diff --git a/.gitignore b/.gitignore new file mode 100644 index 00000000..f7791536 --- /dev/null +++ b/.gitignore @@ -0,0 +1,223 @@ +.idea/ +data/ +checkpoints/ +wandb/ +uv.lock +.vscode/settings.json + +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[codz] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py.cover +.hypothesis/ +.pytest_cache/ +cover/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +.pybuilder/ +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +# For a library or package, you might want to ignore these files since the code is +# intended to run in multiple environments; otherwise, check them in: +# .python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +# Pipfile.lock + +# UV +# Similar to Pipfile.lock, it is generally recommended to include uv.lock in version control. +# This is especially recommended for binary packages to ensure reproducibility, and is more +# commonly ignored for libraries. +# uv.lock + +# poetry +# Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control. +# This is especially recommended for binary packages to ensure reproducibility, and is more +# commonly ignored for libraries. +# https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control +# poetry.lock +# poetry.toml + +# pdm +# Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control. +# pdm recommends including project-wide configuration in pdm.toml, but excluding .pdm-python. +# https://pdm-project.org/en/latest/usage/project/#working-with-version-control +# pdm.lock +# pdm.toml +.pdm-python +.pdm-build/ + +# pixi +# Similar to Pipfile.lock, it is generally recommended to include pixi.lock in version control. +# pixi.lock +# Pixi creates a virtual environment in the .pixi directory, just like venv module creates one +# in the .venv directory. It is recommended not to include this directory in version control. +.pixi + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# Redis +*.rdb +*.aof +*.pid + +# RabbitMQ +mnesia/ +rabbitmq/ +rabbitmq-data/ + +# ActiveMQ +activemq-data/ + +# SageMath parsed files +*.sage.py + +# Environments +.env +.envrc +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ + +# pytype static type analyzer +.pytype/ + +# Cython debug symbols +cython_debug/ + +# PyCharm +# JetBrains specific template is maintained in a separate JetBrains.gitignore that can +# be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore +# and can be added to the global gitignore or merged into this file. For a more nuclear +# option (not recommended) you can uncomment the following to ignore the entire idea folder. +# .idea/ + +# Abstra +# Abstra is an AI-powered process automation framework. +# Ignore directories containing user credentials, local state, and settings. +# Learn more at https://abstra.io/docs +.abstra/ + +# Visual Studio Code +# Visual Studio Code specific template is maintained in a separate VisualStudioCode.gitignore +# that can be found at https://github.com/github/gitignore/blob/main/Global/VisualStudioCode.gitignore +# and can be added to the global gitignore or merged into this file. However, if you prefer, +# you could uncomment the following to ignore the entire vscode folder +# .vscode/ + +# Ruff stuff: +.ruff_cache/ + +# PyPI configuration file +.pypirc + +# Marimo +marimo/_static/ +marimo/_lsp/ +__marimo__/ + +# Streamlit +.streamlit/secrets.toml diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml new file mode 100644 index 00000000..f1c9b3c9 --- /dev/null +++ b/.pre-commit-config.yaml @@ -0,0 +1,38 @@ +repos: +- repo: https://github.com/pre-commit/pre-commit-hooks + rev: v6.0.0 + hooks: + - id: trailing-whitespace # Trim trailing whitespace at the end of lines. + - id: end-of-file-fixer # Make sure files end in a newline and only a newline. + - id: check-added-large-files # Prevent giant files from being committed. + - id: check-case-conflict # Check for files that would conflict in case-insensitive filesystems. + - id: check-docstring-first # Check a common error of defining a docstring after code. + - id: check-merge-conflict # Check for files that contain merge conflict strings. + +- repo: https://github.com/PyCQA/flake8 + rev: 7.3.0 + hooks: + - id: flake8 # Check style and syntax. Does not modify code, issues have to be solved manually. + args: [ + '--ignore=E501,E203,W503,E402', # Ignore line length problems, space after colon problems, line break occurring before a binary operator problems, module level import not at top of file problems. + '--per-file-ignores=*/__init__.py:F401', # Ignore module imported but unused problems in __init__.py files. + ] + +- repo: https://github.com/pycqa/isort + rev: 6.1.0 + hooks: + - id: isort # Sort imports. + args: [ + --multi-line=3, + --line-length=100, + --trailing-comma, + --force-grid-wrap=0, + --use-parentheses, + --ensure-newline-before-comments, + ] + +- repo: https://github.com/psf/black-pre-commit-mirror + rev: 25.9.0 + hooks: + - id: black # Format code. + args: [--line-length=100] diff --git a/.python-version b/.python-version new file mode 100644 index 00000000..24ee5b1b --- /dev/null +++ b/.python-version @@ -0,0 +1 @@ +3.13 diff --git a/.vscode/launch.json b/.vscode/launch.json new file mode 100644 index 00000000..5c47e5dd --- /dev/null +++ b/.vscode/launch.json @@ -0,0 +1,40 @@ +{ + // Use IntelliSense to learn about possible attributes. + // Hover to view descriptions of existing attributes. + // For more information, visit: https://go.microsoft.com/fwlink/?linkid=830387 + "version": "0.2.0", + "configurations": [ + { + "name": "Pretrain Sudoku", + "type": "debugpy", + "request": "launch", + "module": "recursion.pretrain", + "python": "${workspaceFolder}/.venv/bin/python", + "cwd": "${workspaceFolder}", + "args": [ + "arch=trm", + "data_paths=[data/sudoku-extreme-1k-aug-1000]", + "evaluators=[]", + "epochs=50000", + "eval_interval=5000", + "lr=1e-4", + "global_batch_size=1", + "puzzle_emb_lr=1e-4", + "weight_decay=1.0", + "puzzle_emb_weight_decay=1.0", + "arch.mlp_t=True", + "arch.pos_encodings=none", + "arch.L_layers=2", + "arch.H_cycles=1", + "arch.L_cycles=1", + "+run_name=debug", + "ema=True" + ], + "console": "integratedTerminal", + "justMyCode": false, + "env": { + "DISABLE_COMPILE": "1" + } + } + ] +} diff --git a/LICENSE b/LICENSE index 654af602..b88a91d4 100644 --- a/LICENSE +++ b/LICENSE @@ -1,6 +1,7 @@ MIT License Copyright (c) 2025. Samsung Electronics Co., Ltd. All Rights Reserved. +Copyright (c) 2025. Simplex Lab, Matthieu Buot de l'Epine, Pierre Quinton, Valérian Rey. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal @@ -18,4 +19,4 @@ FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. \ No newline at end of file +SOFTWARE. diff --git a/README.md b/README.md index decab5fa..d2572b77 100644 --- a/README.md +++ b/README.md @@ -1,50 +1,52 @@ -# Less is More: Recursive Reasoning with Tiny Networks +# Recursion -This is the codebase for the paper: "Less is More: Recursive Reasoning with Tiny Networks". TRM is a recursive reasoning approach that achieves amazing scores of 45% on ARC-AGI-1 and 8% on ARC-AGI-2 using a tiny 7M parameters neural network. +This repo contains experiments with the goal of finding new and better ways to train RNNs, and / or +new recurrent architectures for modern AI problems. -[Paper](https://arxiv.org/abs/2510.04871) +It is based on the [TRM repo](https://github.com/SamsungSAILMontreal/TinyRecursiveModels). -### Motivation +Recommendations: +- Using `uv`: https://docs.astral.sh/uv/ +- Using `pyenv` to manage python versions: https://github.com/pyenv/pyenv -Tiny Recursion Model (TRM) is a recursive reasoning model that achieves amazing scores of 45% on ARC-AGI-1 and 8% on ARC-AGI-2 with a tiny 7M parameters neural network. The idea that one must rely on massive foundational models trained for millions of dollars by some big corporation in order to achieve success on hard tasks is a trap. Currently, there is too much focus on exploiting LLMs rather than devising and expanding new lines of direction. With recursive reasoning, it turns out that “less is more”: you don’t always need to crank up model size in order for a model to reason and solve hard problems. A tiny model pretrained from scratch, recursing on itself and updating its answers over time, can achieve a lot without breaking the bank. - -This work came to be after I learned about the recent innovative Hierarchical Reasoning Model (HRM). I was amazed that an approach using small models could do so well on hard tasks like the ARC-AGI competition (reaching 40% accuracy when normally only Large Language Models could compete). But I kept thinking that it is too complicated, relying too much on biological arguments about the human brain, and that this recursive reasoning process could be greatly simplified and improved. Tiny Recursion Model (TRM) simplifies recursive reasoning to its core essence, which ultimately has nothing to do with the human brain, does not require any mathematical (fixed-point) theorem, nor any hierarchy. - -### How TRM works - -

- TRM -

- -Tiny Recursion Model (TRM) recursively improves its predicted answer y with a tiny network. It starts with the embedded input question x and initial embedded answer y and latent z. For up to K improvements steps, it tries to improve its answer y. It does so by i) recursively updating n times its latent z given the question x, current answer y, and current latent z (recursive reasoning), and then ii) updating its answer y given the current answer y and current latent z. This recursive process allows the model to progressively improve its answer (potentially addressing any errors from its previous answer) in an extremely parameter-efficient manner while minimizing overfitting. - -### Requirements +Standard install (no GPU or majority of recent Nvidia GPUs): +```bash +uv venv +uv pip install -e . +uv run pre-commit install +``` -Installation should take a few minutes. For the smallest experiments on Sudoku-Extreme (pretrain_mlp_t_sudoku), you need 1 GPU with enough memory. With 1 L40S (48Gb Ram), it takes around 18h to finish. In case that you run into issues due to library versions, here is the requirements with the exact versions used: [specific_requirements.txt](https://github.com/SamsungSAILMontreal/TinyRecursiveModels/blob/main/specific_requirements.txt). +With Nvidia GH200 GPU (need to force CUDA version to be 12.8): +```bash +uv venv +uv pip install -e . --index-strategy unsafe-best-match --extra-index-url https://download.pytorch.org/whl/cu128 +uv run pre-commit install +``` -- Python 3.10 (or similar) -- Cuda 12.6.0 (or similar) +With Nvidia GTX 1080 GPU (need to force CUDA version to be 12.6): +```bash +uv venv +uv pip install -e . --index-strategy unsafe-best-match --extra-index-url https://download.pytorch.org/whl/cu126 +uv run pre-commit install +``` +If you want the logger to sync results to your Weights & Biases (https://wandb.ai/): ```bash -pip install --upgrade pip wheel setuptools -pip install --pre --upgrade torch torchvision torchaudio --index-url https://download.pytorch.org/whl/nightly/cu126 # install torch based on your cuda version -pip install -r requirements.txt # install requirements -pip install --no-cache-dir --no-build-isolation adam-atan2 -wandb login YOUR-LOGIN # login if you want the logger to sync results to your Weights & Biases (https://wandb.ai/) +wandb login YOUR-LOGIN ``` ### Dataset Preparation ```bash # ARC-AGI-1 -python -m dataset.build_arc_dataset \ +uv run python -m recursion.dataset.build_arc_dataset \ --input-file-prefix kaggle/combined/arc-agi \ --output-dir data/arc1concept-aug-1000 \ --subsets training evaluation concept \ --test-set-name evaluation # ARC-AGI-2 -python -m dataset.build_arc_dataset \ +uv run python -m recursion.dataset.build_arc_dataset \ --input-file-prefix kaggle/combined/arc-agi \ --output-dir data/arc2concept-aug-1000 \ --subsets training2 evaluation2 concept \ @@ -53,19 +55,22 @@ python -m dataset.build_arc_dataset \ ## Note: You cannot train on both ARC-AGI-1 and ARC-AGI-2 and evaluate them both because ARC-AGI-2 training data contains some ARC-AGI-1 eval data # Sudoku-Extreme -python dataset/build_sudoku_dataset.py --output-dir data/sudoku-extreme-1k-aug-1000 --subsample-size 1000 --num-aug 1000 # 1000 examples, 1000 augments +uv run python -m recursion.dataset.build_sudoku_dataset --output-dir data/sudoku-extreme-1k-aug-1000 --subsample-size 1000 --num-aug 1000 # 1000 examples, 1000 augments # Maze-Hard -python dataset/build_maze_dataset.py # 1000 examples, 8 augments +uv run python -m recursion.dataset.build_maze_dataset # 1000 examples, 8 augments ``` ## Experiments +If using a GPU that is too old for Triton (CUDA Capability < 7.0, like NVIDIA GeForce GTX 1080), add +`DISABLE_COMPILE=1` before the following commands. + ### Sudoku-Extreme (assuming 1 L40S GPU): ```bash run_name="pretrain_mlp_t_sudoku" -python pretrain.py \ +uv run python -m recursion.pretrain \ arch=trm \ data_paths="[data/sudoku-extreme-1k-aug-1000]" \ evaluators="[]" \ @@ -75,11 +80,13 @@ arch.mlp_t=True arch.pos_encodings=none \ arch.L_layers=2 \ arch.H_cycles=3 arch.L_cycles=6 \ +run_name=${run_name} ema=True +``` Expected: Around 87% exact-accuracy (+- 2%) +```bash run_name="pretrain_att_sudoku" -python pretrain.py \ +uv run python recursion.pretrain \ arch=trm \ data_paths="[data/sudoku-extreme-1k-aug-1000]" \ evaluators="[]" \ @@ -98,7 +105,7 @@ Expected: Around 75% exact-accuracy (+- 2%) ```bash run_name="pretrain_att_maze30x30" -torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 pretrain.py \ +uv run torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 src/recursion/pretrain.py \ arch=trm \ data_paths="[data/maze-30x30-hard-1k]" \ evaluators="[]" \ @@ -115,7 +122,7 @@ Actually, you can run Maze-Hard with 1 L40S GPU by reducing the batch-size with ```bash run_name="pretrain_att_maze30x30_1gpu" -python pretrain.py \ +uv run python -m pretrain \ arch=trm \ data_paths="[data/maze-30x30-hard-1k]" \ evaluators="[]" \ @@ -133,7 +140,7 @@ arch.H_cycles=3 arch.L_cycles=4 \ ```bash run_name="pretrain_att_arc1concept_4" -torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 pretrain.py \ +uv run torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 src/recursion/pretrain.py \ arch=trm \ data_paths="[data/arc1concept-aug-1000]" \ arch.L_layers=2 \ @@ -148,7 +155,7 @@ arch.H_cycles=3 arch.L_cycles=4 \ ```bash run_name="pretrain_att_arc2concept_4" -torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 pretrain.py \ +uv run torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 src/recursion/pretrain.py \ arch=trm \ data_paths="[data/arc2concept-aug-1000]" \ arch.L_layers=2 \ @@ -158,36 +165,3 @@ arch.H_cycles=3 arch.L_cycles=4 \ ``` *Runtime:* ~3 days - - -## Reference - -If you find our work useful, please consider citing: - -```bibtex -@misc{jolicoeurmartineau2025morerecursivereasoningtiny, - title={Less is More: Recursive Reasoning with Tiny Networks}, - author={Alexia Jolicoeur-Martineau}, - year={2025}, - eprint={2510.04871}, - archivePrefix={arXiv}, - primaryClass={cs.LG}, - url={https://arxiv.org/abs/2510.04871}, -} -``` - -and the Hierarchical Reasoning Model (HRM): - -```bibtex -@misc{wang2025hierarchicalreasoningmodel, - title={Hierarchical Reasoning Model}, - author={Guan Wang and Jin Li and Yuhao Sun and Xing Chen and Changling Liu and Yue Wu and Meng Lu and Sen Song and Yasin Abbasi Yadkori}, - year={2025}, - eprint={2506.21734}, - archivePrefix={arXiv}, - primaryClass={cs.AI}, - url={https://arxiv.org/abs/2506.21734}, -} -``` - -This code is based on the Hierarchical Reasoning Model [code](https://github.com/sapientinc/HRM) and the Hierarchical Reasoning Model Analysis [code](https://github.com/arcprize/hierarchical-reasoning-model-analysis). diff --git a/assets/TRM_fig.png b/assets/TRM_fig.png deleted file mode 100644 index b97c56aa..00000000 Binary files a/assets/TRM_fig.png and /dev/null differ diff --git a/assets/TRM_pseudocode.png b/assets/TRM_pseudocode.png deleted file mode 100644 index c932c5b5..00000000 Binary files a/assets/TRM_pseudocode.png and /dev/null differ diff --git a/config/arch/hrm.yaml b/config/arch/hrm.yaml index 0d183bed..19cf88f7 100644 --- a/config/arch/hrm.yaml +++ b/config/arch/hrm.yaml @@ -21,4 +21,4 @@ puzzle_emb_ndim: ${.hidden_size} pos_encodings: