 9, 5, 9, 1, 5, 3, 5, 1, 1, 1, 5, 3, 1, 3, 1],\n[3, 8, 5, 1, 5, 8, 9, 5, 5, 8, 8, 9, 1, 5, 1, 5, 5, 9, 8, 9, 3, 1, 5, 8, 3, 1, 8],\n[9, 1, 9, 1, 5, 9, 9, 1, 9, 3, 3, 8, 3, 1, 1, 3, 1, 8, 5, 1, 3, 3, 5, 3, 5, 9, 5],\n[9, 5, 1, 3, 8, 5, 3, 9, 5, 5, 3, 3, 3, 6, 3, 3, 5, 1, 9, 5, 1, 8, 9, 1, 3, 8, 3],\n[5, 1, 9, 9, 1, 1, 5, 3, 8, 3, 8, 8, 9, 3, 8, 3, 1, 5, 8, 9, 8, 1, 5, 3, 3, 9, 1],\n[1, 3, 8, 9, 3, 5, 3, 5, 3, 5, 3, 8, 1, 5, 1, 8, 3, 8, 8, 3, 8, 9, 8, 3, 9, 1, 1],\n[9, 3, 9, 9, 1, 3, 5, 3, 8, 5, 1, 1, 5, 3, 5, 1, 8, 8, 8, 8, 8, 3, 1, 8, 8, 3, 3],\n[1, 1, 9, 5, 8, 5, 5, 8, 5, 8, 9, 1, 3, 9, 1, 5, 3, 5, 5, 3, 1, 8, 1, 5, 1, 9, 3],\n[5, 3, 8, 9, 9, 1, 3, 8, 1, 5, 1, 9, 8, 1, 8, 9, 1, 3, 1, 9, 1, 3, 1, 1, 9, 1, 5],\n[5, 1, 9, 8, 3, 5, 3, 9, 9, 5, 5, 1, 3, 1, 3, 1, 5, 1, 3, 8, 3, 9, 1, 5, 9, 1, 5],\n[5, 3, 8, 5, 3, 1, 3, 1, 3, 5, 9, 9, 8, 5, 9, 1, 1, 8, 1, 1, 1, 1, 9, 1, 9, 9, 5],\n[8, 1, 9, 9, 1, 3, 1, 1, 5, 9, 9, 8, 5, 5, 3, 9, 3, 8, 9, 9, 1, 5, 9, 3, 1, 5, 8],\n[9, 8, 8, 1, 9, 9, 9, 9, 8, 3, 5, 9, 8, 3, 5, 1, 9, 5, 3, 1, 5, 8, 5, 8, 9, 1, 3],\n[9, 8, 3, 1, 8, 1, 8, 8, 8, 9, 5, 3, 8, 5, 5, 3, 5, 3, 9, 8, 5, 5, 9, 1, 8, 1, 8],\n[5, 8, 9, 5, 8, 8, 8, 1, 1, 3, 3, 8, 3, 8, 9, 8, 5, 1, 9, 8, 9, 5, 5, 9, 1, 1, 9],\n[1, 5, 8, 1, 1, 1, 9, 9, 9, 5, 9, 5, 5, 8, 5, 8, 9, 9, 1, 1, 9, 8, 8, 9, 1, 9, 8],\n[1, 1, 1, 3, 9, 8, 8, 5, 5, 3, 9, 8, 5, 1, 1, 3, 1, 3, 5, 3, 8, 9, 5, 8, 5, 5, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 5, 3, 9, 5, 3, 9, 5, 5, 8, 3, 8, 1, 8, 9, 3, 3, 8, 1, 8, 1, 1, 9, 1, 8, 5, 6],\n[5, 6, 5, 3, 3, 5, 1, 5, 8, 1, 8, 5, 3, 1, 9, 9, 9, 9, 1, 3, 8, 5, 9, 9, 5, 6, 9],\n[1, 8, 6, 3, 5, 3, 8, 3, 5, 3, 8, 8, 8, 5, 8, 1, 1, 5, 3, 5, 8, 3, 1, 5, 6, 8, 9],\n[8, 3, 9, 6, 5, 1, 5, 3, 3, 9, 8, 8, 3, 3, 1, 3, 8, 3, 8, 3, 1, 3, 9, 6, 9, 9, 3],\n[8, 3, 5, 1, 6, 3, 9, 5, 5, 1, 9, 9, 8, 3, 3, 9, 3, 3, 1, 1, 5, 5, 6, 1, 1, 1, 9],\n[5, 9, 1, 9, 9, 6, 8, 8, 8, 8, 5, 3, 3, 5, 9, 1, 5, 5, 1, 5, 8, 6, 1, 5, 8, 1, 9],\n[5, 5, 8, 8, 3, 3, 6, 9, 3, 5, 1, 5, 3, 5, 5, 9, 1, 9, 1, 9, 6, 1, 8, 3, 1, 9, 5],\n[5, 1, 8, 5, 8, 1, 8, 6, 8, 3, 3, 5, 5, 9, 8, 5, 3, 3, 3, 6, 3, 3, 1, 3, 3, 8, 1],\n[1, 8, 3, 5, 8, 5, 1, 9, 6, 5, 3, 1, 5, 8, 9, 9, 5, 1, 6, 3, 8, 5, 3, 8, 5, 5, 5],\n[1, 3, 8, 8, 9, 9, 8, 9, 8, 6, 9, 3, 9, 3, 9, 8, 1, 6, 3, 3, 1, 1, 8, 1, 3, 9, 8],\n[5, 1, 1, 5, 5, 3, 5, 1, 3, 9, 6, 3, 9, 5, 9, 1, 6, 3, 5, 1, 1, 1, 5, 3, 1, 3, 1],\n[3, 8, 5, 1, 5, 8, 9, 5, 5, 8, 8, 6, 1, 5, 1, 6, 5, 9, 8, 9, 3, 1, 5, 8, 3, 1, 8],\n[9, 1, 9, 1, 5, 9, 9, 1, 9, 3, 3, 8, 6, 1, 6, 3, 1, 8, 5, 1, 3, 3, 5, 3, 5, 9, 5],\n[9, 5, 1, 3, 8, 5, 3, 9, 5, 5, 3, 3, 3, 6, 3, 3, 5, 1, 9, 5, 1, 8, 9, 1, 3, 8, 3],\n[5, 1, 9, 9, 1, 1, 5, 3, 8, 3, 8, 8, 6, 3, 6, 3, 1, 5, 8, 9, 8, 1, 5, 3, 3, 9, 1],\n[1, 3, 8, 9, 3, 5, 3, 5, 3, 5, 3, 6, 1, 5, 1, 6, 3, 8, 8, 3, 8, 9, 8, 3, 9, 1, 1],\n[9, 3, 9, 9, 1, 3, 5, 3, 8, 5, 6, 1, 5, 3, 5, 1, 6, 8, 8, 8, 8, 3, 1, 8, 8, 3, 3],\n[1, 1, 9, 5, 8, 5, 5, 8, 5, 6, 9, 1, 3, 9, 1, 5, 3, 6, 5, 3, 1, 8, 1, 5, 1, 9, 3],\n[5, 3, 8, 9, 9, 1, 3, 8, 6, 5, 1, 9, 8, 1, 8, 9, 1, 3, 6, 9, 1, 3, 1, 1, 9, 1, 5],\n[5, 1, 9, 8, 3, 5, 3, 6, 9, 5, 5, 1, 3, 1, 3, 1, 5, 1, 3, 6, 3, 9, 1, 5, 9, 1, 5],\n[5, 3, 8, 5, 3, 1, 6, 1, 3, 5, 9, 9, 8, 5, 9, 1, 1, 8, 1, 1, 6, 1, 9, 1, 9, 9, 5],\n[8, 1, 9, 9, 1, 6, 1, 1, 5, 9, 9, 8, 5, 5, 3, 9, 3, 8, 9, 9, 1, 6, 9, 3, 1, 5, 8],\n[9, 8, 8, 1, 6, 9, 9, 9, 8, 3, 5, 9, 8, 3, 5, 1, 9, 5, 3, 1, 5, 8, 6, 8, 9, 1, 3],\n[9, 8, 3, 6, 8, 1, 8, 8, 8, 9, 5, 3, 8, 5, 5, 3, 5, 3, 9, 8, 5, 5, 9, 6, 8, 1, 8],\n[5, 8, 6, 5, 8, 8, 8, 1, 1, 3, 3, 8, 3, 8, 9, 8, 5, 1, 9, 8, 9, 5, 5, 9, 6, 1, 9],\n[1, 6, 8, 1, 1, 1, 9, 9, 9, 5, 9, 5, 5, 8, 5, 8, 9, 9, 1, 1, 9, 8, 8, 9, 1, 6, 8],\n[6, 1, 1, 3, 9, 8, 8, 5, 5, 3, 9, 8, 5, 1, 1, 3, 1, 3, 5, 3, 8, 9, 5, 8, 5, 5, 6]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 1, 5, 0, 0, 5, 0, 5, 6, 5, 0, 1, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, 6],\n[1, 6, 6, 6, 6, 5, 6, 1, 5, 1, 6, 2, 5, 1, 2, 5, 1, 1, 0, 0, 0, 0, 6],\n[1, 2, 1, 1, 6, 2, 0, 6, 2, 0, 0, 1, 0, 0, 1, 6, 1, 6, 6, 6, 6, 2, 5],\n[6, 2, 2, 6, 0, 5, 1, 5, 5, 6, 5, 6, 0, 1, 5, 2, 1, 5, 5, 0, 5, 0, 2],\n[6, 1, 5, 5, 1, 0, 6, 5, 6, 2, 5, 5, 6, 0, 0, 1, 5, 5, 5, 1, 1, 1, 5],\n[2, 6, 2, 0, 0, 2, 6, 2, 5, 6, 6, 2, 0, 2, 1, 5, 0, 6, 5, 6, 5, 1, 5],\n[1, 6, 6, 5, 2, 6, 6, 5, 2, 2, 0, 1, 6, 0, 2, 1, 2, 5, 2, 1, 1, 2, 0],\n[5, 6, 5, 0, 5, 2, 0, 1, 5, 5, 1, 6, 6, 2, 6, 5, 5, 2, 0, 5, 6, 5, 6],\n[2, 6, 1, 1, 0, 0, 5, 6, 6, 2, 2, 5, 2, 6, 5, 0, 0, 0, 2, 0, 2, 1, 2],\n[2, 6, 1, 5, 2, 1, 0, 1, 5, 6, 2, 5, 5, 5, 2, 0, 1, 2, 5, 2, 1, 5, 2],\n[0, 0, 0, 1, 1, 2, 6, 5, 6, 1, 6, 2, 0, 0, 0, 1, 5, 2, 1, 5, 5, 5, 6],\n[1, 0, 6, 0, 1, 2, 6, 0, 1, 2, 5, 5, 1, 6, 0, 2, 2, 5, 5, 2, 2, 6, 0],\n[0, 6, 0, 2, 2, 0, 0, 5, 2, 5, 1, 8, 5, 2, 1, 6, 2, 2, 5, 1, 0, 0, 2],\n[0, 5, 1, 6, 2, 2, 0, 2, 6, 2, 2, 0, 6, 6, 5, 6, 1, 5, 6, 0, 5, 2, 5],\n[6, 5, 0, 0, 6, 5, 5, 1, 1, 0, 5, 5, 2, 0, 5, 5, 6, 0, 2, 1, 5, 6, 1],\n[1, 2, 6, 1, 2, 1, 2, 6, 6, 2, 1, 0, 2, 6, 1, 0, 0, 5, 6, 1, 5, 1, 0],\n[6, 5, 6, 1, 1, 6, 5, 1, 2, 2, 0, 5, 5, 6, 6, 6, 0, 6, 5, 5, 5, 2, 5],\n[0, 1, 0, 1, 5, 6, 1, 6, 0, 6, 0, 6, 0, 5, 5, 1, 1, 0, 0, 5, 2, 0, 6],\n[5, 2, 1, 1, 6, 1, 6, 2, 1, 6, 2, 2, 6, 6, 1, 6, 0, 6, 2, 6, 2, 0, 2],\n[5, 5, 2, 6, 0, 0, 1, 2, 5, 0, 6, 2, 6, 6, 2, 6, 6, 0, 1, 0, 2, 5, 0],\n[2, 2, 5, 6, 5, 0, 0, 5, 6, 0, 0, 0, 1, 6, 5, 6, 1, 2, 0, 0, 1, 5, 6],\n[1, 6, 5, 5, 2, 5, 0, 1, 5, 5, 2, 5, 6, 1, 0, 0, 5, 1, 6, 2, 5, 0, 1],\n[5, 1, 5, 1, 0, 1, 6, 5, 1, 6, 5, 2, 0, 0, 1, 6, 0, 6, 1, 2, 2, 5, 0],\n[0, 6, 6, 1, 0, 2, 2, 6, 0, 1, 1, 2, 6, 0, 2, 2, 6, 0, 5, 5, 1, 1, 2],\n[1, 6, 5, 6, 6, 5, 5, 5, 2, 0, 2, 0, 0, 1, 5, 6, 0, 0, 2, 2, 1, 5, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 1, 5, 0, 0, 5, 0, 5, 6, 5, 0, 1, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, 6],\n[8, 6, 6, 6, 6, 5, 6, 1, 5, 1, 6, 2, 5, 1, 2, 5, 1, 1, 0, 0, 0, 0, 8],\n[1, 8, 1, 1, 6, 2, 0, 6, 2, 0, 0, 1, 0, 0, 1, 6, 1, 6, 6, 6, 6, 8, 5],\n[6, 2, 8, 6, 0, 5, 1, 5, 5, 6, 5, 6, 0, 1, 5, 2, 1, 5, 5, 0, 8, 0, 2],\n[6, 1, 5, 8, 1, 0, 6, 5, 6, 2, 5, 5, 6, 0, 0, 1, 5, 5, 5, 8, 1, 1, 5],\n[2, 6, 2, 0, 8, 2, 6, 2, 5, 6, 6, 2, 0, 2, 1, 5, 0, 6, 8, 6, 5, 1, 5],\n[1, 6, 6, 5, 2, 8, 6, 5, 2, 2, 0, 1, 6, 0, 2, 1, 2, 8, 2, 1, 1, 2, 0],\n[5, 6, 5, 0, 5, 2, 8, 1, 5, 5, 1, 6, 6, 2, 6, 5, 8, 2, 0, 5, 6, 5, 6],\n[2, 6, 1, 1, 0, 0, 5, 8, 6, 2, 2, 5, 2, 6, 5, 8, 0, 0, 2, 0, 2, 1, 2],\n[2, 6, 1, 5, 2, 1, 0, 1, 8, 6, 2, 5, 5, 5, 8, 0, 1, 2, 5, 2, 1, 5, 2],\n[0, 0, 0, 1, 1, 2, 6, 5, 6, 8, 6, 2, 0, 8, 0, 1, 5, 2, 1, 5, 5, 5, 6],\n[1, 0, 6, 0, 1, 2, 6, 0, 1, 2, 8, 5, 8, 6, 0, 2, 2, 5, 5, 2, 2, 6, 0],\n[0, 6, 0, 2, 2, 0, 0, 5, 2, 5, 1, 8, 5, 2, 1, 6, 2, 2, 5, 1, 0, 0, 2],\n[0, 5, 1, 6, 2, 2, 0, 2, 6, 2, 8, 0, 8, 6, 5, 6, 1, 5, 6, 0, 5, 2, 5],\n[6, 5, 0, 0, 6, 5, 5, 1, 1, 8, 5, 5, 2, 8, 5, 5, 6, 0, 2, 1, 5, 6, 1],\n[1, 2, 6, 1, 2, 1, 2, 6, 8, 2, 1, 0, 2, 6, 8, 0, 0, 5, 6, 1, 5, 1, 0],\n[6, 5, 6, 1, 1, 6, 5, 8, 2, 2, 0, 5, 5, 6, 6, 8, 0, 6, 5, 5, 5, 2, 5],\n[0, 1, 0, 1, 5, 6, 8, 6, 0, 6, 0, 6, 0, 5, 5, 1, 8, 0, 0, 5, 2, 0, 6],\n[5, 2, 1, 1, 6, 8, 6, 2, 1, 6, 2, 2, 6, 6, 1, 6, 0, 8, 2, 6, 2, 0, 2],\n[5, 5, 2, 6, 8, 0, 1, 2, 5, 0, 6, 2, 6, 6, 2, 6, 6, 0, 8, 0, 2, 5, 0],\n[2, 2, 5, 8, 5, 0, 0, 5, 6, 0, 0, 0, 1, 6, 5, 6, 1, 2, 0, 8, 1, 5, 6],\n[1, 6, 8, 5, 2, 5, 0, 1, 5, 5, 2, 5, 6, 1, 0, 0, 5, 1, 6, 2, 8, 0, 1],\n[5, 8, 5, 1, 0, 1, 6, 5, 1, 6, 5, 2, 0, 0, 1, 6, 0, 6, 1, 2, 2, 8, 0],\n[8, 6, 6, 1, 0, 2, 2, 6, 0, 1, 1, 2, 6, 0, 2, 2, 6, 0, 5, 5, 1, 1, 8],\n[1, 6, 5, 6, 6, 5, 5, 5, 2, 0, 2, 0, 0, 1, 5, 6, 0, 0, 2, 2, 1, 5, 1]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 5, 6, 1, 6, 6, 6, 6, 1, 5, 1, 5, 6],\n[1, 1, 6, 5, 1, 5, 1, 6, 5, 1, 5, 6, 1],\n[5, 5, 1, 6, 5, 5, 5, 5, 1, 1, 5, 6, 1],\n[5, 1, 6, 1, 5, 6, 4, 5, 5, 6, 6, 6, 1],\n[6, 6, 1, 5, 6, 5, 1, 6, 5, 1, 6, 6, 5],\n[6, 5, 1, 6, 5, 1, 5, 6, 5, 5, 5, 1, 6],\n[6, 6, 5, 6, 1, 1, 6, 6, 1, 5, 6, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 5, 6, 4, 6, 6, 6, 6, 1, 4, 1, 5, 6],\n[1, 1, 6, 5, 4, 5, 1, 6, 4, 1, 5, 6, 1],\n[5, 5, 1, 6, 5, 4, 5, 4, 1, 1, 5, 6, 1],\n[5, 1, 6, 1, 5, 6, 4, 5, 5, 6, 6, 6, 1],\n[6, 6, 1, 5, 6, 4, 1, 4, 5, 1, 6, 6, 5],\n[6, 5, 1, 6, 4, 1, 5, 6, 4, 5, 5, 1, 6],\n[6, 6, 5, 4, 1, 1, 6, 6, 1, 4, 6, 5, 5]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[9, 0, 2, 9, 2, 9, 9, 0, 2, 0, 0, 2, 0, 2, 2, 9, 9, 2, 2, 0, 0, 9, 0],\n[2, 2, 9, 2, 2, 0, 2, 0, 0, 9, 9, 0, 0, 0, 9, 0, 0, 0, 2, 0, 9, 9, 0],\n[2, 2, 9, 2, 9, 0, 0, 0, 0, 2, 2, 9, 9, 2, 0, 2, 2, 9, 2, 2, 9, 9, 9],\n[2, 0, 9, 2, 0, 0, 0, 0, 9, 9, 9, 2, 9, 0, 0, 9, 9, 2, 2, 0, 0, 0, 0],\n[2, 2, 2, 0, 0, 0, 2, 0, 2, 9, 0, 9, 2, 2, 0, 2, 9, 0, 9, 2, 9, 9, 0],\n[9, 9, 0, 2, 0, 9, 0, 2, 2, 9, 9, 3, 2, 9, 0, 0, 2, 2, 0, 2, 0, 0, 2],\n[2, 2, 2, 2, 2, 9, 2, 2, 2, 2, 9, 2, 9, 2, 2, 0, 0, 9, 0, 0, 2, 9, 9],\n[0, 2, 9, 2, 2, 0, 2, 9, 9, 0, 9, 0, 2, 2, 2, 2, 9, 9, 9, 0, 0, 0, 0],\n[9, 2, 2, 2, 0, 2, 0, 9, 9, 2, 2, 0, 9, 2, 9, 2, 9, 9, 2, 0, 9, 9, 9],\n[9, 9, 2, 2, 2, 9, 2, 9, 9, 9, 0, 2, 9, 0, 0, 2, 9, 2, 9, 2, 2, 0, 0],\n[0, 9, 2, 0, 2, 2, 9, 9, 0, 9, 0, 2, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 9]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[9, 