rope forward_dtype: bfloat16 -mlp_t: False # use mlp on L instead of transformer \ No newline at end of file +mlp_t: False # use mlp on L instead of transformer diff --git a/config/arch/transformers_baseline.yaml b/config/arch/transformers_baseline.yaml index cc08ffee..7e5cc66b 100644 --- a/config/arch/transformers_baseline.yaml +++ b/config/arch/transformers_baseline.yaml @@ -7,12 +7,12 @@ halt_exploration_prob: 0.1 halt_max_steps: 16 H_cycles: 1 # kept for compatibility -H_layers: 8 +H_layers: 8 -hidden_size: 512 +hidden_size: 512 num_heads: 12 expansion: 4 puzzle_emb_ndim: ${.hidden_size} -pos_encodings: rope \ No newline at end of file +pos_encodings: rope diff --git a/config/arch/trm.yaml b/config/arch/trm.yaml index e6b16fb8..041519b8 100644 --- a/config/arch/trm.yaml +++ b/config/arch/trm.yaml @@ -23,4 +23,4 @@ forward_dtype: bfloat16 mlp_t: False # use mlp on L instead of transformer puzzle_emb_len: 16 # if non-zero, its specified to this value -no_ACT_continue: True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense \ No newline at end of file +no_ACT_continue: True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense diff --git a/config/arch/trm_hier6.yaml b/config/arch/trm_hier6.yaml index 43622ec7..2f7711d1 100644 --- a/config/arch/trm_hier6.yaml +++ b/config/arch/trm_hier6.yaml @@ -23,4 +23,4 @@ forward_dtype: bfloat16 mlp_t: False # use mlp on L instead of transformer puzzle_emb_len: 16 # if non-zero, its specified to this value -no_ACT_continue: True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense \ No newline at end of file +no_ACT_continue: True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense diff --git a/config/arch/trm_singlez.yaml b/config/arch/trm_singlez.yaml index cf16aa5d..fac5d1e5 100644 --- a/config/arch/trm_singlez.yaml +++ b/config/arch/trm_singlez.yaml @@ -23,4 +23,4 @@ forward_dtype: bfloat16 mlp_t: False # use mlp on L instead of transformer puzzle_emb_len: 16 # if non-zero, its specified to this value -no_ACT_continue: True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense \ No newline at end of file +no_ACT_continue: True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense diff --git a/config/cfg_pretrain.yaml b/config/cfg_pretrain.yaml index ec45faf5..8d752970 100644 --- a/config/cfg_pretrain.yaml +++ b/config/cfg_pretrain.yaml @@ -39,4 +39,4 @@ min_eval_interval: 0 # when to start the eval ema: False # use Exponential-Moving-Average ema_rate: 0.999 # EMA-rate -freeze_weights: False # If True, freeze weights and only learn the embeddings \ No newline at end of file +freeze_weights: False # If True, freeze weights and only learn the embeddings diff --git a/kaggle/combined/arc-agi_concept_challenges.json b/kaggle/combined/arc-agi_concept_challenges.json index 8ec9df7f..fb59040e 100644 --- a/kaggle/combined/arc-agi_concept_challenges.json +++ b/kaggle/combined/arc-agi_concept_challenges.json @@ -3,39 +3,39 @@ "train": [ { "input": [ - [1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2], - [1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2], - [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], - [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], - [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], - [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], - [3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2], + [1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2], + [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], + [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], + [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], + [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], + [3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1], [3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1] ], "output": [ - [3, 3, 3, 2, 2], - [3, 3, 3, 2, 2], - [3, 3, 3, 3, 3], + [3, 3, 3, 2, 2], + [3, 3, 3, 2, 2], + [3, 3, 3, 3, 3], [3, 3, 3, 3, 3] ] }, { "input": [ - [0, 0, 5, 5, 5, 5, 0, 0], - [0, 0, 5, 3, 3, 5, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 5, 5, 5, 5, 0, 0], - [0, 0, 5, 3, 3, 5, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 5, 5, 5, 5, 0, 0], - [0, 0, 5, 3, 3, 5, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 5, 5, 5, 5, 0, 0], + [0, 0, 5, 3, 3, 5, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 5, 5, 5, 5, 0, 0], + [0, 0, 5, 3, 3, 5, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 5, 5, 5, 5, 0, 0], + [0, 0, 5, 3, 3, 5, 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, 5, 5], [5, 3, 3, 5] ] } @@ -43,40 +43,40 @@ "test": [ { "input": [ - [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], - [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], - [8, 8, 8, 8, 8, 7, 7, 4, 7, 7, 8, 8, 8, 8, 8], - [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], - [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], - [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], - [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], - [7, 7, 4, 7, 7, 8, 8, 8, 8, 8, 7, 7, 4, 7, 7], - [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], + [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], + [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], + [8, 8, 8, 8, 8, 7, 7, 4, 7, 7, 8, 8, 8, 8, 8], + [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], + [8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8], + [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], + [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], + [7, 7, 4, 7, 7, 8, 8, 8, 8, 8, 7, 7, 4, 7, 7], + [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7] ] }, { "input": [ - [6, 1, 6, 4, 4, 4], - [6, 6, 1, 4, 4, 4], - [6, 6, 1, 4, 4, 4], - [4, 4, 4, 6, 1, 6], - [4, 4, 4, 6, 6, 1], - [4, 4, 4, 6, 6, 1], - [6, 1, 6, 4, 4, 4], - [6, 6, 1, 4, 4, 4], + [6, 1, 6, 4, 4, 4], + [6, 6, 1, 4, 4, 4], + [6, 6, 1, 4, 4, 4], + [4, 4, 4, 6, 1, 6], + [4, 4, 4, 6, 6, 1], + [4, 4, 4, 6, 6, 1], + [6, 1, 6, 4, 4, 4], + [6, 6, 1, 4, 4, 4], [6, 6, 1, 4, 4, 4] ] }, { "input": [ - [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], - [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], - [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], - [5, 5, 5, 1, 9, 1, 5, 5, 5, 1, 9, 1], - [5, 5, 5, 1, 9, 1, 5, 5, 5, 1, 9, 1], - [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], - [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], + [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], + [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], + [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], + [5, 5, 5, 1, 9, 1, 5, 5, 5, 1, 9, 1], + [5, 5, 5, 1, 9, 1, 5, 5, 5, 1, 9, 1], + [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], + [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1], [5, 5, 5, 1, 1, 1, 5, 5, 5, 1, 1, 1] ] } @@ -86,51 +86,51 @@ "train": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], - [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 4, 4, 4, 4, 0], - [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 0, 0, 0, 4, 0], - [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 0, 0, 0, 4, 0], - [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 0, 0, 0, 4, 0], - [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 4, 4, 4, 4, 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, 0], + [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 4, 4, 4, 4, 0], + [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 0, 0, 0, 4, 0], + [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 0, 0, 0, 4, 0], + [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 0, 0, 0, 4, 0], + [0, 1, 1, 1, 1, 1, 0, 3, 0, 4, 4, 4, 4, 4, 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, 0] ], "output": [ - [1, 1, 1, 1, 1, 4, 4, 4, 4, 4], - [1, 1, 1, 1, 1, 4, 0, 0, 0, 4], - [1, 1, 1, 1, 1, 4, 0, 0, 0, 4], - [1, 1, 1, 1, 1, 4, 0, 0, 0, 4], + [1, 1, 1, 1, 1, 4, 4, 4, 4, 4], + [1, 1, 1, 1, 1, 4, 0, 0, 0, 4], + [1, 1, 1, 1, 1, 4, 0, 0, 0, 4], + [1, 1, 1, 1, 1, 4, 0, 0, 0, 4], [1, 1, 1, 1, 1, 4, 4, 4, 4, 4] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 3, 0, 0, 0], - [0, 0, 3, 0, 3, 0, 0], - [0, 3, 0, 0, 0, 3, 0], - [0, 0, 3, 0, 3, 0, 0], - [0, 0, 0, 3, 0, 0, 0], - [6, 6, 6, 6, 6, 6, 6], - [6, 6, 6, 6, 6, 6, 6], - [0, 0, 0, 0, 0, 0, 0], - [0, 0, 5, 5, 5, 5, 5], - [0, 0, 5, 5, 5, 5, 5], - [0, 0, 5, 5, 5, 5, 5], - [0, 0, 5, 5, 5, 5, 5], - [0, 0, 5, 5, 5, 5, 5], + [0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 3, 0, 0, 0], + [0, 0, 3, 0, 3, 0, 0], + [0, 3, 0, 0, 0, 3, 0], + [0, 0, 3, 0, 3, 0, 0], + [0, 0, 0, 3, 0, 0, 0], + [6, 6, 6, 6, 6, 6, 6], + [6, 6, 6, 6, 6, 6, 6], + [0, 0, 0, 0, 0, 0, 0], + [0, 0, 5, 5, 5, 5, 5], + [0, 0, 5, 5, 5, 5, 5], + [0, 0, 5, 5, 5, 5, 5], + [0, 0, 5, 5, 5, 5, 5], + [0, 0, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0, 0] ], "output": [ - [0, 0, 3, 0, 0], - [0, 3, 0, 3, 0], - [3, 0, 0, 0, 3], - [0, 3, 0, 3, 0], - [0, 0, 3, 0, 0], - [5, 5, 5, 5, 5], - [5, 5, 5, 5, 5], - [5, 5, 5, 5, 5], - [5, 5, 5, 5, 5], + [0, 0, 3, 0, 0], + [0, 3, 0, 3, 0], + [3, 0, 0, 0, 3], + [0, 3, 0, 3, 0], + [0, 0, 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] ] } @@ -138,44 +138,44 @@ "test": [ { "input": [ - [0, 7, 7, 0, 0], - [0, 7, 7, 0, 0], - [0, 0, 0, 0, 0], - [8, 8, 8, 8, 8], - [0, 0, 0, 0, 0], - [0, 0, 0, 0, 0], - [0, 0, 2, 2, 0], - [0, 0, 2, 2, 0], - [0, 0, 0, 0, 0], + [0, 7, 7, 0, 0], + [0, 7, 7, 0, 0], + [0, 0, 0, 0, 0], + [8, 8, 8, 8, 8], + [0, 0, 0, 0, 0], + [0, 0, 0, 0, 0], + [0, 0, 2, 2, 0], + [0, 0, 2, 2, 0], + [0, 0, 0, 0, 0], [0, 0, 0, 0, 0] ] }, { "input": [ - [0, 0, 0, 0, 0, 5, 5, 0, 3, 3, 3, 3], - [1, 1, 1, 1, 0, 5, 5, 0, 3, 0, 0, 3], - [1, 0, 0, 1, 0, 5, 5, 0, 3, 0, 0, 3], - [1, 0, 0, 1, 0, 5, 5, 0, 3, 3, 3, 3], - [1, 1, 1, 1, 0, 5, 5, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 5, 5, 0, 3, 3, 3, 3], + [1, 1, 1, 1, 0, 5, 5, 0, 3, 0, 0, 3], + [1, 0, 0, 1, 0, 5, 5, 0, 3, 0, 0, 3], + [1, 0, 0, 1, 0, 5, 5, 0, 3, 3, 3, 3], + [1, 1, 1, 1, 0, 5, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0] ] }, { "input": [ - [0, 0, 0, 0, 0, 0], - [0, 6, 6, 6, 6, 0], - [0, 6, 6, 6, 6, 0], - [0, 6, 6, 6, 6, 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, 6, 6, 6, 6, 0], - [0, 6, 6, 6, 6, 0], - [0, 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, 6, 6, 6, 6, 0], + [0, 6, 6, 6, 6, 0], + [0, 6, 6, 6, 6, 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, 6, 6, 6, 6, 0], + [0, 6, 6, 6, 6, 0], + [0, 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] ] } @@ -185,46 +185,46 @@ "train": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], - [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], - [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], - [0, 2, 4, 2, 2, 2, 2, 4, 2, 0], - [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], - [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], - [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], - [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], - [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], - [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], - [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], + [0, 2, 4, 2, 2, 2, 2, 4, 2, 0], + [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], + [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], + [0, 2, 4, 4, 4, 4, 4, 4, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ - [4, 4, 4, 4, 4, 4], - [4, 0, 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, 0, 4], + [4, 4, 4, 4, 4, 4], + [4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4] ] }, { "input": [ - [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, 0, 0], - [0, 0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 0, 0], - [0, 0, 0, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 0, 0], - [0, 0, 0, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 0, 0], - [0, 0, 0, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 0, 0], - [0, 0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 0, 0], - [0, 0, 0, 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, 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, 0, 0], + [0, 0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 0, 0], + [0, 0, 0, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 0, 0], + [0, 0, 0, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 0, 0], + [0, 0, 0, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 0, 0], + [0, 0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 0, 0], + [0, 0, 0, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ - [2, 2, 2, 2], - [2, 0, 2, 2], - [2, 0, 0, 0], - [2, 0, 0, 0], + [2, 2, 2, 2], + [2, 0, 2, 2], + [2, 0, 0, 0], + [2, 0, 0, 0], [2, 2, 2, 2] ] } @@ -232,45 +232,45 @@ "test": [ { "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, 5, 5, 5, 5, 5, 5, 5, 0, 0], - [0, 0, 0, 5, 7, 7, 7, 7, 7, 5, 0, 0], - [0, 0, 0, 5, 7, 7, 5, 7, 7, 5, 0, 0], - [0, 0, 0, 5, 7, 5, 5, 5, 7, 5, 0, 0], - [0, 0, 0, 5, 7, 7, 7, 7, 7, 5, 0, 0], - [0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 0, 0], + [0, 0, 0, 5, 7, 7, 7, 7, 7, 5, 0, 0], + [0, 0, 0, 5, 7, 7, 5, 7, 7, 5, 0, 0], + [0, 0, 0, 5, 7, 5, 5, 5, 7, 5, 0, 0], + [0, 0, 0, 5, 7, 7, 7, 7, 7, 5, 0, 0], + [0, 0, 0, 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] ] }, { "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, 7, 7, 7, 7, 7, 7, 7, 7, 0], - [0, 7, 7, 1, 7, 7, 7, 1, 7, 0], - [0, 7, 7, 1, 1, 1, 1, 1, 7, 0], - [0, 7, 7, 1, 1, 7, 1, 1, 7, 0], - [0, 7, 7, 7, 1, 1, 1, 7, 7, 0], - [0, 7, 7, 7, 7, 7, 7, 7, 7, 0], - [0, 7, 7, 7, 7, 7, 7, 7, 7, 0], - [0, 7, 7, 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, 0, 0, 0, 0, 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, 7, 7, 7, 0], + [0, 7, 7, 1, 7, 7, 7, 1, 7, 0], + [0, 7, 7, 1, 1, 1, 1, 1, 7, 0], + [0, 7, 7, 1, 1, 7, 1, 1, 7, 0], + [0, 7, 7, 7, 1, 1, 1, 7, 7, 0], + [0, 7, 7, 7, 7, 7, 7, 7, 7, 0], + [0, 7, 7, 7, 7, 7, 7, 7, 7, 0], + [0, 7, 7, 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, 0, 0, 0, 0, 0, 0, 0] ] }, { "input": [ - [0, 9, 9, 9, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], - [0, 9, 9, 8, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], - [0, 9, 8, 8, 8, 8, 8, 8, 8, 9, 0, 0, 0, 0], - [0, 9, 9, 8, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], - [0, 9, 9, 9, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], + [0, 9, 9, 9, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], + [0, 9, 9, 8, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], + [0, 9, 8, 8, 8, 8, 8, 8, 8, 9, 0, 0, 0, 0], + [0, 9, 9, 8, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], + [0, 9, 9, 9, 8, 9, 9, 9, 9, 9, 0, 0, 0, 0], [0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0] ] } @@ -280,67 +280,67 @@ "train": [ { "input": [ - [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, 2, 2], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 2, 2, 2, 2, 2, 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2, 2], + [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, 2, 2], + [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, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "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] ] }, { "input": [ - [0, 0, 0, 0, 0, 0], - [6, 6, 6, 6, 6, 6], - [0, 0, 0, 0, 0, 0], - [6, 6, 6, 6, 6, 6], - [0, 6, 6, 6, 6, 0], - [6, 6, 6, 6, 6, 6], - [0, 6, 6, 6, 6, 0], - [6, 6, 6, 6, 6, 6], - [0, 0, 0, 0, 0, 0], - [6, 6, 6, 6, 6, 6], - [0, 0, 0, 0, 0, 0], - [6, 6, 6, 6, 6, 6], - [0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0], + [6, 6, 6, 6, 6, 6], + [0, 0, 0, 0, 0, 0], + [6, 6, 6, 6, 6, 6], + [0, 6, 6, 6, 6, 0], + [6, 6, 6, 6, 6, 6], + [0, 6, 6, 6, 6, 0], + [6, 6, 6, 6, 6, 6], + [0, 0, 0, 0, 0, 0], + [6, 6, 6, 6, 6, 6], + [0, 0, 0, 0, 0, 0], + [6, 6, 6, 6, 6, 6], 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3, 0], - [3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0], - [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0], - [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0], - [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0], + [3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0], + [3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0], + [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0], + [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0], + [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0], [3, 