5, 3, 9, 5, 3, 9, 5, 5, 8, 3, 8, 1, 8, 9, 3, 3, 8, 1, 8, 1, 1, 9, 1, 8, 5, 9], [5, 3, 5, 3, 3, 5, 1, 5, 8, 1, 8, 5, 3, 1, 9, 9, 9, 9, 1, 3, 8, 5, 9, 9, 5, 9, 9], [1, 8, 8, 3, 5, 3, 8, 3, 5, 3, 8, 8, 8, 5, 8, 1, 1, 5, 3, 5, 8, 3, 1, 5, 8, 8, 9], [8, 3, 9, 8, 5, 1, 5, 3, 3, 9, 8, 8, 3, 3, 1, 3, 8, 3, 8, 3, 1, 3, 9, 3, 9, 9, 3], [8, 3, 5, 1, 3, 3, 9, 5, 5, 1, 9, 9, 8, 3, 3, 9, 3, 3, 1, 1, 5, 5, 1, 1, 1, 1, 9], [5, 9, 1, 9, 9, 8, 8, 8, 8, 8, 5, 3, 3, 5, 9, 1, 5, 5, 1, 5, 8, 8, 1, 5, 8, 1, 9], [5, 5, 8, 8, 3, 3, 1, 9, 3, 5, 1, 5, 3, 5, 5, 9, 1, 9, 1, 9, 8, 1, 8, 3, 1, 9, 5], [5, 1, 8, 5, 8, 1, 8, 3, 8, 3, 3, 5, 5, 9, 8, 5, 3, 3, 3, 9, 3, 3, 1, 3, 3, 8, 1], [1, 8, 3, 5, 8, 5, 1, 9, 5, 5, 3, 1, 5, 8, 9, 9, 5, 1, 5, 3, 8, 5, 3, 8, 5, 5, 5], [1, 3, 8, 8, 9, 9, 8, 9, 8, 5, 9, 3, 9, 3, 9, 8, 1, 5, 3, 3, 1, 1, 8, 1, 3, 9, 8], [5, 1, 1, 5, 5, 3, 5, 1, 3, 9, 9, 3, 9, 5, 9, 1, 5, 3, 5, 1, 1, 1, 5, 3, 1, 3, 1], [3, 8, 5, 1, 5, 8, 9, 5, 5, 8, 8, 9, 1, 5, 1, 5, 5, 9, 8, 9, 3, 1, 5, 8, 3, 1, 8], [9, 1, 9, 1, 5, 9, 9, 1, 9, 3, 3, 8, 3, 1, 1, 3, 1, 8, 5, 1, 3, 3, 5, 3, 5, 9, 5], [9, 5, 1, 3, 8, 5, 3, 9, 5, 5, 3, 3, 3, 6, 3, 3, 5, 1, 9, 5, 1, 8, 9, 1, 3, 8, 3], [5, 1, 9, 9, 1, 1, 5, 3, 8, 3, 8, 8, 9, 3, 8, 3, 1, 5, 8, 9, 8, 1, 5, 3, 3, 9, 1], [1, 3, 8, 9, 3, 5, 3, 5, 3, 5, 3, 8, 1, 5, 1, 8, 3, 8, 8, 3, 8, 9, 8, 3, 9, 1, 1], [9, 3, 9, 9, 1, 3, 5, 3, 8, 5, 1, 1, 5, 3, 5, 1, 8, 8, 8, 8, 8, 3, 1, 8, 8, 3, 3], [1, 1, 9, 5, 8, 5, 5, 8, 5, 8, 9, 1, 3, 9, 1, 5, 3, 5, 5, 3, 1, 8, 1, 5, 1, 9, 3], [5, 3, 8, 9, 9, 1, 3, 8, 1, 5, 1, 9, 8, 1, 8, 9, 1, 3, 1, 9, 1, 3, 1, 1, 9, 1, 5], [5, 1, 9, 8, 3, 5, 3, 9, 9, 5, 5, 1, 3, 1, 3, 1, 5, 1, 3, 8, 3, 9, 1, 5, 9, 1, 5], [5, 3, 8, 5, 3, 1, 3, 1, 3, 5, 9, 9, 8, 5, 9, 1, 1, 8, 1, 1, 1, 1, 9, 1, 9, 9, 5], [8, 1, 9, 9, 1, 3, 1, 1, 5, 9, 9, 8, 5, 5, 3, 9, 3, 8, 9, 9, 1, 5, 9, 3, 1, 5, 8], [9, 8, 8, 1, 9, 9, 9, 9, 8, 3, 5, 9, 8, 3, 5, 1, 9, 5, 3, 1, 5, 8, 5, 8, 9, 1, 3], [9, 8, 3, 1, 8, 1, 8, 8, 8, 9, 5, 3, 8, 5, 5, 3, 5, 3, 9, 8, 5, 5, 9, 1, 8, 1, 8], [5, 8, 9, 5, 8, 8, 8, 1, 1, 3, 3, 8, 3, 8, 9, 8, 5, 1, 9, 8, 9, 5, 5, 9, 1, 1, 9], [1, 5, 8, 1, 1, 1, 9, 9, 9, 5, 9, 5, 5, 8, 5, 8, 9, 9, 1, 1, 9, 8, 8, 9, 1, 9, 8], [1, 1, 1, 3, 9, 8, 8, 5, 5, 3, 9, 8, 5, 1, 1, 3, 1, 3, 5, 3, 8, 9, 5, 8, 5, 5, 8]], "output": [[6, 5, 3, 9, 5, 3, 9, 5, 5, 8, 3, 8, 1, 8, 9, 3, 3, 8, 1, 8, 1, 1, 9, 1, 8, 5, 6], [5, 6, 5, 3, 3, 5, 1, 5, 8, 1, 8, 5, 3, 1, 9, 9, 9, 9, 1, 3, 8, 5, 9, 9, 5, 6, 9], [1, 8, 6, 3, 5, 3, 8, 3, 5, 3, 8, 8, 8, 5, 8, 1, 1, 5, 3, 5, 8, 3, 1, 5, 6, 8, 9], [8, 3, 9, 6, 5, 1, 5, 3, 3, 9, 8, 8, 3, 3, 1, 3, 8, 3, 8, 3, 1, 3, 9, 6, 9, 9, 3], [8, 3, 5, 1, 6, 3, 9, 5, 5, 1, 9, 9, 8, 3, 3, 9, 3, 3, 1, 1, 5, 5, 6, 1, 1, 1, 9], [5, 9, 1, 9, 9, 6, 8, 8, 8, 8, 5, 3, 3, 5, 9, 1, 5, 5, 1, 5, 8, 6, 1, 5, 8, 1, 9], [5, 5, 8, 8, 3, 3, 6, 9, 3, 5, 1, 5, 3, 5, 5, 9, 1, 9, 1, 9, 6, 1, 8, 3, 1, 9, 5], [5, 1, 8, 5, 8, 1, 8, 6, 8, 3, 3, 5, 5, 9, 8, 5, 3, 3, 3, 6, 3, 3, 1, 3, 3, 8, 1], [1, 8, 3, 5, 8, 5, 1, 9, 6, 5, 3, 1, 5, 8, 9, 9, 5, 1, 6, 3, 8, 5, 3, 8, 5, 5, 5], [1, 3, 8, 8, 9, 9, 8, 9, 8, 6, 9, 3, 9, 3, 9, 8, 1, 6, 3, 3, 1, 1, 8, 1, 3, 9, 8], [5, 1, 1, 5, 5, 3, 5, 1, 3, 9, 6, 3, 9, 5, 9, 1, 6, 3, 5, 1, 1, 1, 5, 3, 1, 3, 1], [3, 8, 5, 1, 5, 8, 9, 5, 5, 8, 8, 6, 1, 5, 1, 6, 5, 9, 8, 9, 3, 1, 5, 8, 3, 1, 8], [9, 1, 9, 1, 5, 9, 9, 1, 9, 3, 3, 8, 6, 1, 6, 3, 1, 8, 5, 1, 3, 3, 5, 3, 5, 9, 5], [9, 5, 1, 3, 8, 5, 3, 9, 5, 5, 3, 3, 3, 6, 3, 3, 5, 1, 9, 5, 1, 8, 9, 1, 3, 8, 3], [5, 1, 9, 9, 1, 1, 5, 3, 8, 3, 8, 8, 6, 3, 6, 3, 1, 5, 8, 9, 8, 1, 5, 3, 3, 9, 1], [1, 3, 8, 9, 3, 5, 3, 5, 3, 5, 3, 6, 1, 5, 1, 6, 3, 8, 8, 3, 8, 9, 8, 3, 9, 1, 1], [9, 3, 9, 9, 1, 3, 5, 3, 8, 5, 6, 1, 5, 3, 5, 1, 6, 8, 8, 8, 8, 3, 1, 8, 8, 3, 3], [1, 1, 9, 5, 8, 5, 5, 8, 5, 6, 9, 1, 3, 9, 1, 5, 3, 6, 5, 3, 1, 8, 1, 5, 1, 9, 3], [5, 3, 8, 9, 9, 1, 3, 8, 6, 5, 1, 9, 8, 1, 8, 9, 1, 3, 6, 9, 1, 3, 1, 1, 9, 1, 5], [5, 1, 9, 8, 3, 5, 3, 6, 9, 5, 5, 1, 3, 1, 3, 1, 5, 1, 3, 6, 3, 9, 1, 5, 9, 1, 5], [5, 3, 8, 5, 3, 1, 6, 1, 3, 5, 9, 9, 8, 5, 9, 1, 1, 8, 1, 1, 6, 1, 9, 1, 9, 9, 5], [8, 1, 9, 9, 1, 6, 1, 1, 5, 9, 9, 8, 5, 5, 3, 9, 3, 8, 9, 9, 1, 6, 9, 3, 1, 5, 8], [9, 8, 8, 1, 6, 9, 9, 9, 8, 3, 5, 9, 8, 3, 5, 1, 9, 5, 3, 1, 5, 8, 6, 8, 9, 1, 3], [9, 8, 3, 6, 8, 1, 8, 8, 8, 9, 5, 3, 8, 5, 5, 3, 5, 3, 9, 8, 5, 5, 9, 6, 8, 1, 8], [5, 8, 6, 5, 8, 8, 8, 1, 1, 3, 3, 8, 3, 8, 9, 8, 5, 1, 9, 8, 9, 5, 5, 9, 6, 1, 9], [1, 6, 8, 1, 1, 1, 9, 9, 9, 5, 9, 5, 5, 8, 5, 8, 9, 9, 1, 1, 9, 8, 8, 9, 1, 6, 8], [6, 1, 1, 3, 9, 8, 8, 5, 5, 3, 9, 8, 5, 1, 1, 3, 1, 3, 5, 3, 8, 9, 5, 8, 5, 5, 6]]}, {"input": [[6, 1, 5, 0, 0, 5, 0, 5, 6, 5, 0, 1, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, 6], [1, 6, 6, 6, 6, 5, 6, 1, 5, 1, 6, 2, 5, 1, 2, 5, 1, 1, 0, 0, 0, 0, 6], [1, 2, 1, 1, 6, 2, 0, 6, 2, 0, 0, 1, 0, 0, 1, 6, 1, 6, 6, 6, 6, 2, 5], [6, 2, 2, 6, 0, 5, 1, 5, 5, 6, 5, 6, 0, 1, 5, 2, 1, 5, 5, 0, 5, 0, 2], [6, 1, 5, 5, 1, 0, 6, 5, 6, 2, 5, 5, 6, 0, 0, 1, 5, 5, 5, 1, 1, 1, 5], [2, 6, 2, 0, 0, 2, 6, 2, 5, 6, 6, 2, 0, 2, 1, 5, 0, 6, 5, 6, 5, 1, 5], [1, 6, 6, 5, 2, 6, 6, 5, 2, 2, 0, 1, 6, 0, 2, 1, 2, 5, 2, 1, 1, 2, 0], [5, 6, 5, 0, 5, 2, 0, 1, 5, 5, 1, 6, 6, 2, 6, 5, 5, 2, 0, 5, 6, 5, 6], [2, 6, 1, 1, 0, 0, 5, 6, 6, 2, 2, 5, 2, 6, 5, 0, 0, 0, 2, 0, 2, 1, 2], [2, 6, 1, 5, 2, 1, 0, 1, 5, 6, 2, 5, 5, 5, 2, 0, 1, 2, 5, 2, 1, 5, 2], [0, 0, 0, 1, 1, 2, 6, 5, 6, 1, 6, 2, 0, 0, 0, 1, 5, 2, 1, 5, 5, 5, 6], [1, 0, 6, 0, 1, 2, 6, 0, 1, 2, 5, 5, 1, 6, 0, 2, 2, 5, 5, 2, 2, 6, 0], [0, 6, 0, 2, 2, 0, 0, 5, 2, 5, 1, 8, 5, 2, 1, 6, 2, 2, 5, 1, 0, 0, 2], [0, 5, 1, 6, 2, 2, 0, 2, 6, 2, 2, 0, 6, 6, 5, 6, 1, 5, 6, 0, 5, 2, 5], [6, 5, 0, 0, 6, 5, 5, 1, 1, 0, 5, 5, 2, 0, 5, 5, 6, 0, 2, 1, 5, 6, 1], [1, 2, 6, 1, 2, 1, 2, 6, 6, 2, 1, 0, 2, 6, 1, 0, 0, 5, 6, 1, 5, 1, 0], [6, 5, 6, 1, 1, 6, 5, 1, 2, 2, 0, 5, 5, 6, 6, 6, 0, 6, 5, 5, 5, 2, 5], [0, 1, 0, 1, 5, 6, 1, 6, 0, 6, 0, 6, 0, 5, 5, 1, 1, 0, 0, 5, 2, 0, 6], [5, 2, 1, 1, 6, 1, 6, 2, 1, 6, 2, 2, 6, 6, 1, 6, 0, 6, 2, 6, 2, 0, 2], [5, 5, 2, 6, 0, 0, 1, 2, 5, 0, 6, 2, 6, 6, 2, 6, 6, 0, 1, 0, 2, 5, 0], [2, 2, 5, 6, 5, 0, 0, 5, 6, 0, 0, 0, 1, 6, 5, 6, 1, 2, 0, 0, 1, 5, 6], [1, 6, 5, 5, 2, 5, 0, 1, 5, 5, 2, 5, 6, 1, 0, 0, 5, 1, 6, 2, 5, 0, 1], [5, 1, 5, 1, 0, 1, 6, 5, 1, 6, 5, 2, 0, 0, 1, 6, 0, 6, 1, 2, 2, 5, 0], [0, 6, 6, 1, 0, 2, 2, 6, 0, 1, 1, 2, 6, 0, 2, 2, 6, 0, 5, 5, 1, 1, 2], [1, 6, 5, 6, 6, 5, 5, 5, 2, 0, 2, 0, 0, 1, 5, 6, 0, 0, 2, 2, 1, 5, 1]], "output": [[6, 1, 5, 0, 0, 5, 0, 5, 6, 5, 0, 1, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, 6], [8, 6, 6, 6, 6, 5, 6, 1, 5, 1, 6, 2, 5, 1, 2, 5, 1, 1, 0, 0, 0, 0, 8], [1, 8, 1, 1, 6, 2, 0, 6, 2, 0, 0, 1, 0, 0, 1, 6, 1, 6, 6, 6, 6, 8, 5], [6, 2, 8, 6, 0, 5, 1, 5, 5, 6, 5, 6, 0, 1, 5, 2, 1, 5, 5, 0, 8, 0, 2], [6, 1, 5, 8, 1, 0, 6, 5, 6, 2, 5, 5, 6, 0, 0, 1, 5, 5, 5, 8, 1, 1, 5], [2, 6, 2, 0, 8, 2, 6, 2, 5, 6, 6, 2, 0, 2, 1, 5, 0, 6, 8, 6, 5, 1, 5], [1, 6, 6, 5, 2, 8, 6, 5, 2, 2, 0, 1, 6, 0, 2, 1, 2, 8, 2, 1, 1, 2, 0], [5, 6, 5, 0, 5, 2, 8, 1, 5, 5, 1, 6, 6, 2, 6, 5, 8, 2, 0, 5, 6, 5, 6], [2, 6, 1, 1, 0, 0, 5, 8, 6, 2, 2, 5, 2, 6, 5, 8, 0, 0, 2, 0, 2, 1, 2], [2, 6, 1, 5, 2, 1, 0, 1, 8, 6, 2, 5, 5, 5, 8, 0, 1, 2, 5, 2, 1, 5, 2], [0, 0, 0, 1, 1, 2, 6, 5, 6, 8, 6, 2, 0, 8, 0, 1, 5, 2, 1, 5, 5, 5, 6], [1, 0, 6, 0, 1, 2, 6, 0, 1, 2, 8, 5, 8, 6, 0, 2, 2, 5, 5, 2, 2, 6, 0], [0, 6, 0, 2, 2, 0, 0, 5, 2, 5, 1, 8, 5, 2, 1, 6, 2, 2, 5, 1, 0, 0, 2], [0, 5, 1, 6, 2, 2, 0, 2, 6, 2, 8, 0, 8, 6, 5, 6, 1, 5, 6, 0, 5, 2, 5], [6, 5, 0, 0, 6, 5, 5, 1, 1, 8, 5, 5, 2, 8, 5, 5, 6, 0, 2, 1, 5, 6, 1], [1, 2, 6, 1, 2, 1, 2, 6, 8, 2, 1, 0, 2, 6, 8, 0, 0, 5, 6, 1, 5, 1, 0], [6, 5, 6, 1, 1, 6, 5, 8, 2, 2, 0, 5, 5, 6, 6, 8, 0, 6, 5, 5, 5, 2, 5], [0, 1, 0, 1, 5, 6, 8, 6, 0, 6, 0, 6, 0, 5, 5, 1, 8, 0, 0, 5, 2, 0, 6], [5, 2, 1, 1, 6, 8, 6, 2, 1, 6, 2, 2, 6, 6, 1, 6, 0, 8, 2, 6, 2, 0, 2], [5, 5, 2, 6, 8, 0, 1, 2, 5, 0, 6, 2, 6, 6, 2, 6, 6, 0, 8, 0, 2, 5, 0], [2, 2, 5, 8, 5, 0, 0, 5, 6, 0, 0, 0, 1, 6, 5, 6, 1, 2, 0, 8, 1, 5, 6], [1, 6, 8, 5, 2, 5, 0, 1, 5, 5, 2, 5, 6, 1, 0, 0, 5, 1, 6, 2, 8, 0, 1], [5, 8, 5, 1, 0, 1, 6, 5, 1, 6, 5, 2, 0, 0, 1, 6, 0, 6, 1, 2, 2, 8, 0], [8, 6, 6, 1, 0, 2, 2, 6, 0, 1, 1, 2, 6, 0, 2, 2, 6, 0, 5, 5, 1, 1, 8], [1, 6, 5, 6, 6, 5, 5, 5, 2, 0, 2, 0, 0, 1, 5, 6, 0, 0, 2, 2, 1, 5, 1]]}, {"input": [[6, 5, 6, 1, 6, 6, 6, 6, 1, 5, 1, 5, 6], [1, 1, 6, 5, 1, 5, 1, 6, 5, 1, 5, 6, 1], [5, 5, 1, 6, 5, 5, 5, 5, 1, 1, 5, 6, 1], [5, 1, 6, 1, 5, 6, 4, 5, 5, 6, 6, 6, 1], [6, 6, 1, 5, 6, 5, 1, 6, 5, 1, 6, 6, 5], [6, 5, 1, 6, 5, 1, 5, 6, 5, 5, 5, 1, 6], [6, 6, 5, 6, 1, 1, 6, 6, 1, 5, 6, 5, 5]], "output": [[6, 5, 6, 4, 6, 6, 6, 6, 1, 4, 1, 5, 6], [1, 1, 6, 5, 4, 5, 1, 6, 4, 1, 5, 6, 1], [5, 5, 1, 6, 5, 4, 5, 4, 1, 1, 5, 6, 1], [5, 1, 6, 1, 5, 6, 4, 5, 5, 6, 6, 6, 1], [6, 6, 1, 5, 6, 4, 1, 4, 5, 1, 6, 6, 5], [6, 5, 1, 6, 4, 1, 5, 6, 4, 5, 5, 1, 6], [6, 6, 5, 4, 1, 1, 6, 6, 1, 4, 6, 5, 5]]}], "input_grid": [[9, 0, 2, 9, 2, 9, 9, 0, 2, 0, 0, 2, 0, 2, 2, 9, 9, 2, 2, 0, 0, 9, 0], [2, 2, 9, 2, 2, 0, 2, 0, 0, 9, 9, 0, 0, 0, 9, 0, 0, 0, 2, 0, 9, 9, 0], [2, 2, 9, 2, 9, 0, 0, 0, 0, 2, 2, 9, 9, 2, 0, 2, 2, 9, 2, 2, 9, 9, 9], [2, 0, 9, 2, 0, 0, 0, 0, 9, 9, 9, 2, 9, 0, 0, 9, 9, 2, 2, 0, 0, 