0, 3, 3, 3, 3, 3, 0, 3, 0, 3, 0, 3, 0] ] } @@ -387,62 +387,62 @@ "train": [ { "input": [ - [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, 3, 3, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 3, 0, 3, 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, 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, 3, 3, 3, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 3, 0, 3, 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, 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] ], "output": [ - [3, 3, 3], - [0, 0, 3], - [0, 0, 3], - [0, 0, 3], + [3, 3, 3], + [0, 0, 3], + [0, 0, 3], + [0, 0, 3], [0, 0, 3] ] }, { "input": [ - [0, 4, 4, 0, 0, 0, 0, 0, 0, 0], - [4, 4, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 0, 0, 0, 0, 0, 0, 0, 0, 4], - [0, 0, 0, 4, 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, 4, 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], + [4, 4, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 0, 0, 0, 0, 0, 0, 0, 0, 4], + [0, 0, 0, 4, 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, 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, 4, 0, 0] ], "output": [ - [0, 4, 4], - [4, 4, 0], - [4, 0, 0], + [0, 4, 4], + [4, 4, 0], + [4, 0, 0], [4, 0, 0] ] }, { "input": [ - [0, 0, 0, 6, 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, 6, 6, 6, 6, 0, 0, 0, 0, 0], - [0, 6, 0, 0, 6, 6, 6, 6, 0, 0], - [0, 6, 0, 0, 6, 0, 0, 0, 0, 0], - [0, 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, 6, 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, 6, 6, 6, 6, 0, 0, 0, 0, 0], + [0, 6, 0, 0, 6, 6, 6, 6, 0, 0], + [0, 6, 0, 0, 6, 0, 0, 0, 0, 0], + [0, 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], [6, 0, 0, 6, 0, 0, 0, 0, 0, 0] ], "output": [ - [6, 6, 6, 6, 0, 0, 0], - [6, 0, 0, 6, 6, 6, 6], - [6, 0, 0, 6, 0, 0, 0], + [6, 6, 6, 6, 0, 0, 0], + [6, 0, 0, 6, 6, 6, 6], + [6, 0, 0, 6, 0, 0, 0], [6, 6, 6, 6, 0, 0, 0] ] } @@ -450,43 +450,43 @@ "test": [ { "input": [ - [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [8, 8, 8, 8, 8, 8, 8, 0, 0, 0], - [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 8, 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, 8, 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], + [8, 8, 8, 8, 8, 8, 8, 0, 0, 0], + [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 8, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 8, 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, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] }, { "input": [ - [0, 2, 0, 0, 0, 0, 0, 2, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 2, 2, 2, 2, 2, 0, 2], - [0, 0, 0, 2, 0, 0, 0, 2, 0, 0], - [0, 0, 0, 2, 0, 0, 0, 2, 0, 0], - [0, 0, 0, 2, 0, 0, 0, 2, 0, 0], - [0, 2, 0, 2, 2, 2, 2, 2, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 2, 2, 0, 0, 0, 0], + [0, 2, 0, 0, 0, 0, 0, 2, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 2, 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4, 0, 4], + [4, 4, 4, 4, 4, 4, 0, 4, 4, 0, 4], + [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4] ], "output": [ - [0, 4, 0, 4, 4], - [4, 4, 4, 4, 4], + [0, 4, 0, 4, 4], + [4, 4, 4, 4, 4], [0, 4, 0, 4, 4] ] } @@ -637,40 +637,40 @@ "test": [ { "input": [ - [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], - [6, 6, 6, 0, 0, 0, 0, 6, 6, 6, 6], - [6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6], - [6, 0, 6, 6, 6, 6, 6, 6, 0, 6, 6], - [6, 6, 0, 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, 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, 0, 6, 6, 6, 6, 0, 6, 6, 6], + [6, 0, 6, 6, 6, 6, 6, 6, 0, 6, 6], + [6, 6, 0, 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, 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, 0, 1, 1, 1, 1, 1, 1, 1], - [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1], - [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1], - [1, 1, 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5, 5], + [5, 0, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5], + [5, 0, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5], + [5, 0, 5, 5, 5, 0, 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, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5] ] } @@ -680,47 +680,47 @@ "train": [ { "input": [ - [0, 0, 0, 6, 0, 0, 0, 4, 5, 3, 3, 3, 3, 5, 5], - [0, 0, 6, 0, 6, 0, 0, 4, 5, 3, 5, 5, 3, 5, 5], - [0, 6, 0, 0, 0, 6, 0, 4, 5, 3, 5, 5, 3, 5, 5], - [6, 0, 0, 0, 0, 0, 6, 4, 5, 3, 5, 5, 3, 5, 5], - [0, 6, 0, 0, 0, 6, 0, 4, 5, 3, 5, 5, 3, 5, 5], - [0, 0, 6, 0, 6, 0, 0, 4, 5, 3, 5, 5, 3, 5, 5], + [0, 0, 0, 6, 0, 0, 0, 4, 5, 3, 3, 3, 3, 5, 5], + [0, 0, 6, 0, 6, 0, 0, 4, 5, 3, 5, 5, 3, 5, 5], + [0, 6, 0, 0, 0, 6, 0, 4, 5, 3, 5, 5, 3, 5, 5], + [6, 0, 0, 0, 0, 0, 6, 4, 5, 3, 5, 5, 3, 5, 5], + [0, 6, 0, 0, 0, 6, 0, 4, 5, 3, 5, 5, 3, 5, 5], + [0, 0, 6, 0, 6, 0, 0, 4, 5, 3, 5, 5, 3, 5, 5], [0, 0, 0, 6, 0, 0, 0, 4, 5, 3, 3, 3, 3, 5, 5] ], "output": [ - [0, 0, 0, 6, 0, 0, 0, 3, 3, 3, 3], - [0, 0, 6, 0, 6, 0, 0, 3, 0, 0, 3], - [0, 6, 0, 0, 0, 6, 0, 3, 0, 0, 3], - [6, 0, 0, 0, 0, 0, 6, 3, 0, 0, 3], - [0, 6, 0, 0, 0, 6, 0, 3, 0, 0, 3], - [0, 0, 6, 0, 6, 0, 0, 3, 0, 0, 3], + [0, 0, 0, 6, 0, 0, 0, 3, 3, 3, 3], + [0, 0, 6, 0, 6, 0, 0, 3, 0, 0, 3], + [0, 6, 0, 0, 0, 6, 0, 3, 0, 0, 3], + [6, 0, 0, 0, 0, 0, 6, 3, 0, 0, 3], + [0, 6, 0, 0, 0, 6, 0, 3, 0, 0, 3], + [0, 0, 6, 0, 6, 0, 0, 3, 0, 0, 3], [0, 0, 0, 6, 0, 0, 0, 3, 3, 3, 3] ] }, { "input": [ - [7, 7, 7, 7, 7, 7, 7, 7], - [7, 7, 7, 2, 7, 7, 7, 7], - [7, 7, 7, 2, 7, 7, 7, 7], - [7, 7, 7, 2, 7, 7, 7, 7], - [7, 2, 2, 2, 2, 2, 7, 7], - [7, 7, 7, 7, 7, 7, 7, 7], - [7, 7, 7, 7, 7, 7, 7, 7], - [4, 4, 4, 4, 4, 4, 4, 4], - [8, 8, 8, 3, 8, 8, 8, 8], - [8, 8, 3, 3, 3, 8, 8, 8], - [8, 8, 8, 3, 8, 8, 8, 8], - [8, 8, 8, 8, 8, 8, 8, 8], + [7, 7, 7, 7, 7, 7, 7, 7], + [7, 7, 7, 2, 7, 7, 7, 7], + [7, 7, 7, 2, 7, 7, 7, 7], + [7, 7, 7, 2, 7, 7, 7, 7], + [7, 2, 2, 2, 2, 2, 7, 7], + [7, 7, 7, 7, 7, 7, 7, 7], + [7, 7, 7, 7, 7, 7, 7, 7], + [4, 4, 4, 4, 4, 4, 4, 4], + [8, 8, 8, 3, 8, 8, 8, 8], + [8, 8, 3, 3, 3, 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] ], "output": [ - [0, 0, 2, 0, 0], - [0, 0, 2, 0, 0], - [0, 0, 2, 0, 0], - [2, 2, 2, 2, 2], - [0, 0, 3, 0, 0], - [0, 3, 3, 3, 0], + [0, 0, 2, 0, 0], + [0, 0, 2, 0, 0], + [0, 0, 2, 0, 0], + [2, 2, 2, 2, 2], + [0, 0, 3, 0, 0], + [0, 3, 3, 3, 0], [0, 0, 3, 0, 0] ] } @@ -728,42 +728,42 @@ "test": [ { "input": [ - [1, 1, 1, 1, 1, 1], - [1, 1, 1, 1, 1, 1], - [1, 1, 8, 8, 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, 1], - [1, 1, 1, 1, 1, 1], - [1, 1, 1, 1, 1, 1], - [4, 4, 4, 4, 4, 4], - [7, 7, 5, 5, 7, 7], - [7, 7, 5, 5, 7, 7], + [1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1], + [1, 1, 8, 8, 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, 1], + [1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 1, 1], + [4, 4, 4, 4, 4, 4], + [7, 7, 5, 5, 7, 7], + [7, 7, 5, 5, 7, 7], [7, 7, 7, 7, 7, 7] ] }, { "input": [ - [0, 7, 7, 0, 4, 3, 3, 3, 3, 1, 3, 3, 3, 3], - [0, 7, 7, 0, 4, 3, 3, 3, 1, 1, 1, 3, 3, 3], - [0, 7, 7, 0, 4, 3, 3, 1, 1, 1, 1, 1, 3, 3], + [0, 7, 7, 0, 4, 3, 3, 3, 3, 1, 3, 3, 3, 3], + [0, 7, 7, 0, 4, 3, 3, 3, 1, 1, 1, 3, 3, 3], + [0, 7, 7, 0, 4, 3, 3, 1, 1, 1, 1, 1, 3, 3], [0, 7, 7, 0, 4, 3, 1, 1, 1, 1, 1, 1, 1, 3] ] }, { "input": [ - [9, 9, 9, 2, 2, 2, 2, 9, 9, 9, 9, 9], - [9, 9, 9, 2, 2, 2, 2, 9, 9, 9, 9, 9], - [9, 9, 9, 9, 9, 9, 9, 9, 9, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7], - [7, 7, 7, 7, 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, 2, 2, 2, 2, 7, 7, 7, 7], - [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], + [9, 9, 9, 2, 2, 2, 2, 9, 9, 9, 9, 9], + [9, 9, 9, 2, 2, 2, 2, 9, 9, 9, 9, 9], + [9, 9, 9, 9, 9, 9, 9, 9, 9, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7], + [7, 7, 7, 7, 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, 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] ] } @@ -773,76 +773,76 @@ "train": [ { "input": [ - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], - [1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1], - [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], - [1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], + [1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1], + [0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ - [0, 0, 0, 3, 0, 0, 0], - [0, 0, 3, 0, 3, 0, 0], - [0, 3, 0, 0, 0, 3, 0], - [3, 0, 0, 0, 0, 0, 3], - [0, 3, 0, 0, 0, 3, 0], - [0, 0, 3, 0, 3, 0, 0], + [0, 0, 0, 3, 0, 0, 0], + [0, 0, 3, 0, 3, 0, 0], + [0, 3, 0, 0, 0, 3, 0], + [3, 0, 0, 0, 0, 0, 3], + [0, 3, 0, 0, 0, 3, 0], + [0, 0, 3, 0, 3, 0, 0], [0, 0, 0, 3, 0, 0, 0] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 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+ [0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0], + [6, 0, 6, 9, 9, 9, 9, 9, 6, 0, 6, 0, 6, 0, 6, 0], + [0, 6, 0, 6, 0, 6, 0, 6, 0, 6, 0, 6, 0, 6, 0, 6], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0], + [0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0], + [0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ - [9, 9, 9, 9, 9], - [9, 0, 0, 0, 9], - [9, 0, 0, 0, 9], - [9, 0, 0, 0, 9], + [9, 9, 9, 9, 9], + [9, 0, 0, 0, 9], + [9, 0, 0, 0, 9], + [9, 0, 0, 0, 9], [9, 9, 9, 9, 9] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0], - [0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0], - [0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4], - [4, 0, 0, 6, 6, 6, 0, 0, 4, 0, 0], - [0, 4, 0, 4, 0, 6, 0, 4, 0, 4, 0], - [0, 0, 4, 0, 0, 6, 4, 0, 0, 0, 4], - [4, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0], - [0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0], - [0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 4], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0], + [0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0], + [0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4], + [4, 0, 0, 6, 6, 6, 0, 0, 4, 0, 0], + [0, 4, 0, 4, 0, 6, 0, 4, 0, 4, 0], + [0, 0, 4, 0, 0, 6, 4, 0, 0, 0, 4], + [4, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0], + [0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0], + [0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ], "output": [ - [6, 6, 6], - [0, 0, 6], - [0, 0, 6], + [6, 6, 6], + [0, 0, 6], + [0, 0, 6], [6, 6, 6] ] } @@ -850,47 +850,47 @@ "test": [ { "input": [ - [7, 0, 2, 0, 7, 0, 2, 0, 7, 0, 2, 0], - [0, 7, 0, 2, 0, 7, 0, 2, 0, 7, 0, 2], - [2, 0, 7, 0, 2, 0, 7, 0, 2, 0, 7, 0], - [0, 2, 0, 7, 0, 2, 0, 7, 0, 2, 0, 7], - [7, 0, 2, 4, 7, 0, 2, 0, 7, 0, 2, 0], - [0, 7, 4, 4, 4, 7, 0, 2, 0, 7, 0, 2], - [2, 0, 7, 4, 2, 0, 7, 0, 2, 0, 7, 0], - [0, 2, 0, 7, 0, 2, 0, 7, 0, 2, 0, 7], - [7, 0, 2, 0, 7, 0, 2, 0, 7, 0, 2, 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}, { "input": [ - [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], - [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], - [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], - [9, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 9], - [9, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0, 9], - [9, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 9], - [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], - [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], - [9, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 9], - [9, 0, 0, 7, 0, 7, 0, 0, 0, 0, 0, 9], - [9, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 9], + [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9], + [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], + [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], + [9, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 9], + [9, 7, 0, 7, 0, 7, 0, 7, 0, 0, 0, 9], + [9, 7, 7, 7, 0, 7, 7, 7, 0, 0, 0, 9], + [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], + [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9], + [9, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 9], + [9, 0, 0, 7, 0, 7, 0, 0, 0, 0, 0, 9], + [9, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 9], [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9] ] } @@ -1009,17 +1009,17 @@ "train": [ { "input": [ - [0, 0, 0, 0, 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[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0], + [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, 0, 0, 0, 0, 0, 0, 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, 9, 5, 9, 9, 5, 9, 0], - [0, 9, 9, 9, 9, 9, 9, 0], - [0, 9, 9, 9, 9, 9, 9, 0], - [0, 9, 9, 9, 9, 9, 9, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 9, 5, 9, 9, 5, 9, 0], + [0, 9, 9, 9, 9, 9, 9, 0], + [0, 9, 9, 9, 9, 9, 9, 0], + [0, 9, 9, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0] ] } @@ -1419,17 +1419,17 @@ "train": [ { "input": [ - [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, 1, 1, 1, 1, 1, 0, 0, 0, 0, 8, 8], - [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 8, 8], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8], - [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], - [0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0], - [0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], - [0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0], - [0, 1, 1, 1, 1, 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, 0, 0, 0, 8, 8], + [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 8, 8], + [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 8, 8], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8], + [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], + [0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0], + [0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], + [0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0], + [0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0] ], "output": [ @@ -1438,15 +1438,15 @@ }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 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], - [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], - [4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], - [4, 4, 4, 0, 0, 4, 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, 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], + [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], + [4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], + [4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0], [4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ @@ -1455,11 +1455,11 @@ }, { "input": [ - [0, 0, 0, 0], - [7, 4, 7, 4], - [7, 4, 7, 4], - [7, 4, 7, 4], - [7, 4, 7, 4], + [0, 0, 0, 0], + [7, 4, 7, 4], + [7, 4, 7, 4], + [7, 4, 7, 4], + [7, 4, 7, 4], [0, 0, 0, 0] ], "output": [ @@ -1470,37 +1470,37 @@ "test": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6], - [0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6], - [0, 0, 0, 6, 6, 0, 0, 0, 6, 6, 6, 6], - [4, 4, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], - [4, 4, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 6, 6, 0, 0, 6, 6, 6, 6, 6], - [0, 0, 0, 0, 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3, 3, 3, 3, 0], + [0, 3, 3, 3, 3, 0], + [0, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0] ] }, { "input": [ - [6, 6, 6, 6, 6, 6], - [1, 1, 1, 1, 1, 1], - [4, 4, 4, 4, 4, 4], + [6, 6, 6, 6, 6, 6], + [1, 1, 1, 1, 1, 1], + [4, 4, 4, 4, 4, 4], [6, 6, 6, 6, 6, 6] ] } @@ -1510,17 +1510,17 @@ "train": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 2, 2, 2, 0, 0, 6, 6, 6, 0, 0, 0], - [0, 2, 2, 2, 0, 0, 6, 6, 6, 0, 0, 0], - [0, 2, 2, 2, 0, 0, 6, 6, 6, 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, 3, 3, 3, 0, 0, 0], - [0, 7, 7, 7, 7, 0, 3, 3, 3, 0, 0, 0], - [0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0], - [0, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 0], - [0, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 2, 2, 2, 0, 0, 6, 6, 6, 0, 0, 0], + [0, 2, 2, 2, 0, 0, 6, 6, 6, 0, 0, 0], + [0, 2, 2, 2, 0, 0, 6, 6, 6, 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, 3, 3, 3, 0, 0, 0], + [0, 7, 7, 7, 7, 0, 3, 3, 3, 0, 0, 0], + [0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0], + [0, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 0], + [0, 7, 7, 7, 7, 0, 0, 0, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ @@ -1529,16 +1529,16 @@ }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 6, 6, 6, 6, 0, 0, 0, 0, 7, 0, 0], - [0, 6, 0, 0, 6, 0, 0, 0, 7, 0, 7, 0], - [0, 6, 0, 0, 6, 0, 0, 7, 0, 0, 0, 7], - [0, 6, 6, 6, 6, 0, 0, 0, 7, 0, 7, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0], - [0, 0, 5, 5, 0, 0, 8, 8, 0, 0, 0, 0], - [0, 0, 5, 5, 0, 0, 8, 8, 0, 0, 0, 0], - [0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 5, 5, 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, 0, 0, 0, 0, 7, 0, 0], + [0, 6, 0, 0, 6, 0, 0, 0, 7, 0, 7, 0], + [0, 6, 0, 0, 6, 0, 0, 7, 0, 0, 0, 7], + [0, 6, 6, 6, 6, 0, 0, 0, 7, 0, 7, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0], + [0, 0, 5, 5, 0, 0, 8, 8, 0, 0, 0, 0], + [0, 0, 5, 5, 0, 0, 8, 8, 0, 0, 0, 0], + [0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], "output": [ @@ -1547,11 +1547,11 @@ }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 7, 7, 7, 7, 7, 0, 0], - [0, 7, 7, 7, 7, 7, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 4, 4, 4, 0, 4, 4], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 7, 7, 7, 7, 7, 0, 0], + [0, 7, 7, 7, 7, 7, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 4, 4, 4, 0, 4, 4], [0, 0, 4, 4, 4, 0, 4, 4] ], "output": [ @@ -1562,31 +1562,31 @@ "test": [ { "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, 1, 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, 1, 1, 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] ] }, { "input": [ - [0, 0, 0, 0, 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0, 0] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 9, 9, 9, 9, 9, 9, 0], - [0, 9, 0, 0, 0, 0, 9, 0], - [0, 9, 0, 0, 0, 0, 9, 0], - [0, 9, 9, 8, 9, 9, 9, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 9, 9, 9, 9, 9, 9, 0], + [0, 9, 0, 0, 0, 0, 9, 0], + [0, 9, 0, 0, 0, 0, 9, 0], + [0, 9, 9, 8, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0] ] } @@ -1685,12 +1685,12 @@ "train": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0], - [0, 3, 3, 3, 0, 0, 0], - [0, 3, 0, 3, 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, 0], + [0, 3, 3, 3, 0, 0, 0], + [0, 3, 0, 3, 0, 0, 0], + [0, 3, 3, 3, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0] ], "output": [ @@ -1699,12 +1699,12 @@ }, { "input": [ - [0, 0, 0, 0, 0, 0, 0], - [0, 3, 3, 3, 3, 0, 0], - [0, 3, 0, 0, 3, 0, 0], - [0, 3, 0, 0, 3, 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, 3, 3, 3, 0, 0], + [0, 3, 0, 0, 3, 0, 0], + [0, 3, 0, 0, 3, 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9, 9, 9], + [6, 6, 6, 6], + [6, 6, 6, 6], + [0, 0, 0, 0], + [7, 7, 7, 7], + [7, 7, 7, 7], + [0, 0, 0, 0], + [0, 0, 0, 0], + [9, 9, 9, 9], [9, 9, 9, 9] ], "output": [ - [6, 6, 6, 6, 0, 6, 6, 6, 6], - [6, 6, 6, 6, 0, 6, 6, 6, 6], - [0, 0, 0, 0, 0, 0, 0, 0, 0], - [7, 7, 7, 7, 0, 7, 7, 7, 7], - [7, 7, 7, 7, 0, 7, 7, 7, 7], - [0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0], - [9, 9, 9, 9, 0, 9, 9, 9, 9], + [6, 6, 6, 6, 0, 6, 6, 6, 6], + [6, 6, 6, 6, 0, 6, 6, 6, 6], + [0, 0, 0, 0, 0, 0, 0, 0, 0], + [7, 7, 7, 7, 0, 7, 7, 7, 7], + [7, 7, 7, 7, 0, 7, 7, 7, 7], + [0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0], + [9, 9, 9, 9, 0, 9, 9, 9, 9], [9, 9, 9, 9, 0, 9, 9, 9, 9] ] } @@ -2813,36 +2813,36 @@ "test": [ { "input": [ - [6, 6, 6, 6, 0, 1, 1, 1, 1], - [6, 4, 4, 6, 0, 1, 3, 3, 1], - [6, 4, 4, 6, 0, 1, 3, 3, 1], + [6, 6, 6, 6, 0, 1, 1, 1, 1], + [6, 4, 4, 6, 0, 1, 3, 3, 1], + [6, 4, 4, 6, 0, 1, 3, 3, 1], [6, 6, 6, 6, 0, 1, 1, 1, 1] ] }, { "input": [ - [0, 7, 0], - [7, 1, 7], - 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7, 7, 0], - [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 6, 7, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0], + [0, 6, 6, 6, 0, 7, 7, 7, 0, 7, 7, 7, 0], + [0, 7, 7, 7, 0, 6, 6, 7, 0, 7, 7, 7, 0], + [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 6, 7, 0], [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0] ], "output": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0], - [0, 7, 7, 7, 0, 7, 7, 7, 0, 6, 6, 6, 0], - [0, 7, 7, 7, 0, 6, 6, 7, 0, 7, 7, 7, 0], - [0, 7, 6, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0], + [0, 7, 7, 7, 0, 7, 7, 7, 0, 6, 6, 6, 0], + [0, 7, 7, 7, 0, 6, 6, 7, 0, 7, 7, 7, 0], + [0, 7, 6, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0], [0, 7, 7, 7, 0, 7, 7, 7, 0, 7, 7, 7, 0] ] } @@ -5495,31 +5495,31 @@ "test": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [5, 1, 0, 1, 1, 0, 1, 1, 0, 1, 5], - [1, 1, 0, 1, 1, 0, 1, 1, 0, 5, 1], - [5, 1, 0, 5, 1, 0, 1, 1, 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], + [5, 1, 0, 1, 1, 0, 1, 1, 0, 1, 5], + [1, 1, 0, 1, 1, 0, 1, 1, 0, 5, 1], + [5, 1, 0, 5, 1, 0, 1, 1, 0, 1, 1], [1, 1, 0, 1, 1, 0, 1, 1, 0, 5, 1] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], - [8, 8, 8, 8, 8, 8, 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, 0, 8, 8, 8, 8, 8, 4], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4], + [8, 8, 8, 8, 8, 8, 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, 0, 8, 8, 8, 8, 8, 4], [4, 4, 4, 4, 4, 4, 0, 4, 4, 4, 4, 4, 4] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0], - [2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0], - [0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0], - [2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0], + [2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0], + [0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0], + [2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0], [2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0] ] } @@ -5529,45 +5529,45 @@ "train": [ { "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, 5, 5, 0, 2, 2, 0, 4, 4, 0, 3, 3, 0], - [0, 1, 1, 0, 2, 2, 0, 4, 4, 0, 5, 5, 0], - [0, 1, 1, 0, 5, 5, 0, 4, 4, 0, 3, 3, 0], - [0, 1, 1, 0, 2, 2, 0, 5, 5, 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, 5, 5, 0, 2, 2, 0, 4, 4, 0, 3, 3, 0], + [0, 1, 1, 0, 2, 2, 0, 4, 4, 0, 5, 5, 0], + [0, 1, 1, 0, 5, 5, 0, 4, 4, 0, 3, 3, 0], + [0, 1, 1, 0, 2, 2, 0, 5, 5, 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] ], "output": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 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2, 2, 2, 0, 4, 4, 4], [6, 6, 6, 0, 7, 7, 7, 0, 2, 2, 2, 0, 4, 4, 4] ] } @@ -5575,35 +5575,35 @@ "test": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0], - [6, 0, 2, 0, 1, 0, 3, 0, 7], - [4, 0, 2, 0, 1, 0, 3, 0, 7], - [6, 0, 4, 0, 1, 0, 3, 0, 7], - [6, 0, 2, 0, 4, 0, 3, 0, 7], - [6, 0, 2, 0, 1, 0, 4, 0, 7], - [6, 0, 2, 0, 1, 0, 3, 0, 4], + [0, 0, 0, 0, 0, 0, 0, 0, 0], + [6, 0, 2, 0, 1, 0, 3, 0, 7], + [4, 0, 2, 0, 1, 0, 3, 0, 7], + [6, 0, 4, 0, 1, 0, 3, 0, 7], + [6, 0, 2, 0, 4, 0, 3, 0, 7], + [6, 0, 2, 0, 1, 0, 4, 0, 7], + [6, 0, 2, 0, 1, 0, 3, 0, 4], [6, 0, 2, 0, 1, 0, 3, 0, 7] ] }, { "input": [ - [3, 3, 3, 3, 3, 0, 4, 4, 4, 4, 4, 0, 5, 5, 5, 5, 5, 0, 1, 1, 1, 1, 1], - [3, 3, 3, 3, 3, 0, 4, 4, 4, 4, 4, 0, 5, 5, 5, 5, 5, 0, 2, 1, 1, 1, 1], - [3, 2, 3, 3, 3, 0, 4, 4, 4, 4, 4, 0, 5, 5, 5, 5, 5, 0, 2, 1, 1, 1, 1], - [3, 2, 3, 3, 3, 0, 4, 4, 4, 4, 4, 0, 5, 5, 5, 5, 5, 0, 2, 1, 1, 1, 1], - [3, 2, 3, 3, 3, 0, 4, 4, 4, 4, 4, 0, 5, 5, 5, 5, 5, 0, 2, 1, 1, 1, 1], - [3, 2, 3, 3, 3, 0, 4, 2, 4, 4, 4, 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[ - [0, 0, 0, 0, 0, 1], - [0, 3, 0, 0, 0, 1], - [0, 3, 0, 0, 0, 1], - [0, 3, 0, 0, 0, 1], - [0, 3, 6, 6, 6, 6], + [0, 0, 0, 0, 0, 1], + [0, 3, 0, 0, 0, 1], + [0, 3, 0, 0, 0, 1], + [0, 3, 0, 0, 0, 1], + [0, 3, 6, 6, 6, 6], [0, 0, 9, 9, 9, 9] ], "output": [ - [0, 0, 0, 0, 0, 4], - [0, 4, 0, 0, 0, 4], - [0, 4, 0, 0, 0, 4], - [0, 4, 0, 0, 0, 4], - [0, 4, 7, 7, 7, 7], + [0, 0, 0, 0, 0, 4], + [0, 4, 0, 0, 0, 4], + [0, 4, 0, 0, 0, 4], + [0, 4, 0, 0, 0, 4], + [0, 4, 7, 7, 7, 7], [0, 0, 7, 7, 7, 7] ] } @@ -9814,31 +9814,31 @@ "test": [ { "input": [ - [6, 0, 8, 0, 0, 0], - [6, 0, 8, 0, 0, 0], - [6, 0, 8, 0, 0, 0], - [6, 0, 8, 0, 0, 0], - [0, 0, 9, 9, 9, 9], + [6, 0, 8, 0, 0, 0], + [6, 0, 8, 0, 0, 0], + [6, 0, 8, 0, 0, 0], + [6, 0, 8, 0, 0, 0], + [0, 0, 9, 9, 9, 9], [0, 0, 3, 3, 3, 3] ] }, { "input": [ - [7, 7, 7, 7, 0, 0], - [3, 0, 0, 0, 0, 8], - [3, 0, 0, 0, 0, 8], - [3, 0, 0, 0, 0, 8], - [3, 0, 0, 0, 0, 8], + [7, 7, 7, 7, 0, 0], + [3, 0, 0, 0, 0, 8], + [3, 0, 0, 0, 0, 8], + [3, 0, 0, 0, 0, 8], + [3, 0, 0, 0, 0, 8], [0, 0, 7, 7, 7, 7] ] }, { "input": [ - [6, 0, 5, 5, 5, 5], - [6, 5, 0, 0, 0, 0], - [6, 5, 0, 0, 0, 0], - [6, 5, 0, 0, 0, 0], - [0, 6, 6, 6, 6, 6], + [6, 0, 5, 5, 5, 5], + [6, 5, 0, 0, 0, 0], + [6, 5, 0, 0, 0, 0], + [6, 5, 0, 0, 0, 0], + [0, 6, 6, 6, 6, 6], [0, 0, 0, 0, 0, 0] ] } @@ -9848,89 +9848,89 @@ "train": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], - [1, 1, 1, 3, 3, 3, 3, 1, 1, 1], - [1, 1, 1, 3, 3, 3, 3, 1, 1, 1], - [1, 1, 1, 3, 3, 3, 3, 1, 1, 1], - [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], - [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], - [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], - [0, 3, 3, 3, 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], + [1, 1, 1, 3, 3, 3, 3, 1, 1, 1], + [1, 1, 1, 3, 3, 3, 3, 1, 1, 1], + [1, 1, 1, 3, 3, 3, 3, 1, 1, 1], + [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], + [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], + [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], + [0, 3, 3, 3, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ], 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7, 7, 7], - [7, 7, 7, 7, 7], + [7, 7, 7, 7, 7], + [7, 7, 7, 7, 7], [7, 7, 7, 7, 7] ] } @@ -10035,31 +10035,31 @@ "test": [ { "input": [ - [0, 0, 0, 0], - [0, 0, 4, 4], - [0, 8, 8, 4], - [0, 8, 8, 4], - [0, 8, 8, 4], + [0, 0, 0, 0], + [0, 0, 4, 4], + [0, 8, 8, 4], + [0, 8, 8, 4], + [0, 8, 8, 4], [0, 8, 8, 4] ] }, { "input": [ - [0, 0, 0, 0, 0, 0], - [0, 0, 0, 5, 0, 0], - [0, 3, 3, 5, 3, 0], - [0, 3, 4, 5, 4, 4], - [0, 0, 4, 5, 4, 4], + [0, 0, 0, 0, 0, 0], + [0, 0, 0, 5, 0, 0], + [0, 3, 3, 5, 3, 0], + [0, 3, 4, 5, 4, 4], + [0, 0, 4, 5, 4, 4], [0, 0, 0, 5, 0, 0] ] }, { "input": [ - [0, 0, 2, 0, 0, 0], - [0, 5, 2, 5, 0, 0], - [1, 1, 1, 1, 1, 1], - [0, 5, 2, 5, 0, 0], - [0, 0, 2, 0, 0, 0], + [0, 0, 2, 0, 0, 0], + [0, 5, 2, 5, 0, 0], + [1, 1, 1, 1, 1, 1], + [0, 5, 2, 5, 0, 0], + [0, 0, 2, 0, 0, 0], [0, 0, 2, 0, 0, 0] ] } @@ -10069,67 +10069,67 @@ "train": [ { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 2, 2, 2, 0, 0, 0], - [0, 1, 2, 2, 2, 1, 1, 0], - [0, 1, 2, 2, 2, 1, 1, 0], - [0, 1, 2, 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3, 3, 3, 3], + [0, 9, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0] ] }, { "input": [ - [0, 4, 0, 0, 0, 0], - [8, 8, 8, 8, 8, 8], - [0, 4, 0, 0, 0, 0], - [0, 4, 0, 0, 0, 0], - [7, 4, 7, 7, 7, 7], + [0, 4, 0, 0, 0, 0], + [8, 8, 8, 8, 8, 8], + [0, 4, 0, 0, 0, 0], + [0, 4, 0, 0, 0, 0], + [7, 4, 7, 7, 7, 7], [0, 4, 0, 0, 0, 0] ] }, { "input": [ - [0, 5, 0, 0, 0, 0], - [3, 5, 0, 0, 0, 0], - [0, 3, 0, 0, 0, 0], - [0, 5, 3, 0, 0, 0], - [0, 5, 0, 3, 0, 0], + [0, 5, 0, 0, 0, 0], + [3, 5, 0, 0, 0, 0], + [0, 3, 0, 0, 0, 0], + [0, 5, 3, 0, 0, 0], + [0, 5, 0, 3, 0, 0], [0, 5, 0, 0, 3, 0] ] } @@ -10410,59 +10410,59 @@ "train": [ { "input": [ - [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], - [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], - [0, 0, 1, 1, 2, 2, 2, 1, 7, 7, 7, 0], - [0, 3, 3, 3, 2, 2, 2, 1, 7, 7, 7, 0], - [0, 3, 3, 3, 2, 2, 2, 1, 7, 7, 7, 0], - [0, 3, 3, 3, 3, 3, 1, 1, 7, 7, 7, 0], - [0, 3, 3, 3, 3, 3, 1, 1, 0, 0, 0, 0], - [0, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0], + [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], + [0, 0, 1, 1, 1, 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0, 0, 0, 0, 5, 0, 0] ] } @@ -11681,37 +11681,37 @@ "train": [ { "input": [ - [4, 0, 0, 3, 3, 0], - [4, 4, 0, 0, 3, 0], - [0, 0, 0, 0, 0, 0], - [0, 4, 0, 0, 3, 0], - [0, 4, 4, 0, 3, 3], + [4, 0, 0, 3, 3, 0], + [4, 4, 0, 0, 3, 0], + [0, 0, 0, 0, 0, 0], + [0, 4, 0, 0, 3, 0], + [0, 4, 4, 0, 3, 3], [0, 0, 0, 0, 0, 0] ], "output": [ - [4, 3, 0, 3, 3, 0], - [4, 4, 0, 4, 3, 0], - [0, 0, 0, 0, 0, 0], - [0, 4, 3, 0, 3, 4], - [0, 4, 4, 0, 3, 3], + [4, 3, 0, 3, 3, 0], + [4, 4, 0, 4, 3, 0], + [0, 0, 0, 0, 0, 0], + [0, 4, 3, 0, 3, 4], + [0, 4, 4, 0, 3, 3], [0, 0, 0, 0, 0, 0] ] }, { "input": [ - [0, 0, 0, 4, 0, 0], - [3, 3, 0, 4, 4, 0], - [0, 3, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0], - [4, 4, 0, 3, 0, 0], + [0, 0, 0, 4, 0, 0], + [3, 3, 0, 4, 4, 0], + [0, 3, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0], + [4, 4, 0, 3, 0, 0], [0, 4, 0, 3, 3, 0] ], "output": [ - [0, 0, 0, 4, 3, 0], - [3, 3, 0, 4, 4, 0], - [4, 3, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0], - [4, 4, 0, 3, 4, 0], + [0, 0, 0, 4, 3, 0], + [3, 3, 0, 4, 4, 0], + [4, 3, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0], + [4, 4, 0, 3, 4, 0], [3, 4, 0, 3, 3, 0] ] } @@ -11719,39 +11719,39 @@ "test": [ { "input": [ - [3, 0, 0, 0, 0, 0], - [3, 3, 0, 3, 0, 0], - [0, 0, 0, 3, 3, 0], - [4, 4, 0, 0, 0, 0], - [0, 4, 0, 0, 3, 3], + [3, 0, 0, 0, 0, 0], + [3, 3, 0, 3, 0, 0], + [0, 0, 0, 3, 3, 0], + [4, 4, 0, 0, 0, 0], + [0, 4, 0, 0, 3, 3], [0, 0, 0, 0, 0, 3] ] }, { "input": [ - [0, 3, 0, 0, 0, 0, 0, 0, 0, 0], - [3, 3, 0, 3, 0, 0, 0, 3, 0, 0], - [0, 0, 0, 3, 3, 0, 3, 3, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 3, 0, 0, 0, 0, 0, 0, 0, 0], - [3, 3, 0, 3, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 3, 3, 0, 0, 0, 3, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 3, 3], - [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], + [0, 3, 0, 0, 0, 0, 0, 0, 0, 0], + [3, 3, 0, 3, 0, 0, 0, 3, 0, 0], + [0, 0, 0, 3, 3, 0, 3, 3, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 3, 0, 0, 0, 0, 0, 0, 0, 0], + [3, 3, 0, 3, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 3, 3, 0, 0, 0, 3, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 3, 3], + [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], 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+ [0, 7, 7, 7, 7, 7, 7, 7, 0, 6, 0, 0], + [0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 0, 0], + [0, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 0], + [0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 0, 0], + [0, 7, 7, 0, 0, 0, 7, 7, 0, 0, 0, 0], + [0, 7, 7, 0, 6, 0, 7, 7, 0, 0, 0, 0], + [0, 7, 7, 6, 0, 0, 7, 7, 0, 0, 0, 0], + [0, 7, 6, 7, 7, 7, 7, 7, 0, 0, 0, 0], + [0, 6, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] }, { "input": [ - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0], - [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 9, 0], - [0, 8, 0, 0, 9, 9, 9, 9, 8, 0, 9, 0], - [0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0], - [0, 0, 8, 8, 0, 9, 9, 9, 0, 8, 0, 0], - [0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 0], - [0, 0, 8, 0, 9, 9, 9, 9, 9, 0, 8, 0], - [0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0], - [0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 9, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0], + [0, 8, 8, 8, 8, 8, 8, 8, 0, 0, 9, 0], + [0, 8, 0, 0, 9, 9, 9, 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[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], + [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], + [2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2], + [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], + [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], + [0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0], + [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0] ] } @@ -15570,53 +15570,53 @@ "train": [ { "input": [ - [4, 4, 4, 4, 4, 4, 4, 4], - [3, 3, 6, 3, 3, 3, 3, 3], - [4, 4, 4, 4, 4, 4, 4, 4], - [3, 6, 3, 3, 3, 3, 3, 6], - [4, 4, 4, 4, 4, 4, 4, 4], - [3, 3, 3, 3, 3, 3, 6, 3], - [4, 4, 4, 6, 4, 4, 4, 4], + [4, 4, 4, 4, 4, 4, 4, 4], + [3, 3, 6, 3, 3, 3, 3, 3], + [4, 4, 4, 4, 4, 4, 4, 4], + [3, 6, 3, 3, 3, 3, 3, 6], + [4, 4, 4, 4, 4, 4, 4, 4], + [3, 3, 3, 3, 3, 3, 6, 3], + [4, 4, 4, 6, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3, 3, 3] ], "output": [ - [4, 4, 4, 4, 4, 4, 4, 4], - [3, 3, 3, 3, 3, 3, 3, 3], - [4, 4, 4, 4, 4, 4, 4, 4], - [3, 3, 3, 3, 3, 3, 3, 3], - [4, 4, 4, 4, 4, 4, 4, 4], - [3, 3, 3, 3, 3, 3, 3, 3], - [4, 4, 4, 4, 4, 4, 4, 4], + [4, 4, 4, 4, 4, 4, 4, 4], + [3, 3, 3, 3, 3, 3, 3, 3], + [4, 4, 4, 4, 4, 4, 4, 4], + [3, 3, 3, 3, 3, 3, 3, 3], + [4, 4, 4, 4, 4, 4, 4, 4], + [3, 3, 3, 3, 3, 3, 3, 3], + [4, 4, 4, 4, 4, 4, 4, 4], [3, 3, 3, 3, 3, 3, 3, 3] ] }, { "input": [ - [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], - [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], - [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 