0, 0], [2, 2, 2, 0, 0, 0, 2, 0, 2, 9, 0, 9, 2, 2, 0, 2, 9, 0, 9, 2, 9, 9, 0], [9, 9, 0, 2, 0, 9, 0, 2, 2, 9, 9, 3, 2, 9, 0, 0, 2, 2, 0, 2, 0, 0, 2], [2, 2, 2, 2, 2, 9, 2, 2, 2, 2, 9, 2, 9, 2, 2, 0, 0, 9, 0, 0, 2, 9, 9], [0, 2, 9, 2, 2, 0, 2, 9, 9, 0, 9, 0, 2, 2, 2, 2, 9, 9, 9, 0, 0, 0, 0], [9, 2, 2, 2, 0, 2, 0, 9, 9, 2, 2, 0, 9, 2, 9, 2, 9, 9, 2, 0, 9, 9, 9], [9, 9, 2, 2, 2, 9, 2, 9, 9, 9, 0, 2, 9, 0, 0, 2, 9, 2, 9, 2, 2, 0, 0], [0, 9, 2, 0, 2, 2, 9, 9, 0, 9, 0, 2, 0, 0, 0, 0, 9, 9, 9, 9, 0, 0, 9]], "task_key": "ea786f4a"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 3, 6, 6],\n[6, 6, 3, 3, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 3, 6, 6, 3, 6, 6, 6, 6, 6],\n[3, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3],\n[3, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 6, 3, 6],\n[3, 6, 6, 6, 3, 6, 3, 3, 6, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 3, 6, 3, 3],\n[3, 6, 3, 3, 6, 6, 3, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 3, 6, 6, 6],\n[6, 3, 6, 6, 6, 6, 3, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 3, 3, 6],\n[3, 3, 6, 3, 6, 6, 6, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 3, 6, 3],\n[6, 3, 6, 6, 3, 3, 3, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 6, 6, 6],\n[6, 6, 3, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 3, 6, 6, 6, 6, 3, 6, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0],\n[3, 6, 3, 6, 6, 3, 6, 6, 6, 3, 6, 3, 3, 3, 6, 6, 6, 6, 6, 0, 6, 3, 0],\n[6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 3, 3, 0],\n[6, 3, 6, 3, 3, 6, 3, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 3, 6, 0, 6, 6, 0],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 0, 6, 6, 0],\n[6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0],\n[6, 6, 6, 0, 3, 6, 3, 6, 0, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 0, 0, 0, 0],\n[6, 3, 6, 0, 0, 0, 0, 0, 0, 6, 3, 6, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6],\n[3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 3, 3, 6, 6, 6, 6, 6, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3],\n[3, 6, 3, 3],\n[3, 3, 3, 3],\n[3, 6, 6, 3],\n[3, 6, 6, 3],\n[3, 6, 6, 3],\n[3, 3, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 7, 4, 4, 4, 4, 7, 4, 4, 1, 1, 1, 1],\n[4, 7, 7, 4, 4, 4, 4, 4, 4, 1, 4, 7, 1],\n[4, 4, 4, 4, 4, 1, 1, 1, 4, 1, 4, 4, 1],\n[4, 4, 4, 4, 4, 1, 7, 1, 4, 1, 1, 1, 1],\n[4, 7, 4, 4, 4, 1, 1, 1, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4],\n[4, 4, 1, 1, 1, 1, 1, 1, 4, 7, 4, 4, 4],\n[7, 4, 1, 4, 4, 4, 7, 1, 4, 4, 4, 4, 4],\n[4, 4, 1, 4, 4, 7, 4, 1, 4, 4, 4, 7, 4],\n[4, 4, 1, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4],\n[4, 4, 1, 4, 4, 7, 4, 1, 4, 4, 1, 1, 1],\n[4, 4, 1, 1, 1, 1, 1, 1, 4, 4, 1, 7, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 7, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 1, 7, 1],\n[1, 4, 1, 4, 4, 4, 4, 4, 7, 4, 1, 4, 1],\n[1, 7, 1, 4, 4, 4, 4, 4, 4, 4, 1, 7, 1],\n[1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 7, 4, 4],\n[1, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[1, 4, 4, 1, 4, 1, 1, 1, 1, 1, 1, 4, 4],\n[1, 4, 4, 1, 4, 1, 7, 4, 4, 4, 1, 4, 4],\n[1, 7, 4, 1, 4, 1, 4, 4, 4, 4, 1, 4, 4],\n[1, 1, 1, 1, 4, 1, 7, 4, 4, 4, 1, 4, 4],\n[4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 4, 7],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7],\n[7, 7, 7],\n[7, 7, 7],\n[7, 7, 7],\n[7, 4, 7],\n[7, 7, 7],\n[7, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 8, 3, 3, 3, 3],\n[8, 8, 8, 2, 8, 3, 3, 3, 3, 8, 8, 3, 3, 3, 8, 3, 8, 3, 8, 3, 8, 8, 3],\n[8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 8, 3],\n[8, 8, 8, 8, 8, 3, 2, 8, 3, 8, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 3, 3, 3],\n[8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 3, 8, 3, 8, 3, 3, 3, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[3, 3, 3, 3, 8, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 8],\n[3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 3, 8, 8, 8, 3, 8, 3, 8],\n[3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 8, 3, 8],\n[3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 3, 8, 3, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 3, 8],\n[8, 8, 8, 2, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2],\n[2, 8, 8, 2],\n[2, 2, 8, 2],\n[2, 8, 8, 2],\n[2, 8, 8, 2],\n[2, 8, 8, 2],\n[2, 2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2],\n[4, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4],\n[4, 2, 4, 2, 0, 2, 2, 0, 2, 2, 4, 2, 2, 2],\n[2, 4, 4, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 2],\n[2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 4, 2, 2],\n[2, 4, 4, 2, 0, 2, 2, 0, 2, 2, 2, 4, 2, 2],\n[4, 2, 4, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 2],\n[4, 4, 2, 2, 0, 0, 0, 0, 2, 4, 4, 2, 2, 2],\n[2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2],\n[2, 4, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2],\n[4, 4, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 4, 2],\n[4, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 0, 4, 2, 0, 2, 2, 2, 2, 2, 2, 2],\n[4, 2, 2, 0, 2, 2, 0, 2, 4, 2, 4, 2, 2, 2],\n[2, 2, 2, 0, 2, 4, 0, 2, 4, 2, 2, 2, 4, 4],\n[2, 2, 2, 0, 0, 0, 0, 2, 2, 4, 4, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],\n[2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0],\n[2, 0, 4, 2, 0, 2, 2, 2, 0, 4, 2, 2, 2, 0],\n[2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 4, 4, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 3, 6, 6], [6, 6, 3, 3, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 3, 6, 6, 3, 6, 6, 6, 6, 6], [3, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3], [3, 6, 6, 6, 6, 6, 6, 3, 3, 3, 6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 6, 3, 6], [3, 6, 6, 6, 3, 6, 3, 3, 6, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 3, 6, 3, 3], [3, 6, 3, 3, 6, 6, 3, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 3, 6, 6, 6], [6, 3, 6, 6, 6, 6, 3, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 3, 3, 6], [3, 3, 6, 3, 6, 6, 6, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 0, 6, 6, 3, 6, 3], [6, 3, 6, 6, 3, 3, 3, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 6, 6, 6], [6, 6, 3, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 3, 6, 6, 6, 6, 3, 6, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0], [3, 6, 3, 6, 6, 3, 6, 6, 6, 3, 6, 3, 3, 3, 6, 6, 6, 6, 6, 0, 6, 3, 0], [6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 3, 3, 0], [6, 3, 6, 3, 3, 6, 3, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 3, 6, 0, 6, 6, 0], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 0, 6, 6, 0], [6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 0], [6, 6, 6, 0, 3, 6, 3, 6, 0, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 0, 0, 0, 0], [6, 3, 6, 0, 0, 0, 0, 0, 0, 6, 3, 6, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6], [3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 3, 3, 6, 6, 6, 6, 6, 3]], "output": [[3, 3, 3, 3], [3, 6, 3, 3], [3, 3, 3, 3], [3, 6, 6, 3], [3, 6, 6, 3], [3, 6, 6, 3], [3, 3, 3, 3]]}, {"input": [[4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 7, 4, 4, 4, 4, 7, 4, 4, 1, 1, 1, 1], [4, 7, 7, 4, 4, 4, 4, 4, 4, 1, 4, 7, 1], [4, 4, 4, 4, 4, 1, 1, 1, 4, 1, 4, 4, 1], [4, 4, 4, 4, 4, 1, 7, 1, 4, 1, 1, 1, 1], [4, 7, 4, 4, 4, 1, 1, 1, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4], [4, 4, 1, 1, 1, 1, 1, 1, 4, 7, 4, 4, 4], [7, 4, 1, 4, 4, 4, 7, 1, 4, 4, 4, 4, 4], [4, 4, 1, 4, 4, 7, 4, 1, 4, 4, 4, 7, 4], [4, 4, 1, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4], [4, 4, 1, 4, 4, 7, 4, 1, 4, 4, 1, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 4, 4, 1, 7, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 7, 1], [1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 1, 7, 1], [1, 4, 1, 4, 4, 4, 4, 4, 7, 4, 1, 4, 1], [1, 7, 1, 4, 4, 4, 4, 4, 4, 4, 1, 7, 1], [1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 7, 4, 4], [1, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4], [1, 4, 4, 1, 4, 1, 1, 1, 1, 1, 1, 4, 4], [1, 4, 4, 1, 4, 1, 7, 4, 4, 4, 1, 4, 4], [1, 7, 4, 1, 4, 1, 4, 4, 4, 4, 1, 4, 4], [1, 1, 1, 1, 4, 1, 7, 4, 4, 4, 1, 4, 4], [4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 4, 7], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[7, 7, 7], [7, 7, 7], [7, 7, 7], [7, 7, 7], [7, 4, 7], [7, 7, 7], [7, 7, 7]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 8, 3, 3, 3, 3], [8, 8, 8, 2, 8, 3, 3, 3, 3, 8, 8, 3, 3, 3, 8, 3, 8, 3, 8, 3, 8, 8, 3], [8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 8, 3], [8, 8, 8, 8, 8, 3, 2, 8, 3, 8, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 3, 3, 3], [8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 3, 8, 3, 8, 3, 3, 3, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 8, 3, 3, 3, 3, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 8], [3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 3, 8, 8, 8, 3, 8, 3, 8], [3, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 3, 8, 3, 