5, 2, 7], - [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 5, 7], - [7, 5, 7, 2, 7, 5, 7, 2, 7, 5, 7, 2, 7], - [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], - [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 5, 2, 7], - [7, 2, 7, 2, 7, 5, 7, 2, 7, 2, 7, 2, 7], - [7, 5, 7, 2, 7, 2, 7, 2, 5, 2, 7, 2, 7], - [7, 2, 7, 2, 7, 2, 7, 2, 5, 2, 7, 2, 7], - [7, 2, 7, 2, 7, 5, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 5, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 5, 7], + [7, 5, 7, 2, 7, 5, 7, 2, 7, 5, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 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7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], + [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7], [7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7] ] } @@ -15624,39 +15624,39 @@ "test": [ { "input": [ - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 1, 7, 1, 1, 1, 1, 7, 1, 1, 1], - [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 7], - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 7, 1, 1, 1, 1, 7, 1, 1, 1], + [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 7], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1] ] }, { "input": [ - [8, 8, 8, 8, 8, 8], - [9, 9, 9, 9, 9, 9], - [8, 8, 8, 8, 2, 8], - [9, 9, 9, 9, 9, 9], - [8, 8, 8, 8, 8, 8], + [8, 8, 8, 8, 8, 8], + [9, 9, 9, 9, 9, 9], + [8, 8, 8, 8, 2, 8], + [9, 9, 9, 9, 9, 9], + [8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 9] ] }, { "input": [ - [4, 6, 4, 6, 4, 6, 4, 6, 4], - [4, 6, 4, 6, 4, 6, 8, 6, 4], - [2, 6, 2, 6, 4, 6, 4, 6, 4], - [4, 6, 4, 6, 4, 6, 4, 6, 4], - [4, 6, 4, 6, 4, 8, 4, 6, 4], - [4, 6, 8, 6, 4, 6, 4, 6, 4], - [4, 6, 4, 6, 4, 6, 4, 8, 4], - [2, 6, 4, 6, 4, 6, 4, 6, 4], + [4, 6, 4, 6, 4, 6, 4, 6, 4], + [4, 6, 4, 6, 4, 6, 8, 6, 4], + [2, 6, 2, 6, 4, 6, 4, 6, 4], + [4, 6, 4, 6, 4, 6, 4, 6, 4], + [4, 6, 4, 6, 4, 8, 4, 6, 4], + [4, 6, 8, 6, 4, 6, 4, 6, 4], + [4, 6, 4, 6, 4, 6, 4, 8, 4], + [2, 6, 4, 6, 4, 6, 4, 6, 4], [4, 6, 4, 6, 4, 6, 4, 6, 4] ] } @@ -15666,63 +15666,63 @@ "train": [ { "input": [ - [3, 3, 3, 3, 3, 4], - [4, 3, 3, 3, 3, 3], - [3, 3, 3, 4, 3, 3], - [3, 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2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], + [0, 2, 2, 2, 2, 2, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] } @@ -15730,37 +15730,37 @@ "test": [ { "input": [ - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [0, 1, 1, 1, 1, 1, 0, 1, 1, 1], - [1, 1, 1, 1, 0, 1, 1, 1, 1, 1], - [1, 1, 1, 1, 0, 1, 0, 1, 0, 1], - [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], - [1, 1, 0, 1, 0, 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, 0, 1, 1, 1, 0, 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], + [0, 1, 1, 1, 1, 1, 0, 1, 1, 1], + [1, 1, 1, 1, 0, 1, 1, 1, 1, 1], + [1, 1, 1, 1, 0, 1, 0, 1, 0, 1], + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 0, 1, 0, 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, 0, 1, 1, 1, 0, 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, 0, 1, 1, 1, 1] ] }, { "input": [ - [0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0], - [0, 0, 7, 7, 7, 7, 7, 7, 7, 9, 0], - [0, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0], - [0, 0, 7, 7, 9, 7, 7, 7, 7, 0, 0], - [0, 0, 7, 7, 7, 7, 7, 9, 7, 0, 9], + [0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0], + [0, 0, 7, 7, 7, 7, 7, 7, 7, 9, 0], + [0, 0, 7, 7, 7, 7, 7, 7, 7, 0, 0], + [0, 0, 7, 7, 9, 7, 7, 7, 7, 0, 0], + [0, 0, 7, 7, 7, 7, 7, 9, 7, 0, 9], [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, 4, 0, 0], - [0, 0, 0, 0, 0, 0], - [4, 0, 0, 0, 4, 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], + [4, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0] ] } @@ -15770,37 +15770,37 @@ "train": [ { "input": [ - [0, 4, 0, 0, 2, 3], - [4, 1, 1, 2, 1, 0], - [0, 1, 0, 0, 2, 3], - [0, 2, 0, 0, 1, 0], - [0, 2, 1, 1, 1, 0], + [0, 4, 0, 0, 2, 3], + [4, 1, 1, 2, 1, 0], + [0, 1, 0, 0, 2, 3], + [0, 2, 0, 0, 1, 0], + [0, 2, 1, 1, 1, 0], [0, 2, 0, 0, 4, 0] ], "output": [ - [0, 0, 0, 0, 0, 0], - [0, 1, 1, 1, 1, 0], - [0, 1, 0, 0, 1, 0], - [0, 1, 0, 0, 1, 0], - [0, 1, 1, 1, 1, 0], + [0, 0, 0, 0, 0, 0], + [0, 1, 1, 1, 1, 0], + [0, 1, 0, 0, 1, 0], + [0, 1, 0, 0, 1, 0], + [0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0] ] }, { "input": [ - [0, 5, 5, 6, 5, 6], - [0, 5, 0, 0, 0, 6], - [0, 3, 0, 0, 0, 5], - [0, 3, 0, 3, 0, 5], - [0, 5, 5, 5, 5, 5], + [0, 5, 5, 6, 5, 6], + [0, 5, 0, 0, 0, 6], + [0, 3, 0, 0, 0, 5], + [0, 3, 0, 3, 0, 5], + [0, 5, 5, 5, 5, 5], [6, 6, 0, 5, 0, 3] ], "output": [ - [0, 5, 5, 5, 5, 5], - [0, 5, 0, 0, 0, 5], - [0, 5, 0, 0, 0, 5], - [0, 5, 0, 0, 0, 5], - [0, 5, 5, 5, 5, 5], + [0, 5, 5, 5, 5, 5], + [0, 5, 0, 0, 0, 5], + [0, 5, 0, 0, 0, 5], + [0, 5, 0, 0, 0, 5], + [0, 5, 5, 5, 5, 5], [0, 0, 0, 0, 0, 0] ] } @@ -15808,37 +15808,37 @@ "test": [ { "input": [ - [0, 0, 0, 8, 0, 9], - [8, 4, 4, 7, 4, 0], - [4, 0, 0, 0, 4, 0], - [4, 7, 0, 0, 7, 0], - [9, 9, 0, 7, 9, 9], + [0, 0, 0, 8, 0, 9], + [8, 4, 4, 7, 4, 0], + [4, 0, 0, 0, 4, 0], + [4, 7, 0, 0, 7, 0], + [9, 9, 0, 7, 9, 9], [4, 4, 8, 4, 9, 0] ] }, { "input": [ - [3, 4, 3, 4, 3, 6], - [3, 0, 0, 0, 0, 3], - [4, 0, 0, 0, 4, 4], - [3, 0, 0, 0, 0, 3], - [2, 0, 4, 0, 0, 3], + [3, 4, 3, 4, 3, 6], + [3, 0, 0, 0, 0, 3], + [4, 0, 0, 0, 4, 4], + [3, 0, 0, 0, 0, 3], + [2, 0, 4, 0, 0, 3], [3, 2, 2, 4, 3, 4] ] }, { "input": [ - [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, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0], - [2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], - [0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0], - [0, 2, 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, 2, 1, 1, 1, 1], - [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], - [0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1], - [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, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0], + [2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0], + [0, 2, 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, 2, 1, 1, 1, 1], + [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1], + [0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1], + [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 2, 0, 2, 1, 1, 1, 2] ] } @@ -15848,53 +15848,53 @@ "train": [ { "input": [ - [2, 2, 0, 0, 0, 0, 0, 0, 0, 0], - [6, 2, 0, 0, 3, 0, 0, 1, 0, 0], - [0, 0, 1, 6, 0, 0, 0, 0, 0, 0], - [0, 0, 1, 1, 0, 0, 6, 0, 0, 6], - [0, 0, 0, 0, 3, 3, 0, 0, 0, 0], - [0, 3, 0, 0, 3, 3, 0, 1, 0, 0], - [0, 0, 0, 0, 0, 3, 4, 4, 0, 0], - [0, 1, 0, 0, 7, 0, 4, 6, 0, 0], - [7, 0, 0, 0, 0, 0, 0, 0, 5, 5], + [2, 2, 0, 0, 0, 0, 0, 0, 0, 0], + [6, 2, 0, 0, 3, 0, 0, 1, 0, 0], + [0, 0, 1, 6, 0, 0, 0, 0, 0, 0], + [0, 0, 1, 1, 0, 0, 6, 0, 0, 6], + [0, 0, 0, 0, 3, 3, 0, 0, 0, 0], + [0, 3, 0, 0, 3, 3, 0, 1, 0, 0], + [0, 0, 0, 0, 0, 3, 4, 4, 0, 0], + [0, 1, 0, 0, 7, 0, 4, 6, 0, 0], + [7, 0, 0, 0, 0, 0, 0, 0, 5, 5], [0, 0, 0, 0, 3, 0, 0, 0, 7, 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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, 4, 0, 0, 0, 0, 0, 0, 0], - [0, 4, 4, 4, 4, 4, 4, 4, 4], - [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, 4, 0, 0, 0, 0, 0, 0, 0], + [0, 4, 4, 4, 4, 4, 4, 4, 4], + [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] ] ], "ExtendToBoundary4": [ [ - [0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0], - [0, 0, 6, 0, 0, 0], - [0, 0, 6, 0, 0, 0], - [0, 0, 6, 7, 7, 7], + [0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0], + [0, 0, 6, 0, 0, 0], + [0, 0, 6, 0, 0, 0], + [0, 0, 6, 7, 7, 7], [0, 0, 6, 0, 0, 0] ], [ - [0, 0, 0, 8, 0, 0], - [0, 0, 0, 8, 0, 0], - [0, 3, 3, 3, 3, 3], - [0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0], + [0, 0, 0, 8, 0, 0], + [0, 0, 0, 8, 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] ], [ - [2, 0, 0, 0, 0, 8], - [0, 2, 0, 0, 8, 0], - [0, 0, 2, 8, 0, 0], - [0, 0, 8, 0, 0, 0], 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0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], - [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [2, 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, 0, 0, 0], + [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], + [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 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0, 0, 6, 0, 8, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0] ] ], "ExtendToBoundary8": [ [ - [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], - [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0], + [0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0], + [0, 8, 8, 8, 8, 8, 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, 9, 9, 9, 9, 9, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 3, 3, 3, 3, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 0], - [0, 9, 0, 0, 3, 0, 9, 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, 9, 9, 9, 9, 9, 9, 0], + [0, 9, 0, 0, 3, 0, 9, 0], + [0, 9, 0, 0, 3, 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0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 2, 2, 2, 2, 2, 0], + [0, 0, 0, 2, 2, 2, 2, 2, 0], + [0, 0, 0, 0, 0, 1, 2, 2, 0], + [0, 0, 0, 0, 1, 0, 2, 2, 0], + [0, 0, 0, 1, 0, 1, 2, 2, 0], + [0, 0, 1, 0, 1, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 1, 0] ] ] -} \ No newline at end of file +} diff --git a/kaggle/combined/arc-agi_evaluation2_challenges.json b/kaggle/combined/arc-agi_evaluation2_challenges.json index 961abef5..b11ff6ff 100644 --- a/kaggle/combined/arc-agi_evaluation2_challenges.json +++ b/kaggle/combined/arc-agi_evaluation2_challenges.json @@ -1 +1 @@ -{"0934a4d8": {"train": [{"input": [[3, 5, 3, 3, 6, 6, 5, 4, 1, 4, 9, 9, 4, 3, 9, 9, 9, 9, 3, 4, 9, 9, 4, 1, 4, 5, 6, 6, 3, 3], [5, 3, 3, 3, 6, 6, 4, 5, 4, 1, 9, 9, 3, 4, 9, 1, 1, 9, 4, 3, 9, 9, 1, 4, 5, 4, 6, 6, 3, 3], [1, 1, 3, 5, 5, 4, 6, 6, 9, 1, 1, 4, 9, 9, 4, 5, 5, 4, 9, 9, 4, 1, 1, 9, 6, 6, 4, 5, 5, 3], [1, 1, 5, 3, 4, 5, 6, 6, 1, 9, 4, 1, 9, 1, 4, 4, 4, 4, 1, 9, 1, 4, 9, 1, 6, 6, 5, 4, 3, 5], [6, 9, 9, 9, 3, 5, 3, 3, 4, 3, 9, 9, 9, 2, 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9, 5, 3, 3, 6, 6, 4, 6, 7, 9, 9, 9, 9, 7, 6, 4, 6, 6, 3, 3, 5, 9, 9, 3, 9], [2, 3, 7, 9, 5, 7, 4, 4, 1, 4, 3, 3, 4, 6, 7, 4, 4, 7, 6, 4, 3, 3, 4, 1, 4, 4, 7, 5, 9, 7], [3, 2, 9, 9, 7, 5, 4, 4, 4, 1, 3, 3, 6, 4, 4, 7, 7, 4, 4, 6, 3, 3, 1, 4, 4, 4, 5, 7, 9, 9]], "output": [[3, 1, 4, 4, 4], [3, 4, 1, 4, 4], [6, 6, 3, 3, 5], [4, 3, 5, 2, 3]]}, {"input": [[1, 9, 4, 4, 9, 9, 2, 7, 6, 6, 9, 9, 7, 6, 7, 2, 2, 7, 6, 7, 9, 9, 6, 6, 7, 2, 9, 9, 4, 4], [7, 1, 4, 4, 9, 9, 7, 2, 6, 6, 9, 9, 6, 7, 2, 7, 7, 2, 7, 6, 9, 9, 6, 6, 2, 7, 9, 9, 4, 4], [2, 7, 1, 9, 2, 7, 9, 9, 4, 4, 6, 6, 7, 2, 5, 1, 1, 5, 2, 7, 6, 6, 4, 4, 9, 9, 7, 2, 9, 1], [7, 2, 7, 1, 7, 2, 9, 9, 4, 4, 6, 6, 2, 7, 5, 5, 5, 5, 7, 2, 6, 6, 4, 4, 9, 9, 2, 7, 1, 7], [9, 6, 7, 2, 1, 9, 4, 4, 7, 6, 7, 2, 9, 2, 6, 4, 4, 6, 2, 9, 2, 7, 6, 7, 4, 4, 9, 1, 2, 7], [6, 9, 2, 7, 7, 1, 4, 4, 6, 7, 2, 7, 9, 9, 4, 6, 6, 4, 9, 9, 7, 2, 7, 6, 4, 4, 1, 7, 7, 2], [7, 2, 9, 6, 2, 7, 1, 9, 7, 2, 5, 5, 4, 5, 9, 2, 2, 9, 5, 4, 5, 5, 2, 7, 9, 1, 7, 2, 6, 9], [2, 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5, 5], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 8, 8, 8, 8, 8, 8, 8, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 8, 8, 8, 8, 8, 8, 8, 6, 3, 4, 7, 7, 5, 5, 7, 2, 6, 6], [9, 9, 6, 6, 7, 2, 5, 1, 3, 7, 3, 7, 8, 8, 8, 8, 8, 8, 8, 7, 7, 3, 7, 3, 1, 5, 2, 7, 6, 6], [6, 6, 4, 4, 6, 7, 2, 7, 4, 3, 4, 4, 7, 9, 6, 7, 7, 6, 9, 7, 4, 4, 3, 4, 7, 2, 7, 6, 4, 4], [6, 6, 4, 4, 7, 6, 7, 2, 3, 7, 1, 4, 9, 7, 7, 6, 6, 7, 7, 9, 4, 1, 7, 3, 2, 7, 6, 7, 4, 4], [2, 7, 6, 9, 7, 2, 7, 1, 2, 7, 1, 5, 5, 4, 9, 9, 9, 9, 4, 5, 5, 1, 7, 2, 1, 7, 2, 7, 9, 6], [7, 2, 9, 6, 2, 7, 1, 9, 7, 2, 5, 5, 4, 5, 9, 2, 2, 9, 5, 4, 5, 5, 2, 7, 9, 1, 7, 2, 6, 9], [6, 9, 2, 7, 7, 1, 4, 4, 6, 7, 2, 7, 9, 9, 4, 6, 6, 4, 9, 9, 7, 2, 7, 6, 4, 4, 1, 7, 7, 2], [9, 6, 7, 2, 1, 9, 4, 4, 7, 6, 7, 2, 9, 2, 6, 4, 4, 6, 2, 9, 2, 7, 6, 7, 4, 4, 9, 1, 2, 7], [7, 2, 7, 1, 7, 2, 9, 9, 4, 4, 6, 6, 2, 7, 5, 5, 5, 5, 7, 2, 6, 6, 4, 4, 9, 9, 2, 7, 1, 7], [2, 7, 1, 9, 2, 7, 9, 9, 4, 4, 6, 6, 7, 2, 5, 1, 1, 5, 2, 7, 6, 6, 4, 4, 9, 9, 7, 2, 9, 1]], "output": [[3, 7, 4, 4, 4, 4, 7], [6, 7, 7, 9, 9, 7, 7], [7, 6, 9, 7, 7, 9, 6]]}, {"input": [[3, 1, 1, 9, 5, 6, 7, 1, 1, 4, 5, 7, 3, 9, 9, 1, 1, 9, 9, 3, 7, 5, 4, 1, 1, 7, 6, 5, 9, 1], [1, 3, 9, 5, 6, 5, 1, 7, 4, 1, 7, 5, 4, 3, 1, 3, 3, 1, 3, 4, 5, 7, 1, 4, 7, 1, 5, 6, 5, 9], [6, 9, 3, 1, 7, 1, 5, 6, 9, 9, 1, 4, 9, 1, 1, 4, 4, 1, 1, 9, 4, 1, 9, 9, 6, 5, 1, 7, 1, 3], [9, 1, 1, 3, 1, 7, 6, 5, 9, 9, 4, 1, 1, 3, 4, 1, 1, 4, 3, 1, 1, 4, 9, 9, 5, 6, 7, 1, 3, 1], [6, 6, 6, 7, 3, 1, 5, 9, 3, 4, 9, 1, 6, 7, 2, 5, 5, 2, 7, 6, 1, 9, 4, 3, 9, 5, 1, 3, 7, 6], [6, 6, 7, 6, 1, 3, 9, 1, 9, 3, 1, 3, 7, 6, 5, 2, 2, 5, 6, 7, 3, 1, 3, 9, 1, 9, 3, 1, 6, 7], [6, 7, 6, 6, 1, 9, 3, 1, 9, 1, 1, 4, 6, 9, 6, 7, 7, 6, 9, 6, 4, 1, 1, 9, 1, 3, 9, 1, 6, 6], [7, 6, 6, 6, 9, 6, 1, 3, 1, 3, 4, 1, 9, 6, 7, 6, 6, 7, 6, 9, 1, 4, 3, 1, 3, 1, 8, 8, 8, 8], [1, 4, 9, 9, 3, 9, 9, 1, 1, 1, 6, 1, 5, 2, 5, 5, 5, 5, 2, 5, 1, 6, 1, 1, 1, 9, 8, 8, 8, 8], [4, 1, 9, 9, 4, 3, 1, 3, 1, 1, 1, 6, 2, 5, 5, 5, 5, 5, 5, 2, 6, 1, 1, 1, 3, 1, 8, 8, 8, 8], [5, 7, 1, 4, 9, 1, 1, 4, 2, 2, 1, 1, 5, 5, 5, 2, 2, 5, 5, 5, 1, 1, 2, 2, 4, 1, 8, 8, 8, 8], [7, 5, 4, 1, 1, 3, 4, 1, 2, 1, 1, 1, 5, 5, 2, 5, 5, 2, 5, 5, 1, 1, 1, 2, 1, 4, 3, 1, 1, 4], [3, 4, 9, 1, 6, 7, 6, 9, 7, 6, 3, 3, 1, 1, 6, 1, 1, 6, 1, 1, 3, 3, 6, 7, 9, 6, 7, 6, 1, 9], [9, 3, 1, 3, 7, 6, 9, 6, 6, 7, 3, 3, 1, 1, 1, 6, 6, 1, 1, 1, 3, 3, 7, 6, 6, 9, 6, 7, 3, 1], [9, 1, 1, 4, 2, 5, 6, 7, 3, 3, 7, 6, 1, 2, 1, 1, 1, 1, 2, 1, 6, 7, 3, 3, 7, 6, 5, 2, 4, 1], [1, 3, 4, 1, 5, 2, 7, 6, 3, 3, 6, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 3, 3, 6, 7, 2, 5, 1, 4], [1, 3, 4, 1, 5, 2, 7, 6, 3, 3, 6, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 3, 3, 6, 7, 2, 5, 1, 4], [9, 1, 1, 4, 2, 5, 6, 7, 3, 3, 7, 6, 1, 2, 1, 1, 1, 1, 2, 1, 6, 7, 3, 3, 7, 6, 5, 2, 4, 1], [9, 3, 1, 3, 7, 6, 9, 6, 6, 7, 3, 3, 1, 1, 1, 6, 6, 1, 1, 1, 3, 3, 7, 6, 6, 9, 6, 7, 3, 1], [3, 4, 9, 1, 6, 7, 6, 9, 7, 6, 3, 3, 1, 1, 6, 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8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 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, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 4, 3, 3, 3, 3, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 4, 2, 6, 6, 6, 6, 6], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 5, 5, 5, 5, 5], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 1, 1, 1, 1, 1], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[8, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8], [3, 8, 8, 8, 8, 1, 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, 1, 2, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 4, 2, 2, 2, 2, 2, 2, 4, 4, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 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, 1, 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, 1, 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, 1, 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, 1, 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, 4, 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, 4, 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, 2, 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, 2, 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, 2, 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, 2, 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, 2, 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, 2, 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, 4, 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]], "output": [[8, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 6, 8, 3, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 6, 8, 3, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [6, 6, 6, 6, 6, 1, 2, 8, 8, 8, 8, 8, 8, 8, 4, 2, 2, 2, 2, 2, 2, 4, 4, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 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, 1, 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, 1, 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, 1, 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, 1, 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, 