8], [3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 3, 8, 3, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 8, 3, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 3, 8], [8, 8, 8, 2, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 8]], "output": [[2, 2, 2, 2], [2, 8, 8, 2], [2, 2, 8, 2], [2, 8, 8, 2], [2, 8, 8, 2], [2, 8, 8, 2], [2, 2, 2, 2]]}], "input_grid": [[2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2], [4, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4], [4, 2, 4, 2, 0, 2, 2, 0, 2, 2, 4, 2, 2, 2], [2, 4, 4, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 2], [2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 4, 2, 2], [2, 4, 4, 2, 0, 2, 2, 0, 2, 2, 2, 4, 2, 2], [4, 2, 4, 2, 0, 2, 2, 0, 2, 2, 2, 2, 4, 2], [4, 4, 2, 2, 0, 0, 0, 0, 2, 4, 4, 2, 2, 2], [2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2], [2, 4, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2], [4, 4, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 4, 2], [4, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 0, 4, 2, 0, 2, 2, 2, 2, 2, 2, 2], [4, 2, 2, 0, 2, 2, 0, 2, 4, 2, 4, 2, 2, 2], [2, 2, 2, 0, 2, 4, 0, 2, 4, 2, 2, 2, 4, 4], [2, 2, 2, 0, 0, 0, 0, 2, 2, 4, 4, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0], [2, 0, 4, 2, 0, 2, 2, 2, 0, 4, 2, 2, 2, 0], [2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 4, 4, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 4]], "task_key": "fcb5c309"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[8, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 8, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 4, 4, 4, 4, 4, 4, 4, 8],\n[8, 4, 4, 4, 4, 4, 4, 4, 8],\n[8, 4, 4, 4, 4, 4, 4, 4, 8],\n[8, 4, 4, 4, 8, 4, 4, 4, 8],\n[8, 4, 4, 4, 4, 4, 4, 4, 8],\n[8, 4, 4, 4, 4, 4, 4, 4, 8],\n[8, 4, 4, 4, 4, 4, 4, 4, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2],\n[3, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[5, 5, 5, 1, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 1, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4], [8, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 8, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 8]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 4, 4, 4, 4, 4, 4, 8], [8, 4, 4, 4, 4, 4, 4, 4, 8], [8, 4, 4, 4, 4, 4, 4, 4, 8], [8, 4, 4, 4, 8, 4, 4, 4, 8], [8, 4, 4, 4, 4, 4, 4, 4, 8], [8, 4, 4, 4, 4, 4, 4, 4, 8], [8, 4, 4, 4, 4, 4, 4, 4, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2]]}], "input_grid": [[5, 5, 5, 1, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 1, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 1]], "task_key": "5c2c9af4"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4],\n[4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5],\n[4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1],\n[4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2],\n[4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3],\n[4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1],\n[4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],\n[4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7],\n[3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9],\n[9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4],\n[9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7],\n[9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5],\n[9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2],\n[9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5],\n[9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7],\n[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4], [4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4], [4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5], [4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2], [4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3], [4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9], [9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]], "output": [[9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4], [9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7], [9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5], [9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2], [9, 9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5], [9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7]]}], "input_grid": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "task_key": "99fa7670"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 2, 6, 6, 6, 3, 2, 6, 6, 8, 6, 4, 8, 6, 8, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 4, 4, 6, 6, 4, 8, 3, 6, 8, 2, 2, 6, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 2, 3, 8, 8, 8, 6, 3, 8, 1, 8, 1, 1, 1, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 8, 4, 3, 4, 8, 6, 1, 4, 6, 1, 4, 2, 8, 4, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 3, 6, 6, 1, 8, 8, 4, 4, 1, 1, 3, 3, 8, 4, 4, 2, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 1, 4, 8, 6, 6, 2, 8, 6, 4, 2, 2, 3, 8, 8, 8, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 8, 1, 1, 2, 8, 1, 4, 1, 8, 2, 4, 8, 3, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 3, 6, 6, 1, 2, 8, 1, 3, 6, 3, 1, 2, 1, 8, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 1, 1, 2, 2, 3, 2, 3, 8, 1, 6, 4, 2, 3, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 1, 6, 1, 3, 8, 4, 6, 4, 1, 1, 8, 8, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 3, 3, 1, 6, 1, 3, 1, 3, 3, 1, 3, 6, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 4, 4, 1, 8, 4, 1, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 8, 4, 2, 2, 8, 1, 1, 1, 3, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 4, 6, 6, 8, 1, 1, 3, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 2, 6, 6, 8, 3, 8, 6, 1, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 8, 0, 4, 8, 0, 8],\n[0, 0, 0, 4, 4, 0, 0, 4, 8, 3, 0, 8, 2, 2, 0, 3],\n[0, 0, 0, 2, 3, 8, 8, 8, 0, 3, 8, 1, 8, 1, 1, 1],\n[0, 8, 4, 3, 4, 8, 0, 1, 4, 0, 1, 4, 2, 8, 4, 3],\n[3, 0, 0, 1, 8, 8, 4, 4, 1, 1, 3, 3, 8, 4, 4, 2],\n[0, 1, 4, 8, 0, 0, 2, 8, 0, 4, 2, 2, 3, 8, 8, 8],\n[0, 0, 8, 1, 1, 2, 8, 1, 4, 1, 8, 2, 4, 8, 3, 4],\n[0, 3, 0, 0, 1, 2, 8, 1, 3, 0, 3, 1, 2, 1, 8, 4],\n[0, 0, 1, 1, 2, 2, 3, 2, 3, 8, 1, 0, 4, 2, 3, 4],\n[0, 0, 0, 0, 1, 0, 1, 3, 8, 4, 0, 4, 1, 1, 8, 8],\n[0, 0, 0, 3, 3, 1, 0, 1, 3, 1, 3, 3, 1, 3, 0, 4],\n[0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 4, 1, 8, 4, 1, 3],\n[0, 0, 0, 0, 0, 0, 8, 4, 2, 2, 8, 1, 1, 1, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 0, 8, 1, 1, 3],\n[0, 0, 0, 0, 0, 0, 4, 3, 2, 0, 0, 8, 3, 8, 0, 1],\n[0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 2, 8, 4, 6, 6, 4, 4, 6, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 5, 4, 4, 9, 4, 5, 9, 5, 9, 2, 4, 5, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 5, 8, 9, 5, 8, 7, 4, 2, 5, 4, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 9, 4, 2, 9, 6, 4, 4, 6, 4, 2, 8, 5, 8, 5, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 6, 2, 5, 9, 9, 5, 7, 2, 9, 6, 6, 8, 2, 4, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 8, 6, 7, 9, 7, 9, 9, 2, 5, 2, 7, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 5, 0, 8, 4, 6, 6, 4, 4, 6, 4, 0, 0, 0],\n[0, 0, 5, 4, 4, 9, 4, 5, 9, 5, 9, 0, 4, 5, 6],\n[8, 5, 8, 9, 5, 8, 7, 4, 0, 5, 4, 8, 8, 0, 0],\n[9, 4, 0, 9, 6, 4, 4, 6, 4, 0, 8, 5, 8, 5, 8],\n[6, 0, 5, 9, 9, 5, 7, 0, 9, 6, 6, 8, 0, 4, 8],\n[0, 0, 8, 6, 7, 9, 7, 9, 9, 0, 5, 0, 7, 5, 0]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 5],\n[0, 4, 3],\n[5, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 9, 7],\n[1, 3, 7],\n[1, 3, 7],\n[1, 1, 9],\n[1, 4, 2],\n[1, 2, 7],\n[1, 4, 3],\n[1, 4, 1],\n[1, 2, 1],\n[1, 1, 1],\n[1, 1, 1],\n[1, 1, 1]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 2, 6, 6, 6, 3, 2, 6, 6, 8, 6, 4, 8, 6, 8, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 4, 4, 6, 6, 4, 8, 3, 6, 8, 2, 2, 6, 3, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 2, 3, 8, 8, 8, 6, 3, 8, 1, 8, 1, 1, 1, 6, 6, 6, 6, 6, 6], [6, 6, 6, 8, 4, 3, 4, 8, 6, 1, 4, 6, 1, 4, 2, 8, 4, 3, 6, 6, 6, 6, 6, 6], [6, 6, 3, 6, 6, 1, 8, 8, 4, 4, 1, 1, 3, 3, 8, 4, 4, 2, 6, 6, 6, 6, 6, 6], [6, 6, 6, 1, 4, 8, 6, 6, 2, 8, 6, 4, 2, 2, 3, 8, 8, 8, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 8, 1, 1, 2, 8, 1, 4, 1, 8, 2, 4, 8, 3, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 3, 6, 6, 1, 2, 8, 1, 3, 6, 3, 1, 2, 1, 8, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 1, 1, 2, 2, 3, 2, 3, 8, 1, 6, 4, 2, 3, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 1, 6, 1, 3, 8, 4, 6, 4, 1, 1, 8, 8, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 3, 3, 1, 6, 1, 3, 1, 3, 3, 1, 3, 6, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 4, 4, 1, 8, 4, 1, 3, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 8, 4, 2, 2, 8, 1, 1, 1, 3, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 4, 6, 6, 8, 1, 1, 3, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 2, 6, 6, 8, 3, 8, 6, 1, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6]], "output": [[0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 8, 0, 4, 8, 0, 8], [0, 0, 0, 4, 4, 0, 0, 4, 8, 3, 0, 8, 2, 2, 0, 3], [0, 0, 0, 2, 3, 8, 8, 8, 0, 3, 8, 1, 8, 1, 1, 1], [0, 8, 4, 3, 4, 8, 0, 1, 4, 0, 1, 4, 2, 8, 4, 3], [3, 0, 0, 1, 8, 8, 4, 4, 1, 1, 3, 3, 8, 4, 4, 2], [0, 1, 4, 8, 0, 0, 2, 8, 0, 4, 2, 2, 3, 8, 8, 8], [0, 0, 8, 1, 1, 2, 8, 1, 4, 1, 8, 2, 4, 8, 3, 4], [0, 3, 0, 0, 1, 2, 8, 1, 3, 0, 3, 1, 2, 1, 8, 4], [0, 0, 1, 1, 2, 2, 3, 2, 3, 8, 1, 0, 4, 2, 3, 4], [0, 0, 0, 0, 1, 0, 1, 3, 8, 4, 0, 4, 1, 1, 8, 8], [0, 0, 0, 3, 3, 1, 0, 1, 3, 1, 3, 3, 1, 3, 0, 4], [0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 4, 1, 8, 4, 1, 3], [0, 0, 0, 0, 0, 0, 8, 4, 2, 2, 8, 1, 1, 1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 0, 8, 1, 1, 3], [0, 0, 0, 0, 0, 0, 4, 3, 2, 0, 0, 8, 3, 8, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 2, 8, 4, 6, 6, 4, 4, 6, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 5, 4, 4, 9, 4, 5, 9, 5, 9, 2, 4, 5, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 5, 8, 9, 5, 8, 7, 4, 2, 5, 4, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 9, 4, 2, 9, 6, 4, 4, 6, 4, 2, 8, 5, 8, 5, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 6, 2, 5, 9, 9, 5, 7, 2, 9, 6, 6, 8, 2, 4, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 6, 7, 9, 7, 9, 9, 2, 5, 2, 7, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[0, 0, 5, 0, 8, 4, 6, 6, 4, 4, 6, 4, 0, 0, 0], [0, 0, 5, 4, 4, 9, 4, 5, 9, 5, 9, 0, 4, 5, 6], [8, 5, 8, 9, 5, 8, 7, 4, 0, 5, 4, 8, 8, 0, 0], [9, 4, 0, 9, 6, 4, 4, 6, 4, 0, 8, 5, 8, 5, 8], [6, 0, 5, 9, 9, 5, 7, 0, 9, 6, 6, 8, 0, 4, 8], [0, 0, 8, 6, 7, 9, 7, 9, 9, 0, 5, 0, 7, 5, 0]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], "output": [[0, 0, 5], [0, 4, 3], [5, 0, 0]]}], "input_grid": [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 9, 7], [1, 3, 7], [1, 3, 7], [1, 1, 9], [1, 4, 2], [1, 2, 7], [1, 4, 3], [1, 4, 1], [1, 2, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]], "task_key": "a740d043"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9],\n[8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 9, 9],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 9, 9, 9],\n[8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 8],\n[8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 8, 8],\n[8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 9, 9, 9, 8, 8],\n[8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 8]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 5, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 2, 5, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 5, 5, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 0, 2, 6, 6, 6, 6],\n[6, 6, 6, 6, 2, 0, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 0, 0],\n[6, 6, 6, 6, 6, 6, 6, 6, 2, 2],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 0],\n[6, 6, 6, 6, 6, 6, 6, 6, 0, 0],\n[6, 6, 6, 6, 6, 6, 6, 0, 0, 0],\n[6, 6, 6, 6, 6, 6, 0, 0, 0, 6],\n[6, 6, 6, 6, 6, 0, 0, 0, 6, 6],\n[6, 6, 6, 6, 0, 0, 0, 6, 6, 6],\n[6, 6, 6, 0, 0, 0, 6, 6, 6, 6],\n[6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[6, 0, 0, 0, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 6, 6, 6, 6, 6, 0, 0],\n[0, 0, 6, 6, 6, 6, 6, 0, 0, 0],\n[0, 6, 6, 6, 6, 6, 0, 0, 0, 0],\n[6, 6, 6, 6, 6, 0, 0, 0, 6, 6],\n[6, 6, 6, 6, 0, 0, 0, 6, 6, 6],\n[6, 6, 6, 0, 0, 0, 6, 6, 6, 6],\n[6, 6, 0, 0, 0, 6, 6, 6, 6, 6],\n[6, 0, 0, 0, 6, 6, 6, 6, 6, 6],\n[0, 0, 0, 6, 6, 6, 6, 6, 6, 6],\n[0, 0, 6, 6, 6, 6, 6, 6, 6, 6],\n[0, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9], [8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 9, 9], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 9, 9, 9], [8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 8], [8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 8, 8], [8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 9, 9, 9, 8, 8], [8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 9, 9, 9, 8]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 5, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 2, 5, 7, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7], [7, 7, 5, 5, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 7, 7, 7, 7, 7, 7, 7], [7, 7, 5, 5, 7, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 0, 2, 6, 6, 6, 6], [6, 6, 6, 6, 2, 0, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 0, 0], [6, 6, 6, 6, 6, 6, 6, 6, 2, 2], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 0], [6, 6, 6, 6, 6, 6, 6, 6, 0, 0], [6, 6, 6, 6, 6, 6, 6, 0, 0, 0], [6, 6, 6, 6, 6, 6, 0, 0, 0, 6], [6, 6, 6, 6, 6, 0, 0, 0, 6, 6], [6, 6, 6, 6, 0, 0, 0, 6, 6, 6], [6, 6, 6, 0, 0, 0, 6, 6, 6, 6], [6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [6, 0, 0, 0, 6, 6, 6, 6, 6, 6], [0, 0, 0, 6, 6, 6, 6, 6, 0, 0], [0, 0, 6, 6, 6, 6, 6, 0, 0, 0], [0, 6, 6, 6, 6, 6, 0, 0, 0, 0], [6, 6, 6, 6, 6, 0, 0, 0, 6, 6], [6, 6, 6, 6, 0, 0, 0, 6, 6, 6], [6, 6, 6, 0, 0, 0, 6, 6, 6, 6], [6, 6, 0, 0, 0, 6, 6, 6, 6, 6], [6, 0, 0, 0, 6, 6, 6, 6, 6, 6], [0, 0, 0, 6, 6, 6, 6, 6, 6, 6], [0, 0, 6, 6, 6, 6, 6, 6, 6, 6], [0, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6]]}], "input_grid": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "task_key": "1f0c79e5"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 8, 3, 3, 8, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0],\n[0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0],\n[0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0],\n[0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0],\n[8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6],\n[8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6],\n[8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6],\n[8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6],\n[8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6],\n[3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3],\n[3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3],\n[3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3],\n[3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3],\n[3, 3, 3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0],\n[4, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4],\n[4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 4, 4],\n[3, 3, 3, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 3],\n[3, 0, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1],\n[1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1],\n[8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8],\n[7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 7, 7, 0, 7, 7],\n[0, 7, 7, 7, 7, 0, 0, 7, 0, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 0, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0, 0, 3, 3, 0, 3, 3, 3, 3, 3, 0, 0, 3, 0, 3, 3, 0, 3, 0],\n[3, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0, 0, 3, 3, 0, 3, 3, 3, 3, 3, 0, 0, 3, 0, 3, 3, 0, 3, 0],\n[4, 0, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4],\n[4, 0, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4],\n[3, 0, 3, 0, 0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3],\n[3, 0, 3, 0, 0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3],\n[7, 7, 7, 7, 7, 0, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 0, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1],\n[1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1],\n[8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8],\n[0, 7, 0, 7, 7, 0, 0, 0, 0, 7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 0, 7, 7, 0, 0, 7, 7, 0, 0, 7],\n[0, 7, 0, 7, 7, 0, 0, 0, 0, 7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 0, 7, 7, 0, 0, 7, 7, 0, 0, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7],\n[6, 7, 7, 7, 7],\n[5, 5, 6, 5, 5],\n[5, 5, 5, 6, 5],\n[9, 9, 9, 9, 9],\n[6, 9, 6, 9, 9],\n[8, 8, 8, 8, 8],\n[6, 8, 6, 8, 8],\n[6, 5, 5, 5, 5],\n[5, 6, 5, 5, 5],\n[0, 0, 0, 0, 0],\n[0, 6, 0, 0, 0],\n[8, 8, 8, 8, 8],\n[8, 8, 8, 6, 8],\n[6, 3, 3, 3, 3],\n[3, 3, 3, 6, 3],\n[8, 8, 8, 8, 8],\n[8, 8, 6, 6, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 7, 7, 7, 7],\n[6, 7, 7, 7, 7],\n[5, 5, 6, 6, 5],\n[5, 5, 6, 6, 5],\n[6, 9, 6, 9, 9],\n[6, 9, 6, 9, 9],\n[6, 8, 6, 8, 8],\n[6, 8, 6, 8, 8],\n[6, 6, 5, 5, 5],\n[6, 6, 5, 5, 5],\n[0, 6, 0, 0, 0],\n[0, 6, 0, 0, 0],\n[8, 8, 8, 6, 8],\n[8, 8, 8, 6, 8],\n[6, 3, 3, 6, 3],\n[6, 3, 3, 6, 3],\n[8, 8, 6, 6, 8],\n[8, 8, 6, 6, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[6, 6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5],\n[4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 8, 3, 3, 8, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 8, 3, 3, 3]], "output": [[0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0], [0, 8, 8, 0, 0, 8, 0, 0, 8, 8, 8, 8, 8, 0, 8, 8, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0], [8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6], [8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6], [8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6], [8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6], [8, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6], [3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3], [3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3], [3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3], [3, 