4, 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, 4, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 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, 2, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 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, 2, 1, 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, 2, 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, 2, 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, 4, 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]]}], "test": [{"input": [[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], [9, 8, 8, 8, 4, 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, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 2, 2, 2, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 4, 4, 4, 4, 4, 1, 8, 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1, 1]]}]}, "bf45cf4b": {"train": [{"input": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 2, 2, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 2, 4, 2, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 8, 3, 8, 4, 4, 4, 4, 4, 4, 4, 4], [4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4], [4, 8, 3, 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]], "output": [[8, 3, 8, 8, 3, 8, 4, 4, 4, 8, 3, 8], [3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3], [8, 3, 8, 8, 3, 8, 4, 4, 4, 8, 3, 8], [8, 3, 8, 4, 4, 4, 8, 3, 8, 8, 3, 8], [3, 4, 3, 4, 4, 4, 3, 4, 3, 3, 4, 3], [8, 3, 8, 4, 4, 4, 8, 3, 8, 8, 3, 8], [4, 4, 4, 8, 3, 8, 4, 4, 4, 8, 3, 8], [4, 4, 4, 3, 4, 3, 4, 4, 4, 3, 4, 3], [4, 4, 4, 8, 3, 8, 4, 4, 4, 8, 3, 8]]}, {"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, 1, 3, 3, 3, 3, 3, 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8, 8, 8, 8, 8, 8, 8, 8, 8], [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, 8, 8, 1, 1, 1, 8, 8, 8, 6, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 7, 7, 7, 8, 8, 8, 1, 8, 8, 8, 8, 8, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 7, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 6, 6, 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, 8, 8, 8], [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, 8, 4, 8, 8, 2, 2, 8, 8, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 4, 8, 4, 8, 8, 2, 2, 2, 8, 8, 5, 8, 8, 8, 8, 1, 1, 8, 8, 8], [8, 8, 4, 4, 4, 8, 8, 8, 2, 8, 8, 8, 5, 5, 8, 8, 8, 1, 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, 9, 8, 8, 8, 8, 6, 6, 6, 8, 8, 8, 4, 8, 8, 8, 2, 2, 2, 8, 8], [8, 8, 9, 9, 9, 8, 8, 6, 8, 6, 8, 8, 4, 4, 4, 8, 8, 2, 8, 2, 8, 8], [8, 8, 8, 8, 9, 8, 8, 6, 8, 6, 8, 8, 8, 4, 8, 8, 8, 2, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 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9, 9, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 7, 8, 8, 8, 3, 1, 1, 1, 3, 8, 8, 6, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 7, 7, 7, 8, 3, 3, 1, 3, 3, 8, 8, 8, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 7, 8, 8, 8, 3, 1, 1, 1, 3, 8, 8, 6, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 4, 8, 4, 8, 3, 2, 2, 3, 3, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 4, 8, 4, 8, 3, 2, 2, 2, 3, 8, 5, 8, 8, 8, 8, 1, 1, 8, 8, 8], [8, 8, 4, 4, 4, 8, 3, 3, 2, 3, 3, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 3, 6, 6, 6, 3, 8, 8, 4, 8, 8, 8, 2, 2, 2, 8, 8], [8, 8, 9, 9, 9, 8, 3, 6, 3, 6, 3, 8, 4, 4, 4, 8, 8, 2, 8, 2, 8, 8], [8, 8, 8, 8, 9, 8, 3, 6, 3, 6, 3, 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8], [8, 8, 9, 9, 9, 8, 8, 6, 8, 6, 8, 8, 4, 4, 4, 8, 3, 2, 3, 2, 3, 8], [8, 8, 8, 8, 9, 8, 8, 6, 8, 6, 8, 8, 8, 4, 8, 8, 3, 2, 2, 2, 3, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8], [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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 8, 8, 2, 2, 8, 8, 8, 7, 8, 8, 8, 8, 8, 6, 6, 8, 8], [8, 8, 0, 0, 0, 8, 8, 2, 2, 2, 8, 8, 7, 7, 7, 8, 8, 8, 8, 6, 8, 8], [8, 8, 0, 0, 0, 8, 8, 8, 2, 8, 8, 8, 7, 8, 8, 8, 8, 8, 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], [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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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, 2, 8, 8, 0, 8, 8, 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8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 2, 8, 8, 0, 8, 8, 8, 8, 8, 8, 7, 8, 8, 9, 8, 9, 8, 8], [8, 8, 8, 2, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 7, 8, 8, 9, 9, 8, 8, 8], [8, 8, 2, 8, 2, 8, 8, 0, 8, 0, 8, 8, 7, 7, 7, 8, 8, 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, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8], [8, 3, 7, 3, 3, 3, 8, 1, 1, 1, 8, 3, 3, 6, 6, 3, 3, 0, 0, 0, 3, 8], [8, 3, 7, 7, 7, 3, 8, 8, 1, 8, 8, 3, 3, 3, 6, 3, 3, 0, 0, 0, 3, 8], [8, 3, 7, 3, 3, 3, 8, 1, 1, 1, 8, 3, 3, 6, 6, 3, 3, 0, 0, 0, 3, 8], [8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 4, 8, 4, 8, 3, 2, 2, 3, 3, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 4, 8, 4, 8, 3, 2, 2, 2, 3, 8, 5, 8, 8, 8, 8, 1, 1, 8, 8, 8], [8, 8, 4, 4, 4, 8, 3, 3, 2, 3, 3, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 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7, 4, 3, 4, 4, 7, 9, 6, 7, 7, 6, 9, 7, 4, 4, 3, 4, 7, 2, 7, 6, 4, 4], [9, 9, 6, 6, 7, 2, 5, 1, 3, 7, 3, 7, 7, 6, 9, 7, 7, 9, 6, 7, 7, 3, 7, 3, 1, 5, 2, 7, 6, 6], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 6, 7, 7, 9, 9, 7, 7, 6, 3, 4, 7, 7, 5, 5, 7, 2, 6, 6], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 3, 7, 4, 4, 4, 4, 7, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 2, 5, 5, 6, 4, 9, 9, 5, 9, 6, 6, 7, 7, 3, 7, 7, 3, 7, 7, 6, 6, 9, 5, 9, 9, 4, 6, 5, 5], [2, 7, 1, 5, 4, 6, 2, 9, 9, 5, 6, 6, 7, 3, 4, 3, 3, 4, 3, 7, 6, 6, 5, 9, 9, 2, 6, 4, 5, 1], [2, 7, 1, 5, 4, 6, 2, 9, 9, 5, 6, 6, 7, 3, 4, 3, 3, 4, 3, 7, 6, 6, 5, 9, 9, 2, 6, 4, 5, 1], [7, 2, 5, 5, 6, 4, 9, 9, 5, 9, 6, 6, 7, 7, 3, 7, 7, 3, 7, 7, 6, 6, 9, 5, 9, 9, 4, 6, 5, 5], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 8, 8, 8, 8, 8, 8, 8, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 8, 8, 8, 8, 8, 8, 8, 6, 3, 4, 7, 7, 5, 5, 7, 2, 6, 6], [9, 9, 6, 6, 7, 2, 5, 1, 3, 7, 3, 7, 8, 8, 8, 8, 8, 8, 8, 7, 7, 3, 7, 3, 1, 5, 2, 7, 6, 6], [6, 6, 4, 4, 6, 7, 2, 7, 4, 3, 4, 4, 7, 9, 6, 7, 7, 6, 9, 7, 4, 4, 3, 4, 7, 2, 7, 6, 4, 4], [6, 6, 4, 4, 7, 6, 7, 2, 3, 7, 1, 4, 9, 7, 7, 6, 6, 7, 7, 9, 4, 1, 7, 3, 2, 7, 6, 7, 4, 4], [2, 7, 6, 9, 7, 2, 7, 1, 2, 7, 1, 5, 5, 4, 9, 9, 9, 9, 4, 5, 5, 1, 7, 2, 1, 7, 2, 7, 9, 6], [7, 2, 9, 6, 2, 7, 1, 9, 7, 2, 5, 5, 4, 5, 9, 2, 2, 9, 5, 4, 5, 5, 2, 7, 9, 1, 7, 2, 6, 9], [6, 9, 2, 7, 7, 1, 4, 4, 6, 7, 2, 7, 9, 9, 4, 6, 6, 4, 9, 9, 7, 2, 7, 6, 4, 4, 1, 7, 7, 2], [9, 6, 7, 2, 1, 9, 4, 4, 7, 6, 7, 2, 9, 2, 6, 4, 4, 6, 2, 9, 2, 7, 6, 7, 4, 4, 9, 1, 2, 7], [7, 2, 7, 1, 7, 2, 9, 9, 4, 4, 6, 6, 2, 7, 5, 5, 5, 5, 7, 2, 6, 6, 4, 4, 9, 9, 2, 7, 1, 7], [2, 7, 1, 9, 2, 7, 9, 9, 4, 4, 6, 6, 7, 2, 5, 1, 1, 5, 2, 7, 6, 6, 4, 4, 9, 9, 7, 2, 9, 1]], "output": [[3, 7, 4, 4, 4, 4, 7], [6, 7, 7, 9, 9, 7, 7], [7, 6, 9, 7, 7, 9, 6]]}, {"input": [[3, 1, 1, 9, 5, 6, 7, 1, 1, 4, 5, 7, 3, 9, 9, 1, 1, 9, 9, 3, 7, 5, 4, 1, 1, 7, 6, 5, 9, 1], [1, 3, 9, 5, 6, 5, 1, 7, 4, 1, 7, 5, 4, 3, 1, 3, 3, 1, 3, 4, 5, 7, 1, 4, 7, 1, 5, 6, 5, 9], [6, 9, 3, 1, 7, 1, 5, 6, 9, 9, 1, 4, 9, 1, 1, 4, 4, 1, 1, 9, 4, 1, 9, 9, 6, 5, 1, 7, 1, 3], [9, 1, 1, 3, 1, 7, 6, 5, 9, 9, 4, 1, 1, 3, 4, 1, 1, 4, 3, 1, 1, 4, 9, 9, 5, 6, 7, 1, 3, 1], [6, 6, 6, 7, 3, 1, 5, 9, 3, 4, 9, 1, 6, 7, 2, 5, 5, 2, 7, 6, 1, 9, 4, 3, 9, 5, 1, 3, 7, 6], [6, 6, 7, 6, 1, 3, 9, 1, 9, 3, 1, 3, 7, 6, 5, 2, 2, 5, 6, 7, 3, 1, 3, 9, 1, 9, 3, 1, 6, 7], [6, 7, 6, 6, 1, 9, 3, 1, 9, 1, 1, 4, 6, 9, 6, 7, 7, 6, 9, 6, 4, 1, 1, 9, 1, 3, 9, 1, 6, 6], [7, 6, 6, 6, 9, 6, 1, 3, 1, 3, 4, 1, 9, 6, 7, 6, 6, 7, 6, 9, 1, 4, 3, 1, 3, 1, 8, 8, 8, 8], [1, 4, 9, 9, 3, 9, 9, 1, 1, 1, 6, 1, 5, 2, 5, 5, 5, 5, 2, 5, 1, 6, 1, 1, 1, 9, 8, 8, 8, 8], [4, 1, 9, 9, 4, 3, 1, 3, 1, 1, 1, 6, 2, 5, 5, 5, 5, 5, 5, 2, 6, 1, 1, 1, 3, 1, 8, 8, 8, 8], [5, 7, 1, 4, 9, 1, 1, 4, 2, 2, 1, 1, 5, 5, 5, 2, 2, 5, 5, 5, 1, 1, 2, 2, 4, 1, 8, 8, 8, 8], [7, 5, 4, 1, 1, 3, 4, 1, 2, 1, 1, 1, 5, 5, 2, 5, 5, 2, 5, 5, 1, 1, 1, 2, 1, 4, 3, 1, 1, 4], [3, 4, 9, 1, 6, 7, 6, 9, 7, 6, 3, 3, 1, 1, 6, 1, 1, 6, 1, 1, 3, 3, 6, 7, 9, 6, 7, 6, 1, 9], [9, 3, 1, 3, 7, 6, 9, 6, 6, 7, 3, 3, 1, 1, 1, 6, 6, 1, 1, 1, 3, 3, 7, 6, 6, 9, 6, 7, 3, 1], [9, 1, 1, 4, 2, 5, 6, 7, 3, 3, 7, 6, 1, 2, 1, 1, 1, 1, 2, 1, 6, 7, 3, 3, 7, 6, 5, 2, 4, 1], [1, 3, 4, 1, 5, 2, 7, 6, 3, 3, 6, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 3, 3, 6, 7, 2, 5, 1, 4], [1, 3, 4, 1, 5, 2, 7, 6, 3, 3, 6, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 3, 3, 6, 7, 2, 5, 1, 4], [9, 1, 1, 4, 2, 5, 6, 7, 3, 3, 7, 6, 1, 2, 1, 1, 1, 1, 2, 1, 6, 7, 3, 3, 7, 6, 5, 2, 4, 1], [9, 3, 1, 3, 7, 6, 9, 6, 6, 7, 3, 3, 1, 1, 1, 6, 6, 1, 1, 1, 3, 3, 7, 6, 6, 9, 6, 7, 3, 1], [3, 4, 9, 1, 6, 7, 6, 9, 7, 6, 3, 3, 1, 1, 6, 1, 1, 6, 1, 1, 3, 3, 6, 7, 9, 6, 7, 6, 1, 9], [7, 5, 4, 1, 1, 3, 4, 1, 2, 1, 1, 1, 5, 5, 2, 5, 5, 2, 5, 5, 1, 1, 1, 2, 1, 4, 3, 1, 1, 4], [5, 7, 1, 4, 9, 1, 1, 4, 2, 2, 1, 1, 5, 5, 5, 2, 2, 5, 5, 5, 1, 1, 2, 2, 4, 1, 1, 9, 4, 1], [4, 1, 9, 9, 4, 3, 1, 3, 1, 1, 1, 6, 2, 5, 5, 5, 5, 5, 5, 2, 6, 1, 1, 1, 3, 1, 3, 4, 9, 9], [1, 4, 9, 9, 3, 9, 9, 1, 1, 1, 6, 1, 5, 2, 5, 5, 5, 5, 2, 5, 1, 6, 1, 1, 1, 9, 9, 3, 9, 9], [7, 6, 6, 6, 9, 6, 1, 3, 1, 3, 4, 1, 9, 6, 7, 6, 6, 7, 6, 9, 1, 4, 3, 1, 3, 1, 6, 9, 6, 6], [6, 7, 6, 6, 1, 9, 3, 1, 9, 1, 1, 4, 6, 9, 6, 7, 7, 6, 9, 6, 4, 1, 1, 9, 1, 3, 9, 1, 6, 6], [6, 6, 7, 6, 1, 3, 9, 1, 9, 3, 1, 3, 7, 6, 5, 2, 2, 5, 6, 7, 3, 1, 3, 9, 1, 9, 3, 1, 6, 7], [6, 6, 6, 7, 3, 1, 5, 9, 3, 4, 9, 1, 6, 7, 2, 5, 5, 2, 7, 6, 1, 9, 4, 3, 9, 5, 1, 3, 7, 6], [9, 1, 1, 3, 1, 7, 6, 5, 9, 9, 4, 1, 1, 3, 4, 1, 1, 4, 3, 1, 1, 4, 9, 9, 5, 6, 7, 1, 3, 1], [6, 9, 3, 1, 7, 1, 5, 6, 9, 9, 1, 4, 9, 1, 1, 4, 4, 1, 1, 9, 4, 1, 9, 9, 6, 5, 1, 7, 1, 3]], "output": [[6, 9, 6, 6], [9, 3, 9, 9], [3, 4, 9, 9], [1, 9, 4, 1]]}], "test": [{"input": [[4, 4, 1, 3, 5, 7, 7, 9, 6, 1, 6, 6, 4, 4, 7, 7, 7, 7, 4, 4, 6, 6, 1, 6, 9, 7, 7, 5, 3, 1], [4, 4, 3, 3, 7, 5, 9, 7, 6, 6, 6, 6, 4, 4, 7, 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7, 7, 2, 2, 6, 4, 6, 2, 2, 2, 2, 6, 4, 6, 2, 2, 7, 7, 7, 4, 4, 1, 5], [4, 7, 7, 9, 4, 3, 4, 4, 7, 2, 9, 9, 4, 7, 7, 9, 9, 7, 7, 4, 9, 9, 2, 7, 4, 4, 3, 4, 9, 7], [7, 4, 9, 7, 3, 4, 4, 4, 7, 7, 9, 1, 7, 4, 9, 7, 7, 9, 4, 7, 1, 9, 7, 7, 4, 4, 4, 3, 7, 9], [7, 9, 4, 7, 4, 4, 3, 1, 4, 4, 7, 2, 7, 9, 2, 3, 3, 2, 9, 7, 2, 7, 4, 4, 1, 3, 4, 4, 7, 4], [9, 7, 7, 4, 4, 4, 3, 3, 4, 4, 7, 7, 9, 7, 3, 2, 2, 3, 7, 9, 7, 7, 4, 4, 3, 3, 4, 4, 4, 7], [4, 3, 4, 4, 9, 7, 7, 5, 1, 5, 6, 6, 7, 2, 1, 9, 9, 1, 2, 7, 6, 6, 5, 1, 5, 7, 7, 9, 4, 4], [3, 4, 4, 4, 7, 9, 5, 7, 5, 1, 6, 1, 7, 7, 9, 9, 9, 9, 7, 7, 1, 6, 1, 5, 7, 5, 9, 7, 4, 4]]}]}, "135a2760": {"train": [{"input": [[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, 3], [3, 2, 1, 3, 1, 3, 1, 3, 3, 3, 1, 2, 3], [3, 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]], "output": [[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, 3], [3, 2, 1, 3, 1, 3, 1, 3, 1, 3, 1, 2, 3], 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8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8], [8, 8, 7, 7, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 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, 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, 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, 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, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 1, 1, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 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3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3], [4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 3, 3, 3, 3], [4, 3, 3, 4, 3, 4, 4, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3], [4, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 4, 4, 1, 1, 1, 1, 1], [1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 4, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 4, 4, 4, 1, 1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 4, 4, 4, 1, 1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1], [1, 1, 4, 4, 1, 1, 1, 4, 4, 4, 1, 1, 1, 1, 1, 1], [1, 1, 1, 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]], "output": [[4, 4, 4, 4, 4], [4, 1, 1, 1, 4], [4, 1, 4, 1, 4], [4, 1, 1, 1, 4], [4, 4, 4, 4, 4]]}, {"input": [[4, 4, 4, 4, 9, 9, 9, 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9, 9], [9, 4, 4, 4, 9], [9, 4, 9, 4, 9], [9, 4, 4, 4, 9], [9, 4, 9, 4, 9], [9, 4, 4, 4, 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, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 4, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 4, 4, 2, 2, 2, 4, 4, 4, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2], [2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2], [2, 2, 2, 2, 4, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 2, 4, 2, 2, 2, 2], [2, 2, 2, 2, 4, 4, 2, 4, 2, 4, 4, 4, 2, 4, 2, 4, 4, 2, 2, 2, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 2, 4, 4, 4, 2, 2, 4, 4, 2, 2, 2, 4, 4, 4, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 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, 4, 4, 4, 4, 4], [4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4], [4, 2, 4, 4, 4, 4, 4, 2, 2, 2, 4], [4, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4], [4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4], [4, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4], [4, 2, 4, 4, 4, 4, 4, 2, 2, 2, 4], [4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}], "test": 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 1, 3, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 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]], "output": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 8, 8, 8, 8, 8, 1, 4, 4, 4, 4, 4, 1], [1, 8, 1, 1, 8, 8, 1, 4, 1, 4, 1, 4, 1], [1, 8, 1, 1, 8, 8, 1, 4, 1, 1, 1, 4, 1], [1, 8, 8, 8, 1, 8, 1, 4, 4, 1, 4, 4, 1], [1, 8, 8, 8, 8, 8, 1, 4, 4, 4, 4, 4, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 3, 3, 3, 3, 3, 1, 9, 9, 9, 9, 9, 1], [1, 3, 1, 1, 1, 3, 1, 9, 1, 9, 1, 9, 1], [1, 3, 3, 1, 3, 3, 1, 9, 1, 1, 9, 9, 1], [1, 3, 3, 1, 3, 3, 1, 9, 9, 1, 9, 9, 1], [1, 3, 3, 3, 3, 3, 1, 9, 9, 9, 9, 9, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}], "test": [{"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, 2, 2, 3, 3, 9, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 8, 8, 8, 8, 8, 3], [3, 3, 2, 3, 3, 3, 9, 9, 3, 3, 3, 4, 4, 4, 4, 4, 3, 8, 8, 8, 8, 8, 3], [3, 2, 2, 2, 3, 3, 3, 9, 3, 3, 3, 4, 4, 4, 4, 4, 3, 8, 8, 8, 8, 8, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 8, 8, 8, 8, 8, 3], [3, 5, 3, 3, 3, 1, 1, 1, 3, 3, 3, 4, 4, 4, 4, 4, 3, 8, 8, 8, 8, 8, 3], [3, 3, 5, 5, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 5, 3, 5, 3, 1, 3, 1, 3, 3, 3, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 3], [3, 8, 8, 8, 3, 7, 7, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 3], [3, 8, 3, 8, 3, 3, 7, 7, 3, 3, 3, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 3], [3, 3, 8, 3, 3, 7, 7, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 1, 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, 3], [3, 6, 3, 3, 3, 4, 4, 3, 3, 3, 3, 6, 6, 6, 6, 6, 3, 9, 9, 9, 9, 9, 3], [3, 3, 6, 6, 3, 3, 4, 3, 3, 3, 3, 6, 6, 6, 6, 6, 3, 9, 9, 9, 9, 9, 3], [3, 6, 3, 3, 3, 3, 4, 4, 3, 3, 3, 6, 6, 6, 6, 6, 3, 9, 9, 9, 9, 9, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 3, 9, 9, 9, 9, 9, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 3, 9, 9, 9, 9, 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]]}]}, "5961cc34": {"train": [{"input": [[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, 1, 1, 1, 1, 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, 1, 1, 1, 1, 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, 4, 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, 2, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 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8], [8, 8, 1, 1, 8, 8, 8, 8, 8, 1, 1, 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, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 8, 8, 1, 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, 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, 1, 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, 