8, 3, 3, 8, 3, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 8, 3, 8, 3, 3, 8, 8, 3, 8, 8, 8, 3, 3]]}, {"input": [[3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 0, 3, 3], [3, 3, 3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3, 0], [4, 0, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4], [4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 4, 4], [3, 3, 3, 0, 0, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 3], [3, 0, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 0, 3, 3, 3, 3], [7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1], [8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8], [7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 7, 0, 7, 7, 7, 0, 7, 7, 0, 7, 7], [0, 7, 7, 7, 7, 0, 0, 7, 0, 7, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 7, 7, 7, 7, 0, 7]], "output": [[3, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0, 0, 3, 3, 0, 3, 3, 3, 3, 3, 0, 0, 3, 0, 3, 3, 0, 3, 0], [3, 3, 3, 0, 3, 0, 3, 3, 0, 0, 0, 0, 3, 3, 0, 3, 3, 3, 3, 3, 0, 0, 3, 0, 3, 3, 0, 3, 0], [4, 0, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4], [4, 0, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4], [3, 0, 3, 0, 0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3], [3, 0, 3, 0, 0, 3, 0, 3, 0, 3, 3, 3, 3, 3, 3, 0, 3, 3, 3, 0, 3, 3, 0, 3, 0, 3, 0, 3, 3], [7, 7, 7, 7, 7, 0, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 0, 7, 0, 7, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1], [8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8], [8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8], [0, 7, 0, 7, 7, 0, 0, 0, 0, 7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 0, 7, 7, 0, 0, 7, 7, 0, 0, 7], [0, 7, 0, 7, 7, 0, 0, 0, 0, 7, 7, 0, 7, 7, 7, 7, 0, 7, 7, 0, 7, 7, 0, 0, 7, 7, 0, 0, 7]]}, {"input": [[7, 7, 7, 7, 7], [6, 7, 7, 7, 7], [5, 5, 6, 5, 5], [5, 5, 5, 6, 5], [9, 9, 9, 9, 9], [6, 9, 6, 9, 9], [8, 8, 8, 8, 8], [6, 8, 6, 8, 8], [6, 5, 5, 5, 5], [5, 6, 5, 5, 5], [0, 0, 0, 0, 0], [0, 6, 0, 0, 0], [8, 8, 8, 8, 8], [8, 8, 8, 6, 8], [6, 3, 3, 3, 3], [3, 3, 3, 6, 3], [8, 8, 8, 8, 8], [8, 8, 6, 6, 8]], "output": [[6, 7, 7, 7, 7], [6, 7, 7, 7, 7], [5, 5, 6, 6, 5], [5, 5, 6, 6, 5], [6, 9, 6, 9, 9], [6, 9, 6, 9, 9], [6, 8, 6, 8, 8], [6, 8, 6, 8, 8], [6, 6, 5, 5, 5], [6, 6, 5, 5, 5], [0, 6, 0, 0, 0], [0, 6, 0, 0, 0], [8, 8, 8, 6, 8], [8, 8, 8, 6, 8], [6, 3, 3, 6, 3], [6, 3, 3, 6, 3], [8, 8, 6, 6, 8], [8, 8, 6, 6, 8]]}], "input_grid": [[6, 6, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5], [4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4]], "task_key": "855e0971"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[4, 4, 4, 0, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4, 4, 4, 4],\n[4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 4],\n[0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 4, 4],\n[4, 0, 0, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4],\n[4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 0, 4, 4, 1, 4, 0, 4, 0, 0, 0, 0, 4, 0, 4, 4],\n[4, 4, 4, 0, 4, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 4, 1, 4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4],\n[4, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 0, 0, 1, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 4, 4],\n[0, 0, 0, 0, 4, 0, 4, 4, 4, 0, 4, 4, 4, 0, 0, 1, 1, 0, 1, 0, 4, 0, 0, 0, 0, 0, 4, 4, 4],\n[4, 4, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 4, 4, 1, 1, 4, 4, 0, 4, 4, 0, 0, 4, 0, 4, 4],\n[4, 0, 0, 4, 4, 4, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4],\n[4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 4, 4, 1, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4, 4, 4, 4],\n[4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 1, 4, 4, 4],\n[0, 0, 1, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 1, 0, 0, 4, 4],\n[4, 1, 1, 4, 1, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 1, 1, 4, 4, 0, 4],\n[4, 4, 1, 1, 1, 4, 4, 4, 0, 4, 4, 4, 4, 4, 0, 4, 4, 1, 4, 0, 4, 0, 0, 1, 1, 4, 1, 4, 4],\n[4, 4, 4, 1, 4, 4, 4, 0, 4, 4, 1, 4, 4, 4, 0, 4, 1, 4, 4, 4, 4, 0, 1, 1, 1, 1, 4, 4, 4],\n[4, 4, 4, 1, 4, 4, 0, 4, 4, 1, 4, 4, 4, 0, 1, 0, 1, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4],\n[0, 0, 1, 1, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 1, 1, 1, 4, 4, 4],\n[4, 4, 4, 1, 1, 4, 4, 0, 1, 1, 4, 1, 0, 1, 4, 4, 1, 1, 4, 4, 0, 4, 4, 1, 1, 4, 0, 4, 4],\n[4, 0, 0, 4, 4, 4, 4, 0, 4, 1, 1, 4, 1, 1, 0, 1, 4, 0, 0, 4, 0, 0, 4, 1, 1, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 0, 0, 0, 4, 0, 4, 1, 1, 1, 1, 1, 4, 4],\n[4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 0, 5, 5, 5],\n[0, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 5, 0, 5],\n[0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 0, 0, 5, 0],\n[5, 5, 5, 0, 5, 0, 0, 5, 5, 5, 0, 0, 5, 0, 5],\n[0, 0, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 0, 5, 0, 0, 5, 5, 0, 5, 5, 5, 0],\n[0, 5, 5, 5, 0, 5, 0, 0, 0, 5, 5, 0, 5, 5, 5],\n[0, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 5],\n[5, 5, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0],\n[5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0],\n[5, 5, 5, 5, 5, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0],\n[5, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 5],\n[0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 5, 5],\n[5, 0, 5, 0, 0, 5, 0, 5, 0, 5, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 5, 0],\n[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 0],\n[5, 5, 5, 0, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 5, 0, 5, 5, 0, 5, 5, 0, 0, 5, 5, 0, 5, 0],\n[5, 4, 4, 4, 4, 5, 0, 0, 5, 5, 5, 5, 5, 5, 0],\n[5, 5, 5, 0, 4, 0, 0, 5, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 5, 5, 4, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5],\n[0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 5, 5],\n[5, 5, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 5, 5, 0],\n[5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 5, 5, 5],\n[5, 5, 5, 0, 5, 0, 0, 5, 0, 5, 5, 0, 5, 0, 0],\n[5, 5, 5, 0, 5, 5, 5, 5, 0, 5, 0, 0, 5, 5, 5],\n[5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 0, 5, 5, 5],\n[0, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 0, 5, 5, 0, 5],\n[0, 5, 5, 5, 5, 5, 5, 5, 4, 5, 0, 0, 0, 5, 0],\n[5, 5, 5, 0, 5, 0, 0, 5, 5, 5, 0, 0, 5, 0, 5],\n[0, 0, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5],\n[5, 5, 5, 5, 0, 5, 4, 4, 5, 5, 0, 5, 5, 5, 0],\n[0, 5, 5, 5, 0, 5, 4, 4, 0, 5, 5, 0, 5, 5, 5],\n[0, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 5],\n[5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 4, 4, 4, 4],\n[5, 5, 0, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4],\n[5, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 4, 5, 4],\n[5, 5, 0, 4, 4, 4, 4, 5, 4, 0, 0, 5, 4, 0, 5],\n[4, 4, 4, 4, 5, 0, 4, 5, 4, 4, 4, 4, 4, 5, 5],\n[5, 0, 5, 4, 0, 5, 4, 5, 0, 5, 0, 4, 4, 4, 4],\n[4, 4, 4, 4, 0, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4],\n[5, 0, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 0, 5, 4],\n[5, 5, 5, 4, 5, 4, 5, 0, 4, 4, 0, 4, 4, 4, 4],\n[0, 5, 0, 5, 5, 4, 5, 5, 4, 4, 5, 5, 0, 5, 4],\n[5, 4, 4, 4, 4, 5, 0, 0, 5, 5, 5, 5, 5, 5, 4],\n[5, 5, 5, 0, 4, 0, 0, 5, 0, 5, 5, 5, 5, 5, 0],\n[0, 0, 5, 5, 4, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5],\n[0, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 5, 0, 5, 5],\n[5, 5, 5, 5, 0, 5, 5, 4, 4, 4, 4, 4, 5, 5, 0],\n[5, 0, 5, 5, 0, 5, 5, 4, 5, 5, 4, 4, 5, 5, 5],\n[5, 5, 5, 0, 5, 0, 0, 5, 0, 5, 5, 4, 5, 0, 0],\n[5, 5, 5, 0, 5, 5, 5, 5, 0, 5, 0, 0, 5, 5, 5],\n[5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[4, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 4, 0],\n[4, 4, 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, 4, 0],\n[4, 0, 4, 4, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4],\n[4, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 4],\n[4, 0, 0, 0, 0, 0, 0, 4, 1, 1, 0, 0, 4, 4, 4, 4, 4, 0, 4, 4],\n[0, 0, 4, 4, 0, 4, 4, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0],\n[0, 0, 0, 0, 4, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0],\n[0, 4, 0, 4, 0, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4, 4, 4, 0, 0],\n[4, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 4],\n[4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 4, 0, 0, 4, 4, 4, 4, 0, 0, 0],\n[4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 0, 0],\n[4, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0],\n[4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4],\n[0, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 4],\n[4, 4, 0, 4, 4, 4, 4, 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 0],\n[0, 0, 4, 0, 0, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4],\n[4, 0, 0, 4, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 4, 4],\n[4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 4, 0],\n[0, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 4, 4],\n[0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0],\n[4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 4, 0, 4, 0, 4, 4],\n[4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 4, 4, 0, 4, 0],\n[0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4],\n[0, 4, 0, 0, 0, 0, 4, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 0, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[4, 0, 0, 4, 1, 1, 4, 4, 0, 0, 1, 1, 4, 4, 4, 1, 1, 1, 4, 0],\n[4, 4, 0, 4, 1, 1, 0, 4, 4, 4, 1, 0, 4, 0, 4, 1, 1, 4, 4, 0],\n[4, 0, 4, 4, 1, 4, 0, 0, 0, 4, 4, 0, 0, 4, 4, 1, 1, 1, 1, 4],\n[4, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 4, 0, 0, 4, 1, 4, 1, 4, 4],\n[4, 1, 1, 0, 1, 1, 0, 4, 1, 1, 1, 1, 4, 4, 4, 4, 4, 0, 4, 4],\n[1, 1, 4, 4, 1, 4, 4, 4, 1, 0, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1],\n[1, 1, 1, 1, 4, 0, 4, 0, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],\n[4, 1, 1, 1, 4, 0, 4, 0, 4, 4, 1, 4, 1, 1, 4, 1, 1, 1, 4, 0],\n[0, 4, 1, 4, 0, 4, 4, 4, 4, 1, 1, 4, 1, 4, 4, 4, 4, 4, 1, 1],\n[4, 4, 4, 0, 4, 4, 0, 1, 1, 1, 1, 4, 1, 1, 4, 0, 0, 4, 1, 4],\n[4, 0, 1, 1, 4, 4, 4, 1, 1, 1, 4, 0, 1, 4, 4, 4, 4, 0, 1, 1],\n[4, 4, 1, 1, 1, 0, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 1, 1],\n[4, 0, 1, 1, 4, 0, 4, 4, 1, 1, 0, 4, 0, 4, 0, 4, 4, 4, 1, 1],\n[4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 0, 4, 4, 0, 4, 4, 1, 4],\n[0, 0, 4, 1, 1, 4, 1, 4, 4, 4, 1, 1, 0, 4, 0, 0, 4, 4, 0, 4],\n[4, 4, 0, 4, 4, 4, 4, 4, 1, 1, 1, 4, 1, 1, 4, 4, 0, 0, 4, 0],\n[0, 0, 4, 0, 0, 4, 4, 4, 1, 4, 4, 4, 1, 4, 0, 4, 4, 1, 1, 4],\n[4, 1, 1, 4, 4, 0, 0, 4, 1, 1, 4, 4, 0, 4, 4, 0, 1, 1, 4, 4],\n[4, 1, 4, 0, 0, 4, 1, 1, 1, 4, 0, 4, 4, 0, 0, 4, 1, 4, 4, 0],\n[0, 4, 4, 4, 4, 4, 1, 4, 0, 4, 1, 1, 1, 4, 4, 0, 4, 0, 4, 4],\n[0, 0, 0, 0, 1, 1, 1, 0, 4, 4, 1, 1, 4, 0, 4, 0, 4, 1, 1, 0],\n[4, 4, 4, 4, 1, 1, 4, 1, 1, 1, 1, 4, 0, 4, 4, 0, 4, 1, 4, 4],\n[4, 4, 4, 0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 0, 4, 4, 0, 4, 0],\n[1, 1, 4, 4, 1, 4, 1, 1, 4, 4, 4, 0, 1, 1, 1, 4, 1, 1, 0, 4],\n[1, 4, 0, 0, 0, 0, 4, 4, 4, 0, 4, 4, 1, 1, 4, 4, 1, 4, 0, 4]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2],\n[2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0],\n[2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2],\n[0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0],\n[2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0],\n[2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0],\n[0, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0],\n[0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0],\n[0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0],\n[2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[4, 4, 4, 0, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4, 4, 4, 4], [4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 4], [0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 4, 4], [4, 0, 0, 4, 0, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, 4, 0, 4, 4, 1, 4, 0, 4, 0, 0, 0, 0, 4, 0, 4, 4], [4, 4, 4, 0, 4, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 4, 1, 4, 4, 4, 4, 0, 0, 0, 0, 0, 4, 4, 4], [4, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 4, 0, 0, 0, 1, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 4, 4], [0, 0, 0, 0, 4, 0, 4, 4, 4, 0, 4, 4, 4, 0, 0, 1, 1, 0, 1, 0, 4, 0, 0, 0, 0, 0, 4, 4, 4], [4, 4, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 4, 4, 1, 1, 4, 4, 0, 4, 4, 0, 0, 4, 0, 4, 4], [4, 0, 0, 4, 4, 4, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4], [4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 4, 4, 4]], "output": [[4, 4, 4, 1, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4, 0, 4, 4, 4, 4], [4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 1, 4, 4, 4], [0, 0, 1, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 1, 0, 0, 4, 4], [4, 1, 1, 4, 1, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 4, 0, 4, 4, 0, 4, 4, 1, 1, 4, 4, 0, 4], [4, 4, 1, 1, 1, 4, 4, 4, 0, 4, 4, 4, 4, 4, 0, 4, 4, 1, 4, 0, 4, 0, 0, 1, 1, 4, 1, 4, 4], [4, 4, 4, 1, 4, 4, 4, 0, 4, 4, 1, 4, 4, 4, 0, 4, 1, 4, 4, 4, 4, 0, 1, 1, 1, 1, 4, 4, 4], [4, 4, 4, 1, 4, 4, 0, 4, 4, 1, 4, 4, 4, 0, 1, 0, 1, 4, 4, 4, 4, 4, 4, 1, 1, 4, 4, 4, 4], [0, 0, 1, 1, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 1, 1, 1, 4, 4, 4], [4, 4, 4, 1, 1, 4, 4, 0, 1, 1, 4, 1, 0, 1, 4, 4, 1, 1, 4, 4, 0, 4, 4, 1, 1, 4, 0, 4, 4], [4, 0, 0, 4, 4, 4, 4, 0, 4, 1, 1, 4, 1, 1, 0, 1, 4, 0, 0, 4, 0, 0, 4, 1, 1, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 4, 0, 0, 0, 4, 0, 4, 1, 1, 1, 1, 1, 4, 4], [4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 4, 4, 4]]}, {"input": [[5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 0, 5, 5, 5], [0, 5, 5, 5, 5, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 5, 0, 5], [0, 5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 0, 0, 5, 0], [5, 5, 5, 0, 5, 0, 0, 5, 5, 5, 0, 0, 5, 0, 5], [0, 0, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 0, 5, 0, 0, 5, 5, 0, 5, 5, 5, 0], [0, 5, 5, 5, 0, 5, 0, 0, 0, 5, 5, 0, 5, 5, 5], [0, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 5], [5, 5, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 0], [5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0], [5, 5, 5, 5, 5, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0], [5, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 5], [0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 5, 5], [5, 0, 5, 0, 0, 5, 0, 5, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 5, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 5, 0], [5, 5, 5, 0, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 5, 5, 0, 5, 5, 0, 0, 5, 5, 0, 5, 0], [5, 4, 4, 4, 4, 5, 0, 0, 5, 5, 5, 5, 5, 5, 0], [5, 5, 5, 0, 4, 0, 0, 5, 0, 5, 5, 5, 5, 5, 0], [0, 0, 5, 5, 4, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5], [0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 5, 5], [5, 5, 5, 5, 0, 5, 5, 0, 0, 0, 0, 0, 5, 5, 0], [5, 0, 5, 5, 0, 5, 5, 0, 5, 5, 0, 0, 5, 5, 5], [5, 5, 5, 0, 5, 0, 0, 5, 0, 5, 5, 0, 5, 0, 0], [5, 5, 5, 0, 5, 5, 5, 5, 0, 5, 0, 0, 5, 5, 5], [5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5]], "output": [[5, 5, 5, 5, 5, 5, 5, 0, 5, 0, 5, 0, 5, 5, 5], [0, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 0, 5, 5, 0, 5], [0, 5, 5, 5, 5, 5, 5, 5, 4, 5, 0, 0, 0, 5, 0], [5, 5, 5, 0, 5, 0, 0, 5, 5, 5, 0, 0, 5, 0, 5], [0, 0, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 0, 5, 4, 4, 5, 5, 0, 5, 5, 5, 0], [0, 5, 5, 5, 0, 5, 4, 4, 0, 5, 5, 0, 5, 5, 5], [0, 0, 5, 5, 0, 5, 5, 5, 0, 5, 0, 0, 0, 0, 5], [5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 4, 4, 4, 4], [5, 5, 0, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4], [5, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 4, 5, 4], [5, 5, 0, 4, 4, 4, 4, 5, 4, 0, 0, 5, 4, 0, 5], [4, 4, 4, 4, 5, 0, 4, 5, 4, 4, 4, 4, 4, 5, 5], [5, 0, 5, 4, 0, 5, 4, 5, 0, 5, 0, 4, 4, 4, 4], [4, 4, 4, 4, 0, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4], [5, 0, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 0, 5, 4], [5, 5, 5, 4, 5, 4, 5, 0, 4, 4, 0, 4, 4, 4, 4], [0, 5, 0, 5, 5, 4, 5, 5, 4, 4, 5, 5, 0, 5, 4], [5, 4, 4, 4, 4, 5, 0, 0, 5, 5, 5, 5, 5, 5, 4], [5, 5, 5, 0, 4, 0, 0, 5, 0, 5, 5, 5, 5, 5, 0], [0, 0, 5, 5, 4, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5], [0, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 5, 0, 5, 5], [5, 5, 5, 5, 0, 5, 5, 4, 4, 4, 4, 4, 5, 5, 0], [5, 0, 5, 5, 0, 5, 5, 4, 5, 5, 4, 4, 5, 5, 5], [5, 5, 5, 0, 5, 0, 0, 5, 0, 5, 5, 4, 5, 0, 0], [5, 5, 5, 0, 5, 5, 5, 5, 0, 5, 0, 0, 5, 5, 5], [5, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5]]}, {"input": [[4, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 4, 0], [4, 4, 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, 4, 0], [4, 0, 4, 4, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 4], [4, 0, 0, 0, 0, 0, 0, 4, 1, 1, 0, 0, 4, 4, 4, 4, 4, 0, 4, 4], [0, 0, 4, 4, 0, 4, 4, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 4, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0], [0, 4, 0, 4, 0, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4, 4, 4, 0, 0], [4, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 4], [4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 4, 0, 0, 4, 4, 4, 4, 0, 0, 0], [4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 0, 0], [4, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0], [4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4], [0, 0, 4, 0, 0, 4, 0, 4, 4, 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 4, 4, 4, 4, 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 0], [0, 0, 4, 0, 0, 4, 4, 4, 0, 4, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4], [4, 0, 0, 4, 4, 0, 0, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 4, 4], [4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 4, 0], [0, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0], [4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 4, 0, 4, 0, 4, 4], [4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 4, 4, 0, 4, 0], [0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4], [0, 4, 0, 0, 0, 0, 4, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 0, 4]], "output": [[4, 0, 0, 4, 1, 1, 4, 4, 0, 0, 1, 1, 4, 4, 4, 1, 1, 1, 4, 0], [4, 4, 0, 4, 1, 1, 0, 4, 4, 4, 1, 0, 4, 0, 4, 1, 1, 4, 4, 0], [4, 0, 4, 4, 1, 4, 0, 0, 0, 4, 4, 0, 0, 4, 4, 1, 1, 1, 1, 4], [4, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 4, 0, 0, 4, 1, 4, 1, 4, 4], [4, 1, 1, 0, 1, 1, 0, 4, 1, 1, 1, 1, 4, 4, 4, 4, 4, 0, 4, 4], [1, 1, 4, 4, 1, 4, 4, 4, 1, 0, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1], [1, 1, 1, 1, 4, 0, 4, 0, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [4, 1, 1, 1, 4, 0, 4, 0, 4, 4, 1, 4, 1, 1, 4, 1, 1, 1, 4, 0], [0, 4, 1, 4, 0, 4, 4, 4, 4, 1, 1, 4, 1, 4, 4, 4, 4, 4, 1, 1], [4, 4, 4, 0, 4, 4, 0, 1, 1, 1, 1, 4, 1, 1, 4, 0, 0, 4, 1, 4], [4, 0, 1, 1, 4, 4, 4, 1, 1, 1, 4, 0, 1, 4, 4, 4, 4, 0, 1, 1], [4, 4, 1, 1, 1, 0, 4, 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 4, 1, 1], [4, 0, 1, 1, 4, 0, 4, 4, 1, 1, 0, 4, 0, 4, 0, 4, 4, 4, 1, 1], [4, 4, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 0, 4, 4, 0, 4, 4, 1, 4], [0, 0, 4, 1, 1, 4, 1, 4, 4, 4, 1, 1, 0, 4, 0, 0, 4, 4, 0, 4], [4, 4, 0, 4, 4, 4, 4, 4, 1, 1, 1, 4, 1, 1, 4, 4, 0, 0, 4, 0], [0, 0, 4, 0, 0, 4, 4, 4, 1, 4, 4, 4, 1, 4, 0, 4, 4, 1, 1, 4], [4, 1, 1, 4, 4, 0, 0, 4, 1, 1, 4, 4, 0, 4, 4, 0, 1, 1, 4, 4], [4, 1, 4, 0, 0, 4, 1, 1, 1, 4, 0, 4, 4, 0, 0, 4, 1, 4, 4, 0], [0, 4, 4, 4, 4, 4, 1, 4, 0, 4, 1, 1, 1, 4, 4, 0, 4, 0, 4, 4], [0, 0, 0, 0, 1, 1, 1, 0, 4, 4, 1, 1, 4, 0, 4, 0, 4, 1, 1, 0], [4, 4, 4, 4, 1, 1, 4, 1, 1, 1, 1, 4, 0, 4, 4, 0, 4, 1, 4, 4], [4, 4, 4, 0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 0, 4, 4, 0, 4, 0], [1, 1, 4, 4, 1, 4, 1, 1, 4, 4, 4, 0, 1, 1, 1, 4, 1, 1, 0, 4], [1, 4, 0, 0, 0, 0, 4, 4, 4, 0, 4, 4, 1, 1, 4, 4, 1, 4, 0, 4]]}], "input_grid": [[0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2], [2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0], [2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2], [0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0], [2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0], [0, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0], [0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0], [0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0], [2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2]], "task_key": "e5062a87"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 4, 1],\n[4, 4, 4],\n[4, 4, 4],\n[4, 4, 4]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 3, 4, 1, 0, 0, 0],\n[0, 0, 0, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 4, 4, 4, 0, 0, 0],\n[0, 0, 0, 4, 4, 4, 0, 0, 0],\n[3, 4, 1, 3, 4, 1, 3, 4, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[3, 4, 1, 3, 4, 1, 3, 4, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[3, 4, 1, 3, 4, 1, 3, 4, 1],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4],\n[4, 4, 4, 4, 4, 4, 4, 4, 4]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[5, 9, 3, 3],\n[3, 6, 9, 8],\n[3, 8, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 5, 9, 3, 3, 5, 9, 3, 3],\n[0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 9, 8, 3, 6, 9, 8],\n[0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 3, 3, 3, 8, 3, 3],\n[5, 9, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 6, 9, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[3, 8, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[5, 9, 3, 3, 0, 0, 0, 0, 5, 9, 3, 3, 5, 9, 3, 3],\n[3, 6, 9, 8, 0, 0, 0, 0, 3, 6, 9, 8, 3, 6, 9, 8],\n[3, 8, 3, 3, 0, 0, 0, 0, 3, 8, 3, 3, 3, 8, 3, 3]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[9, 9, 9],\n[5, 9, 5],\n[9, 9, 9],\n[9, 5, 5]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[5, 9, 5, 5, 9, 5, 5, 9, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 5, 5, 9, 5, 5, 9, 5, 5],\n[0, 0, 0, 9, 9, 9, 0, 0, 0],\n[0, 0, 0, 5, 9, 5, 0, 0, 0],\n[0, 0, 0, 9, 9, 9, 0, 0, 0],\n[0, 0, 0, 9, 5, 5, 0, 0, 0],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[5, 9, 5, 5, 9, 5, 5, 9, 5],\n[9, 9, 9, 9, 9, 9, 9, 9, 9],\n[9, 5, 5, 9, 5, 5, 9, 5, 5],\n[9, 9, 9, 0, 0, 0, 0, 0, 0],\n[5, 9, 5, 0, 0, 0, 0, 0, 0],\n[9, 9, 9, 0, 0, 0, 0, 0, 0],\n[9, 5, 5, 0, 0, 0, 0, 0, 0]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[2, 6, 6, 7, 4],\n[7, 7, 5, 7, 7],\n[3, 7, 7, 3, 7],\n[7, 1, 7, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 4, 1], [4, 4, 4], [4, 4, 4], [4, 4, 4]], "output": [[0, 0, 0, 3, 4, 1, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0], [0, 0, 0, 4, 4, 4, 0, 0, 0], [3, 4, 1, 3, 4, 1, 3, 4, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [3, 4, 1, 3, 4, 1, 3, 4, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [3, 4, 1, 3, 4, 1, 3, 4, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4]]}, {"input": [[5, 9, 3, 3], [3, 6, 9, 8], [3, 8, 3, 3]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 5, 9, 3, 3, 5, 9, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 9, 8, 3, 6, 9, 8], [0, 0, 0, 0, 0, 0, 0, 0, 3, 8, 3, 3, 3, 8, 3, 3], [5, 9, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 6, 9, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 8, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 9, 3, 3, 0, 0, 0, 0, 5, 9, 3, 3, 5, 9, 3, 3], [3, 6, 9, 8, 0, 0, 0, 0, 3, 6, 9, 8, 3, 6, 9, 8], [3, 8, 3, 3, 0, 0, 0, 0, 3, 8, 3, 3, 3, 8, 3, 3]]}, {"input": [[9, 9, 9], [5, 9, 5], [9, 9, 9], [9, 5, 5]], "output": [[9, 9, 9, 9, 9, 9, 9, 9, 9], [5, 9, 5, 5, 9, 5, 5, 9, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 5, 5, 9, 5, 5, 9, 5, 5], [0, 0, 0, 9, 9, 9, 0, 0, 0], [0, 0, 0, 5, 9, 5, 0, 0, 0], [0, 0, 0, 9, 9, 9, 0, 0, 0], [0, 0, 0, 9, 5, 5, 0, 0, 0], [9, 9, 9, 9, 9, 9, 9, 9, 9], [5, 9, 5, 5, 9, 5, 5, 9, 5], [9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 5, 5, 9, 5, 5, 9, 5, 5], [9, 9, 9, 0, 0, 0, 0, 0, 0], [5, 9, 5, 0, 0, 0, 0, 0, 0], [9, 9, 9, 0, 0, 0, 0, 0, 0], [9, 5, 5, 0, 0, 0, 0, 0, 0]]}], "input_grid": [[2, 6, 6, 7, 4], [7, 7, 5, 7, 7], [3, 7, 7, 3, 7], [7, 1, 7, 7, 7]], "task_key": "c3e719e8"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2],\n[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9],\n[6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9],\n[6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],\n[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3],\n[2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8],\n[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[3, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[7, 7, 7, 7],\n[2, 7, 7, 7],\n[7, 7, 7, 7],\n[2, 7, 7, 7]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2]]}, {"input": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]], "output": [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9], [6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]], "output": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8]]}], "input_grid": [[7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [3, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7, 7], [2, 7, 7, 7], [7, 7, 7, 7], [2, 7, 7, 7]], "task_key": "99fa7670"}}
{"data_source": "Arc", "prompt": "### **ARC Puzzle Simple Question Template**\n\n1. **Problem Description** \n - There is a logical relationship between the input and output grids. The goal is to deduce the rule and solve the test grid.\n\n2. **Example Explanation** \n- Example 1: \n **Input**: \n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0],\n[0, 0, 1, 0, 4, 4, 0, 0, 0, 0],\n[0, 0, 0, 5, 0, 4, 0, 0, 3, 0]\n]\n```\n\n- Example 2: \n **Input**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],\n[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]\n]\n```\n\n- Example 3: \n **Input**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n``` \n **Output**: \n```arcmatrix\n[\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],\n[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n]\n```\n\n3. **Test Grid** \n **Input**:\n```arcmatrix\n[\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 9, 0, 8, 0, 0, 0, 0],\n[2, 6, 0, 7, 0, 0, 0, 0, 0],\n[0, 7, 8, 6, 0, 0, 0, 0, 0],\n[9, 0, 0, 4, 5, 0, 0, 0, 0],\n[0, 1, 0, 0, 0, 0, 0, 0, 0],\n[3, 1, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0],\n[0, 0, 0, 0, 0, 0, 0, 0, 0]\n]\n```\n**Output**: \n?", "ground_truth": {"hint_examples": [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0], [0, 0, 1, 0, 4, 4, 0, 0, 0, 0], [0, 0, 0, 5, 0, 4, 0, 0, 3, 0]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]], "output": [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]}], "input_grid": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 0, 8, 0, 0, 0, 0], [2, 6, 0, 7, 0, 0, 0, 0, 0], [0, 7, 8, 6, 0, 0, 0, 0, 0], [9, 0, 0, 4, 5, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]], "task_key": "8eb1be9a"}}
Reference in a new issue View git blame Copy permalink