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, 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, 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, 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, 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, 2, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 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, 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, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 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, 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, 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, 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, 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, 2, 2, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 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, 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, 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, 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, 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, 2, 8, 8, 8, 8, 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, 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, 1, 1, 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, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 3, 1, 1, 1, 1, 1, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 3, 1, 1, 1, 1, 1, 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, 8, 8, 8, 3, 3, 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, 1, 1, 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, 8, 8], [8, 8, 3, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 3, 1, 1, 1, 1, 1, 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, 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, 4, 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, 2, 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, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8], [8, 8, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 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, 8, 8], [8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [8, 8, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 2, 2, 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, 2, 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, 2, 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, 2, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 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, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 3, 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, 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, 1, 1, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 1, 1, 1, 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, 8, 8, 4, 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, 2, 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]], "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, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 2, 2, 2, 2, 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, 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], [8, 8, 8, 2, 2, 2, 2, 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, 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, 2, 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, 2, 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, 2, 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, 2, 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, 2, 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, 2, 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]]}], "test": [{"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, 1, 1, 1, 1, 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, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 3, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 3, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 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, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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, 8, 8, 8, 8, 1, 1, 1, 1, 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, 1, 1, 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, 1, 1, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 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, 8, 8, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}]}, "5dbc8537": {"train": [{"input": [[9, 4, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4], [9, 4, 4, 4, 4, 4, 9, 4, 4, 4, 8, 8, 8, 8, 8], [9, 9, 4, 4, 9, 9, 9, 4, 4, 4, 8, 8, 8, 8, 8], [9, 9, 4, 4, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4], [9, 9, 4, 4, 9, 9, 9, 4, 3, 3, 4, 1, 1, 4, 4], [9, 9, 4, 4, 9, 9, 9, 4, 3, 3, 4, 1, 1, 4, 4], [9, 9, 4, 4, 4, 9, 9, 4, 3, 3, 4, 4, 4, 4, 4], [9, 9, 4, 4, 9, 9, 9, 4, 3, 3, 4, 5, 5, 5, 5], [9, 4, 4, 9, 9, 9, 9, 4, 3, 3, 4, 4, 4, 4, 4], [9, 4, 4, 9, 9, 9, 9, 4, 3, 3, 4, 4, 4, 4, 4], [9, 9, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 7, 7], [9, 9, 9, 4, 4, 9, 9, 4, 5, 5, 5, 5, 4, 7, 7], [9, 9, 9, 4, 4, 9, 9, 4, 4, 4, 4, 4, 4, 7, 7], [9, 9, 9, 4, 4, 9, 9, 4, 4, 0, 4, 4, 4, 4, 4], [9, 9, 4, 4, 4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4]], "output": [[9, 8, 8, 8, 8, 8, 9], [9, 8, 8, 8, 8, 8, 9], [9, 9, 3, 3, 9, 9, 9], [9, 9, 3, 3, 9, 9, 9], [9, 9, 3, 3, 9, 9, 9], [9, 9, 3, 3, 9, 9, 9], [9, 9, 3, 3, 0, 9, 9], [9, 9, 3, 3, 9, 9, 9], [9, 1, 1, 9, 9, 9, 9], [9, 1, 1, 9, 9, 9, 9], [9, 9, 5, 5, 5, 5, 9], [9, 9, 9, 7, 7, 9, 9], [9, 9, 9, 7, 7, 9, 9], [9, 9, 9, 7, 7, 9, 9], [9, 9, 5, 5, 5, 5, 9]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 7, 4, 7, 4, 7, 8, 8, 8, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8], [8, 7, 4, 7, 4, 7, 4, 8, 9, 8, 6, 6, 8, 8, 1, 1, 1, 8, 8, 8], [8, 4, 7, 4, 7, 4, 7, 8, 9, 8, 6, 6, 8, 8, 1, 9, 1, 8, 8, 8], [8, 7, 4, 7, 4, 7, 4, 8, 9, 8, 6, 6, 8, 8, 1, 1, 1, 8, 0, 8], [8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 6, 6, 8, 8, 1, 9, 1, 8, 8, 8], [8, 8, 5, 5, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8], [8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8], [8, 8, 5, 5, 8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 8, 4, 4, 8, 8, 8], [8, 8, 5, 5, 8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 8, 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], [2, 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, 8, 8, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 8, 8, 8, 2, 2, 2, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2], [8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 8, 8, 8, 8, 8, 2, 2, 2, 8, 2, 2, 8, 8, 8, 8, 8, 8, 2], [2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 8, 2], [2, 2, 8, 8, 2, 2, 2, 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, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 3, 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, 3, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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6, 6, 7, 3, 1, 5, 9, 3, 4, 9, 1, 6, 7, 2, 5, 5, 2, 7, 6, 1, 9, 4, 3, 9, 5, 1, 3, 7, 6], [9, 1, 1, 3, 1, 7, 6, 5, 9, 9, 4, 1, 1, 3, 4, 1, 1, 4, 3, 1, 1, 4, 9, 9, 5, 6, 7, 1, 3, 1], [6, 9, 3, 1, 7, 1, 5, 6, 9, 9, 1, 4, 9, 1, 1, 4, 4, 1, 1, 9, 4, 1, 9, 9, 6, 5, 1, 7, 1, 3]], "output": [[6, 9, 6, 6], [9, 3, 9, 9], [3, 4, 9, 9], [1, 9, 4, 1]]}, {"input": [[9, 9, 2, 3, 4, 4, 7, 5, 3, 3, 6, 6, 3, 5, 6, 4, 4, 6, 5, 3, 6, 6, 3, 3, 5, 7, 4, 4, 3, 2], [7, 9, 3, 5, 4, 4, 5, 7, 3, 3, 6, 6, 6, 3, 4, 6, 6, 4, 3, 6, 6, 6, 3, 3, 7, 5, 4, 4, 5, 3], [3, 2, 9, 9, 7, 5, 4, 4, 4, 1, 3, 3, 6, 4, 4, 7, 7, 4, 4, 6, 3, 8, 8, 8, 8, 8, 5, 7, 9, 9], [2, 3, 7, 9, 5, 7, 4, 4, 1, 4, 3, 3, 4, 6, 7, 4, 4, 7, 6, 4, 3, 8, 8, 8, 8, 8, 7, 5, 9, 7], [7, 7, 9, 3, 9, 9, 5, 3, 3, 6, 6, 4, 6, 7, 9, 9, 9, 9, 7, 6, 4, 8, 8, 8, 8, 8, 9, 9, 3, 9], [7, 7, 3, 9, 7, 9, 3, 2, 5, 3, 4, 6, 2, 6, 9, 9, 9, 9, 6, 2, 6, 8, 8, 8, 8, 8, 9, 7, 9, 3], [9, 3, 7, 7, 3, 2, 9, 9, 6, 4, 4, 7, 9, 2, 6, 7, 7, 6, 2, 9, 7, 4, 4, 6, 9, 9, 2, 3, 7, 7], [3, 9, 7, 7, 2, 3, 7, 9, 4, 6, 7, 4, 2, 9, 2, 6, 6, 2, 9, 2, 4, 7, 6, 4, 9, 7, 3, 2, 7, 7], [3, 3, 4, 1, 3, 5, 6, 4, 2, 4, 7, 7, 1, 6, 7, 2, 2, 7, 6, 1, 7, 7, 4, 2, 4, 6, 5, 3, 1, 4], [3, 3, 1, 4, 6, 3, 4, 6, 2, 2, 7, 1, 6, 1, 2, 7, 7, 2, 1, 6, 1, 7, 2, 2, 6, 4, 3, 6, 4, 1], [6, 6, 3, 3, 6, 4, 4, 7, 1, 1, 2, 4, 7, 2, 1, 6, 6, 1, 2, 7, 4, 2, 1, 1, 7, 4, 4, 6, 3, 3], [6, 6, 3, 3, 4, 6, 7, 4, 1, 3, 2, 2, 2, 7, 6, 1, 1, 6, 7, 2, 2, 2, 3, 1, 4, 7, 6, 4, 3, 3], [3, 6, 6, 4, 6, 2, 9, 2, 9, 9, 9, 7, 2, 4, 1, 7, 7, 1, 4, 2, 7, 9, 9, 9, 2, 9, 2, 6, 4, 6], [5, 3, 4, 6, 7, 6, 2, 9, 9, 9, 7, 9, 2, 2, 7, 7, 7, 7, 2, 2, 9, 7, 9, 9, 9, 2, 6, 7, 6, 4], [6, 4, 4, 7, 9, 9, 6, 2, 9, 7, 9, 9, 3, 1, 2, 4, 4, 2, 1, 3, 9, 9, 7, 9, 2, 6, 9, 9, 7, 4], [4, 6, 7, 4, 9, 9, 7, 6, 7, 9, 9, 9, 1, 1, 2, 2, 2, 2, 1, 1, 9, 9, 9, 7, 6, 7, 9, 9, 4, 7], [4, 6, 7, 4, 9, 9, 7, 6, 7, 9, 9, 9, 1, 1, 2, 2, 2, 2, 1, 1, 9, 9, 9, 7, 6, 7, 9, 9, 4, 7], [6, 4, 4, 7, 9, 9, 6, 2, 9, 7, 9, 9, 3, 1, 2, 4, 4, 2, 1, 3, 9, 9, 7, 9, 2, 6, 9, 9, 7, 4], [5, 3, 4, 6, 7, 6, 2, 9, 9, 9, 7, 9, 2, 2, 7, 7, 7, 7, 2, 2, 9, 7, 9, 9, 9, 2, 6, 7, 6, 4], [3, 6, 6, 4, 6, 2, 9, 2, 9, 9, 9, 7, 2, 4, 1, 7, 7, 1, 4, 2, 7, 9, 9, 9, 2, 9, 2, 6, 4, 6], [6, 6, 3, 3, 4, 6, 7, 4, 1, 3, 2, 2, 2, 7, 6, 1, 1, 6, 7, 2, 2, 2, 3, 1, 4, 7, 6, 4, 3, 3], [6, 6, 3, 3, 6, 4, 4, 7, 1, 1, 2, 4, 7, 2, 1, 6, 6, 1, 2, 7, 4, 2, 1, 1, 7, 4, 4, 6, 3, 3], [3, 3, 1, 4, 6, 3, 4, 6, 2, 2, 7, 1, 6, 1, 2, 7, 7, 2, 1, 6, 1, 7, 2, 2, 6, 4, 3, 6, 4, 1], [3, 3, 4, 1, 3, 5, 6, 4, 2, 4, 7, 7, 1, 6, 7, 2, 2, 7, 6, 1, 7, 7, 4, 2, 4, 6, 5, 3, 1, 4], [3, 9, 7, 7, 2, 3, 7, 9, 4, 6, 7, 4, 2, 9, 2, 6, 6, 2, 9, 2, 4, 7, 6, 4, 9, 7, 3, 2, 7, 7], [9, 3, 7, 7, 3, 2, 9, 9, 6, 4, 4, 7, 9, 2, 6, 7, 7, 6, 2, 9, 7, 4, 4, 6, 9, 9, 2, 3, 7, 7], [7, 7, 3, 9, 7, 9, 3, 2, 5, 3, 4, 6, 2, 6, 9, 9, 9, 9, 6, 2, 6, 4, 3, 5, 2, 3, 9, 7, 9, 3], [7, 7, 9, 3, 9, 9, 5, 3, 3, 6, 6, 4, 6, 7, 9, 9, 9, 9, 7, 6, 4, 6, 6, 3, 3, 5, 9, 9, 3, 9], [2, 3, 7, 9, 5, 7, 4, 4, 1, 4, 3, 3, 4, 6, 7, 4, 4, 7, 6, 4, 3, 3, 4, 1, 4, 4, 7, 5, 9, 7], [3, 2, 9, 9, 7, 5, 4, 4, 4, 1, 3, 3, 6, 4, 4, 7, 7, 4, 4, 6, 3, 3, 1, 4, 4, 4, 5, 7, 9, 9]], "output": [[3, 1, 4, 4, 4], [3, 4, 1, 4, 4], [6, 6, 3, 3, 5], [4, 3, 5, 2, 3]]}, {"input": [[3, 5, 3, 3, 6, 6, 5, 4, 1, 4, 9, 9, 4, 3, 9, 9, 9, 9, 3, 4, 9, 9, 4, 1, 4, 5, 6, 6, 3, 3], [5, 3, 3, 3, 6, 6, 4, 5, 4, 1, 9, 9, 3, 4, 9, 1, 1, 9, 4, 3, 9, 9, 1, 4, 5, 4, 6, 6, 3, 3], [1, 1, 3, 5, 5, 4, 6, 6, 9, 1, 1, 4, 9, 9, 4, 5, 5, 4, 9, 9, 4, 1, 1, 9, 6, 6, 4, 5, 5, 3], [1, 1, 5, 3, 4, 5, 6, 6, 1, 9, 4, 1, 9, 1, 4, 4, 4, 4, 1, 9, 1, 4, 9, 1, 6, 6, 5, 4, 3, 5], [6, 9, 9, 9, 3, 5, 3, 3, 4, 3, 9, 9, 9, 2, 6, 9, 9, 6, 2, 9, 9, 9, 3, 4, 3, 3, 5, 3, 9, 9], [9, 6, 9, 9, 5, 3, 3, 3, 3, 4, 9, 1, 9, 9, 9, 6, 6, 9, 9, 9, 1, 9, 4, 3, 3, 3, 3, 5, 9, 9], [9, 9, 6, 9, 1, 1, 3, 5, 9, 9, 4, 4, 6, 9, 9, 2, 2, 9, 9, 6, 4, 4, 9, 9, 5, 3, 1, 1, 9, 6], [9, 9, 9, 6, 1, 1, 5, 3, 9, 1, 5, 4, 9, 6, 9, 9, 9, 9, 6, 9, 4, 5, 1, 9, 3, 5, 1, 1, 6, 9], [1, 4, 9, 1, 4, 3, 9, 9, 5, 5, 7, 2, 4, 3, 2, 4, 4, 2, 3, 4, 2, 7, 5, 5, 9, 9, 3, 4, 1, 9], [4, 1, 1, 9, 3, 4, 9, 1, 4, 5, 2, 7, 3, 4, 4, 2, 2, 4, 4, 3, 7, 2, 5, 4, 1, 9, 4, 3, 9, 1], [9, 9, 1, 4, 9, 9, 4, 5, 6, 4, 5, 5, 2, 4, 4, 3, 3, 4, 4, 2, 5, 5, 4, 6, 5, 4, 9, 9, 4, 1], [9, 9, 4, 1, 9, 1, 4, 4, 4, 5, 4, 5, 4, 2, 3, 4, 4, 3, 2, 4, 5, 4, 5, 4, 4, 4, 1, 9, 1, 4], [4, 3, 9, 9, 9, 9, 6, 9, 5, 9, 7, 7, 5, 5, 7, 2, 2, 7, 5, 5, 7, 7, 9, 5, 9, 6, 9, 9, 9, 9], [3, 4, 9, 1, 2, 9, 9, 6, 9, 5, 7, 7, 4, 5, 2, 7, 7, 2, 5, 4, 7, 7, 5, 9, 6, 9, 9, 2, 1, 9], [9, 9, 4, 4, 6, 9, 9, 9, 7, 7, 5, 9, 5, 4, 5, 5, 5, 5, 4, 5, 9, 5, 7, 7, 9, 8, 8, 8, 8, 4], [9, 1, 5, 4, 9, 6, 2, 9, 7, 7, 9, 5, 4, 6, 4, 5, 5, 4, 6, 4, 5, 9, 7, 7, 9, 8, 8, 8, 8, 5], [9, 1, 5, 4, 9, 6, 2, 9, 7, 7, 9, 5, 4, 6, 4, 5, 5, 4, 6, 4, 5, 9, 7, 7, 9, 8, 8, 8, 8, 5], [9, 9, 4, 4, 6, 9, 9, 9, 7, 7, 5, 9, 5, 4, 5, 5, 5, 5, 4, 5, 9, 5, 7, 7, 9, 8, 8, 8, 8, 4], [3, 4, 9, 1, 2, 9, 9, 6, 9, 5, 7, 7, 4, 5, 2, 7, 7, 2, 5, 4, 7, 7, 5, 9, 6, 8, 8, 8, 8, 9], [4, 3, 9, 9, 9, 9, 6, 9, 5, 9, 7, 7, 5, 5, 7, 2, 2, 7, 5, 5, 7, 7, 9, 5, 9, 8, 8, 8, 8, 9], [9, 9, 4, 1, 9, 1, 4, 4, 4, 5, 4, 5, 4, 2, 3, 4, 4, 3, 2, 4, 5, 4, 5, 4, 4, 8, 8, 8, 8, 4], [9, 9, 1, 4, 9, 9, 4, 5, 6, 4, 5, 5, 2, 4, 4, 3, 3, 4, 4, 2, 5, 5, 4, 6, 5, 8, 8, 8, 8, 1], [4, 1, 1, 9, 3, 4, 9, 1, 4, 5, 2, 7, 3, 4, 4, 2, 2, 4, 4, 3, 7, 2, 5, 4, 1, 8, 8, 8, 8, 1], [1, 4, 9, 1, 4, 3, 9, 9, 5, 5, 7, 2, 4, 3, 2, 4, 4, 2, 3, 4, 2, 7, 5, 5, 9, 9, 3, 4, 1, 9], [9, 9, 9, 6, 1, 1, 5, 3, 9, 1, 5, 4, 9, 6, 9, 9, 9, 9, 6, 9, 4, 5, 1, 9, 3, 5, 1, 1, 6, 9], [9, 9, 6, 9, 1, 1, 3, 5, 9, 9, 4, 4, 6, 9, 9, 2, 2, 9, 9, 6, 4, 4, 9, 9, 5, 3, 1, 1, 9, 6], [9, 6, 9, 9, 5, 3, 3, 3, 3, 4, 9, 1, 9, 9, 9, 6, 6, 9, 9, 9, 1, 9, 4, 3, 3, 3, 3, 5, 9, 9], [6, 9, 9, 9, 3, 5, 3, 3, 4, 3, 9, 9, 9, 2, 6, 9, 9, 6, 2, 9, 9, 9, 3, 4, 3, 3, 5, 3, 9, 9], [1, 1, 5, 3, 4, 5, 6, 6, 1, 9, 4, 1, 9, 1, 4, 4, 4, 4, 1, 9, 1, 4, 9, 1, 6, 6, 5, 4, 3, 5], [1, 1, 3, 5, 5, 4, 6, 6, 9, 1, 1, 4, 9, 9, 4, 5, 5, 4, 9, 9, 4, 1, 1, 9, 6, 6, 4, 5, 5, 3]], "output": [[9, 9, 6, 4], [2, 6, 9, 4], [2, 6, 9, 4], [9, 9, 6, 4], [9, 9, 2, 1], [6, 9, 9, 9], [4, 1, 9, 1], [4, 9, 9, 4], [9, 4, 3, 9]]}, {"input": [[1, 9, 4, 4, 9, 9, 2, 7, 6, 6, 9, 9, 7, 6, 7, 2, 2, 7, 6, 7, 9, 9, 6, 6, 7, 2, 9, 9, 4, 4], [7, 1, 4, 4, 9, 9, 7, 2, 6, 6, 9, 9, 6, 7, 2, 7, 7, 2, 7, 6, 9, 9, 6, 6, 2, 7, 9, 9, 4, 4], [2, 7, 1, 9, 2, 7, 9, 9, 4, 4, 6, 6, 7, 2, 5, 1, 1, 5, 2, 7, 6, 6, 4, 4, 9, 9, 7, 2, 9, 1], [7, 2, 7, 1, 7, 2, 9, 9, 4, 4, 6, 6, 2, 7, 5, 5, 5, 5, 7, 2, 6, 6, 4, 4, 9, 9, 2, 7, 1, 7], [9, 6, 7, 2, 1, 9, 4, 4, 7, 6, 7, 2, 9, 2, 6, 4, 4, 6, 2, 9, 2, 7, 6, 7, 4, 4, 9, 1, 2, 7], [6, 9, 2, 7, 7, 1, 4, 4, 6, 7, 2, 7, 9, 9, 4, 6, 6, 4, 9, 9, 7, 2, 7, 6, 4, 4, 1, 7, 7, 2], [7, 2, 9, 6, 2, 7, 1, 9, 7, 2, 5, 5, 4, 5, 9, 2, 2, 9, 5, 4, 5, 5, 2, 7, 9, 1, 7, 2, 6, 9], [2, 7, 6, 9, 7, 2, 7, 1, 2, 7, 1, 5, 5, 4, 9, 9, 9, 9, 4, 5, 5, 1, 7, 2, 1, 7, 2, 7, 9, 6], [6, 6, 4, 4, 7, 6, 7, 2, 3, 7, 1, 4, 9, 7, 7, 6, 6, 7, 7, 9, 4, 1, 7, 3, 2, 7, 6, 7, 4, 4], [6, 6, 4, 4, 6, 7, 2, 7, 4, 3, 4, 4, 7, 9, 6, 7, 7, 6, 9, 7, 4, 4, 3, 4, 7, 2, 7, 6, 4, 4], [9, 9, 6, 6, 7, 2, 5, 1, 3, 7, 3, 7, 7, 6, 9, 7, 7, 9, 6, 7, 7, 3, 7, 3, 1, 5, 2, 7, 6, 6], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 6, 7, 7, 9, 9, 7, 7, 6, 3, 4, 7, 7, 5, 5, 7, 2, 6, 6], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 3, 7, 4, 4, 4, 4, 7, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 2, 5, 5, 6, 4, 9, 9, 5, 9, 6, 6, 7, 7, 3, 7, 7, 3, 7, 7, 6, 6, 9, 5, 9, 9, 4, 6, 5, 5], [2, 7, 1, 5, 4, 6, 2, 9, 9, 5, 6, 6, 7, 3, 4, 3, 3, 4, 3, 7, 6, 6, 5, 9, 9, 2, 6, 4, 5, 1], [2, 7, 1, 5, 4, 6, 2, 9, 9, 5, 6, 6, 7, 3, 4, 3, 3, 4, 3, 7, 6, 6, 5, 9, 9, 2, 6, 4, 5, 1], [7, 2, 5, 5, 6, 4, 9, 9, 5, 9, 6, 6, 7, 7, 3, 7, 7, 3, 7, 7, 6, 6, 9, 5, 9, 9, 4, 6, 5, 5], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 8, 8, 8, 8, 8, 8, 8, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 8, 8, 8, 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3, 2, 6, 6, 2, 9, 9, 2, 6, 6, 2, 3, 3, 8, 8, 8, 4, 4, 4, 4], [5, 9, 4, 4, 4, 3, 8, 8, 6, 9, 2, 6, 6, 2, 9, 8, 8, 9, 2, 6, 6, 2, 9, 6, 8, 8, 3, 4, 4, 4], [9, 5, 5, 4, 4, 3, 8, 3, 2, 6, 6, 6, 8, 6, 8, 9, 9, 8, 6, 8, 6, 6, 6, 2, 3, 8, 3, 4, 4, 5], [4, 5, 5, 9, 3, 8, 3, 3, 2, 6, 9, 2, 8, 6, 6, 2, 2, 6, 6, 8, 2, 9, 6, 2, 3, 3, 8, 3, 9, 5], [4, 4, 9, 5, 8, 8, 4, 4, 6, 6, 6, 9, 6, 8, 8, 6, 6, 8, 8, 6, 9, 6, 6, 6, 4, 4, 8, 8, 5, 9], [2, 3, 3, 8, 6, 2, 2, 6, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 6, 2, 2, 6, 8, 3], [3, 8, 8, 3, 9, 6, 6, 6, 9, 5, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 9, 6, 6, 6, 9, 3, 8], [8, 2, 8, 3, 2, 6, 9, 6, 4, 8, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 8, 4, 6, 9, 6, 2, 3, 8], [2, 8, 3, 2, 6, 6, 2, 9, 8, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 8, 9, 2, 6, 6, 2, 3], [6, 9, 2, 6, 6, 8, 8, 6, 9, 9, 9, 6, 9, 9, 9, 8, 8, 9, 9, 9, 6, 9, 9, 9, 6, 8, 8, 6, 6, 2], [2, 6, 6, 6, 2, 6, 6, 8, 9, 9, 9, 9, 9, 5, 8, 8, 8, 8, 5, 9, 9, 9, 9, 9, 8, 6, 6, 2, 6, 6], [7, 7, 7, 7, 7, 7, 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4, 2, 2, 2, 2, 2, 1, 1, 4, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 4, 4, 1, 1, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 4, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 3, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 2, 2, 2, 1, 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], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 2, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [8, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 2, 2, 2, 3, 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], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}], "test": [{"input": [[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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 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], [4, 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], [4, 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], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}]}, "9ba4a9aa": {"train": [{"input": [[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, 2, 9, 2, 8, 8, 8], [1, 3, 1, 2, 8, 2, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 9, 2, 9, 8, 8, 8], [1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 9, 2, 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, 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, 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8], [8, 8, 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, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 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, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 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, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 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, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 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, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 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, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 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, 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4, 4, 4, 4, 4, 4], [4, 2, 4, 2, 4, 1, 4, 2, 4, 2, 4, 2, 4, 1, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4], [4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4], [4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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]], "output": [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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2, 4, 2, 4, 2, 4, 2, 4, 2, 4], [4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 2, 4, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 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]]}, {"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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 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, 2, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 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, 2, 8, 3, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 3, 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, 2, 8, 3, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 3, 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, 2, 8, 3, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 3, 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, 2, 8, 3, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 3, 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, 2, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8], [8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8, 8, 8], [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], [8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 9, 8, 9, 8, 9, 8, 8, 8, 1, 8, 1, 8, 8, 8, 8], [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], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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], [8, 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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8], [8, 8, 8, 8, 8, 8, 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1, 1], [8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1]], "output": [[8]]}], "test": [{"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, 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], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 4, 2, 2, 2, 2, 2, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 4, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 4, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 4, 2, 2, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8], [1, 1, 1, 1, 4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 4, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}]}, "de493100": {"train": [{"input": [[4, 3, 3, 8, 8, 8, 4, 4, 2, 3, 8, 2, 6, 2, 2, 6, 6, 2, 2, 6, 2, 8, 3, 2, 4, 4, 8, 8, 8, 3], [4, 3, 8, 8, 8, 8, 4, 4, 3, 8, 2, 8, 9, 6, 6, 6, 6, 6, 6, 9, 8, 2, 8, 3, 4, 4, 8, 8, 8, 8], [8, 8, 3, 3, 4, 4, 8, 8, 3, 8, 8, 3, 2, 6, 9, 6, 6, 9, 6, 2, 3, 8, 8, 3, 8, 8, 4, 4, 3, 3], [8, 3, 4, 4, 4, 4, 8, 8, 8, 3, 3, 2, 6, 6, 2, 9, 9, 2, 6, 6, 2, 3, 3, 8, 8, 8, 4, 4, 4, 4], [5, 9, 4, 4, 4, 3, 8, 8, 6, 9, 2, 6, 6, 2, 9, 8, 8, 9, 2, 6, 6, 2, 9, 6, 8, 8, 3, 4, 4, 4], [9, 5, 5, 4, 4, 3, 8, 3, 2, 6, 6, 6, 8, 6, 8, 9, 9, 8, 6, 8, 6, 6, 6, 2, 3, 8, 3, 4, 4, 5], [4, 5, 5, 9, 3, 8, 3, 3, 2, 6, 9, 2, 8, 6, 6, 2, 2, 6, 6, 8, 2, 9, 6, 2, 3, 3, 8, 3, 9, 5], [4, 4, 9, 5, 8, 8, 4, 4, 6, 6, 6, 9, 6, 8, 8, 6, 6, 8, 8, 6, 9, 6, 6, 6, 4, 4, 8, 8, 5, 9], [2, 3, 3, 8, 6, 2, 2, 6, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 6, 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6, 9, 8, 9, 2, 6, 6, 9], [6, 6, 6, 9, 8, 9, 2, 6, 6, 9], [2, 6, 9, 2, 9, 8, 6, 8, 9, 9], [2, 6, 6, 6, 2, 6, 6, 8, 9, 9], [6, 9, 2, 6, 6, 8, 8, 6, 9, 9], [2, 8, 3, 2, 6, 6, 2, 9, 8, 4], [8, 2, 8, 3, 2, 6, 9, 6, 4, 8], [3, 8, 8, 3, 9, 6, 6, 6, 9, 5], [2, 3, 3, 8, 6, 2, 2, 6, 9, 9]]}, {"input": [[3, 3, 2, 2, 8, 9, 9, 8, 8, 5, 5, 5, 1, 3, 3, 1, 1, 3, 3, 1, 5, 7, 7, 7, 7, 7, 9, 8, 2, 2], [1, 1, 2, 1, 9, 8, 8, 9, 5, 2, 5, 5, 3, 1, 1, 9, 9, 1, 1, 3, 5, 7, 7, 7, 7, 7, 8, 9, 1, 2], [2, 2, 1, 3, 9, 8, 8, 9, 8, 5, 2, 5, 3, 1, 9, 2, 2, 9, 1, 3, 5, 7, 7, 7, 7, 7, 8, 9, 3, 1], [2, 9, 1, 3, 8, 9, 9, 8, 5, 8, 5, 8, 1, 9, 1, 9, 9, 1, 9, 1, 8, 7, 7, 7, 7, 7, 9, 8, 3, 1], [8, 3, 8, 1, 3, 3, 1, 2, 1, 3, 3, 1, 9, 4, 9, 8, 8, 9, 4, 9, 1, 7, 7, 7, 7, 7, 3, 3, 1, 8], [3, 8, 3, 8, 1, 1, 2, 2, 3, 1, 1, 9, 2, 8, 8, 9, 9, 8, 8, 2, 9, 7, 7, 7, 7, 7, 1, 1, 8, 3], [8, 3, 8, 3, 9, 2, 1, 3, 3, 1, 9, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 7, 7, 7, 7, 7, 2, 9, 3, 8], [1, 8, 3, 8, 2, 2, 1, 3, 1, 9, 2, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 2, 9, 1, 3, 1, 2, 2, 8, 3], [8, 5, 8, 5, 1, 3, 3, 1, 3, 2, 6, 2, 9, 9, 6, 9, 9, 6, 9, 9, 2, 6, 2, 3, 1, 3, 3, 1, 5, 8], [5, 2, 5, 8, 3, 1, 1, 9, 1, 1, 2, 2, 9, 9, 4, 6, 6, 4, 9, 9, 2, 2, 1, 1, 9, 1, 1, 3, 8, 5], [5, 5, 2, 5, 3, 1, 9, 2, 6, 3, 1, 2, 6, 4, 9, 9, 9, 9, 4, 6, 2, 1, 3, 6, 2, 9, 1, 3, 5, 2], [5, 5, 5, 8, 1, 9, 1, 9, 3, 6, 1, 3, 9, 6, 9, 9, 9, 9, 6, 9, 3, 1, 6, 3, 9, 1, 9, 1, 8, 5], [1, 3, 3, 1, 9, 2, 9, 9, 8, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 8, 9, 9, 2, 9, 1, 3], [3, 1, 1, 9, 4, 8, 9, 9, 4, 8, 2, 3, 1, 1, 2, 6, 6, 2, 1, 1, 3, 2, 8, 4, 9, 9, 8, 4, 9, 1], [3, 1, 9, 1, 9, 8, 8, 2, 3, 2, 8, 4, 6, 3, 1, 2, 2, 1, 3, 6, 4, 8, 2, 3, 2, 8, 8, 9, 1, 9], [1, 9, 2, 9, 8, 9, 4, 9, 2, 3, 4, 8, 3, 6, 1, 3, 3, 1, 6, 3, 8, 4, 3, 2, 9, 4, 9, 8, 9, 2], [1, 9, 2, 9, 8, 9, 4, 9, 2, 3, 4, 8, 3, 6, 1, 3, 3, 1, 6, 3, 8, 4, 3, 2, 9, 4, 9, 8, 9, 2], [3, 1, 9, 1, 9, 8, 8, 2, 3, 2, 8, 4, 6, 3, 1, 2, 2, 1, 3, 6, 4, 8, 2, 3, 2, 8, 8, 9, 1, 9], [3, 1, 1, 9, 4, 8, 9, 9, 4, 8, 2, 3, 1, 1, 2, 6, 6, 2, 1, 1, 3, 2, 8, 4, 9, 9, 8, 4, 9, 1], [1, 3, 3, 1, 9, 2, 9, 9, 8, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 8, 9, 9, 2, 9, 1, 3], [5, 5, 5, 8, 1, 9, 1, 9, 3, 6, 1, 3, 9, 6, 9, 9, 9, 9, 6, 9, 3, 1, 6, 3, 9, 1, 9, 1, 8, 5], [5, 5, 2, 5, 3, 1, 9, 2, 6, 3, 1, 2, 6, 4, 9, 9, 9, 9, 4, 6, 2, 1, 3, 6, 2, 9, 1, 3, 5, 2], [5, 2, 5, 8, 3, 1, 1, 9, 1, 1, 2, 2, 9, 9, 4, 6, 6, 4, 9, 9, 2, 2, 1, 1, 9, 1, 1, 3, 8, 5], [8, 5, 8, 5, 1, 3, 3, 1, 3, 2, 6, 2, 9, 9, 6, 9, 9, 6, 9, 9, 2, 6, 2, 3, 1, 3, 3, 1, 5, 8], [1, 8, 3, 8, 2, 2, 1, 3, 1, 9, 2, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 2, 9, 1, 3, 1, 2, 2, 8, 3], [8, 3, 8, 3, 9, 2, 1, 3, 3, 1, 9, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 9, 1, 3, 3, 1, 2, 9, 3, 8], [3, 8, 3, 8, 1, 1, 2, 2, 3, 1, 1, 9, 2, 8, 8, 9, 9, 8, 8, 2, 9, 1, 1, 3, 2, 2, 1, 1, 8, 3], [8, 3, 8, 1, 3, 3, 1, 2, 1, 3, 3, 1, 9, 4, 9, 8, 8, 9, 4, 9, 1, 3, 3, 1, 2, 1, 3, 3, 1, 8], [2, 9, 1, 3, 8, 9, 9, 8, 5, 8, 5, 8, 1, 9, 1, 9, 9, 1, 9, 1, 8, 5, 8, 5, 8, 9, 9, 8, 3, 1], [2, 2, 1, 3, 9, 8, 8, 9, 8, 5, 2, 5, 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[1, 3, 3, 3, 3, 1], [3, 1, 3, 3, 1, 3], [3, 3, 1, 1, 3, 3]]}, {"input": [[4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4], [4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4], [2, 4, 4, 7, 4, 2, 4, 4, 4, 4, 4, 4, 4], [2, 4, 4, 4, 4, 8, 8, 4, 4, 5, 4, 4, 4], [4, 2, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 4], [4, 4, 2, 8, 4, 4, 4, 4, 8, 4, 4, 4, 4], [4, 4, 4, 8, 4, 4, 4, 4, 3, 3, 4, 4, 4], [4, 4, 4, 4, 8, 4, 4, 3, 4, 4, 3, 4, 4], [4, 5, 4, 4, 4, 8, 3, 4, 4, 4, 4, 3, 4], [4, 4, 7, 4, 4, 4, 3, 4, 4, 5, 4, 3, 4], [4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 3, 4, 4]], "output": [[4, 4, 3, 3, 4, 4], [4, 3, 4, 4, 3, 4], [3, 4, 4, 4, 4, 3], [3, 4, 4, 4, 4, 3], [4, 3, 4, 4, 3, 4], [4, 4, 3, 3, 4, 4], [4, 4, 8, 8, 4, 4], [4, 8, 4, 4, 8, 4], [8, 4, 4, 4, 4, 8], [8, 4, 4, 4, 4, 8], [4, 8, 4, 4, 8, 4], [4, 4, 8, 8, 4, 4], [4, 4, 2, 2, 4, 4], [4, 2, 4, 4, 2, 4], [2, 4, 4, 4, 4, 2], [2, 4, 4, 4, 4, 2], [4, 2, 4, 4, 2, 4], [4, 4, 2, 2, 4, 4]]}, {"input": [[8, 8, 8, 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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, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 4, 3, 4, 8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 4, 4, 4, 8, 8, 8, 4, 6, 4, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 4, 6, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 4, 4, 1, 1, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 1, 1, 1, 1, 4, 1, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 3, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 2, 2, 2, 1, 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], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 1, 1, 1, 1, 2, 1, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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], [8, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [8, 2, 2, 2, 2, 2, 3, 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], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}], "test": [{"input": [[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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 8, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 3, 3, 3, 3], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [4, 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], [4, 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], [4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 8, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 3, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 4, 4, 4, 3, 3, 3, 3, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 3, 3], [4, 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], [4, 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], [4, 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], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]}]}, "9ba4a9aa": {"train": [{"input": [[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, 2, 9, 2, 8, 8, 8], [1, 3, 1, 2, 8, 2, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 9, 2, 9, 8, 8, 8], [1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 9, 2, 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, 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, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 4, 8, 4, 8, 3, 8, 3, 8, 3, 8, 3, 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, 8], [8, 8, 8, 4, 8, 8, 8, 5, 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, 8], [8, 8, 8, 4, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8], [8, 8, 9, 9, 9, 8, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 4, 9, 8, 5, 2, 5, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8], [8, 8, 9, 9, 9, 8, 5, 5, 5, 8, 8, 8, 8, 8, 6, 6, 6, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 7, 6, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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]], "output": [[6, 6, 6], [6, 7, 6], [6, 6, 6]]}, {"input": [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8, 1, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 1, 8, 1, 4, 2, 4, 2, 4, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8, 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, 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, 1, 1, 1, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 3, 2, 3, 1, 3, 1, 2, 2], [2, 9, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2], [2, 9, 5, 9, 9, 2, 9, 2, 9, 2, 4, 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, 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, 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, 4, 2, 4, 2, 4, 2, 4, 2, 8, 2, 8, 2, 8, 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, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 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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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8], [8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 1, 8, 8, 8, 8], [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], [8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 9, 8, 9, 8, 9, 8, 8, 8, 1, 8, 1, 8, 8, 8, 8], [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], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [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], [8, 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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 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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, 3, 3, 3, 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, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 4, 2, 2, 2, 2, 2, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 4, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 4, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 4, 2, 2, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8], [1, 1, 1, 1, 4, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 4, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}]}, "de493100": {"train": [{"input": [[4, 3, 3, 8, 8, 8, 4, 4, 2, 3, 8, 2, 6, 2, 2, 6, 6, 2, 2, 6, 2, 8, 3, 2, 4, 4, 8, 8, 8, 3], [4, 3, 8, 8, 8, 8, 4, 4, 3, 8, 2, 8, 9, 6, 6, 6, 6, 6, 6, 9, 8, 2, 8, 3, 4, 4, 8, 8, 8, 8], [8, 8, 3, 3, 4, 4, 8, 8, 3, 8, 8, 3, 2, 6, 9, 6, 6, 9, 6, 2, 3, 8, 8, 3, 8, 8, 4, 4, 3, 3], [8, 3, 4, 4, 4, 4, 8, 8, 8, 3, 3, 2, 6, 6, 2, 9, 9, 2, 6, 6, 2, 3, 3, 8, 8, 8, 4, 4, 4, 4], [5, 9, 4, 4, 4, 3, 8, 8, 6, 9, 2, 6, 6, 2, 9, 8, 8, 9, 2, 6, 6, 2, 9, 6, 8, 8, 3, 4, 4, 4], [9, 5, 5, 4, 4, 3, 8, 3, 2, 6, 6, 6, 8, 6, 8, 9, 9, 8, 6, 8, 6, 6, 6, 2, 3, 8, 3, 4, 4, 5], [4, 5, 5, 9, 3, 8, 3, 3, 2, 6, 9, 2, 8, 6, 6, 2, 2, 6, 6, 8, 2, 9, 6, 2, 3, 3, 8, 3, 9, 5], [4, 4, 9, 5, 8, 8, 4, 4, 6, 6, 6, 9, 6, 8, 8, 6, 6, 8, 8, 6, 9, 6, 6, 6, 4, 4, 8, 8, 5, 9], [2, 3, 3, 8, 6, 2, 2, 6, 9, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 6, 2, 2, 6, 8, 3], [3, 8, 8, 3, 9, 6, 6, 6, 9, 5, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 9, 6, 6, 6, 9, 3, 8], [8, 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2, 3], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 8, 4, 6, 9, 6, 2, 3, 8], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 5, 9, 6, 6, 6, 9, 3, 8], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 9, 9, 6, 2, 2, 6, 8, 3], [4, 4, 9, 5, 8, 8, 4, 4, 6, 6, 6, 9, 6, 8, 8, 6, 6, 8, 8, 6, 9, 6, 6, 6, 4, 4, 8, 8, 5, 9], [4, 5, 5, 9, 3, 8, 3, 3, 2, 6, 9, 2, 8, 6, 6, 2, 2, 6, 6, 8, 2, 9, 6, 2, 3, 3, 8, 3, 9, 5], [9, 5, 5, 4, 4, 3, 8, 3, 2, 6, 6, 6, 8, 6, 8, 9, 9, 8, 6, 8, 6, 6, 6, 2, 3, 8, 3, 4, 4, 5], [5, 9, 4, 4, 4, 3, 8, 8, 6, 9, 2, 6, 6, 2, 9, 8, 8, 9, 2, 6, 6, 2, 9, 6, 8, 8, 3, 4, 4, 4], [8, 3, 4, 4, 4, 4, 8, 8, 8, 3, 3, 2, 6, 6, 2, 9, 9, 2, 6, 6, 2, 3, 3, 8, 8, 8, 4, 4, 4, 4], [8, 8, 3, 3, 4, 4, 8, 8, 3, 8, 8, 3, 2, 6, 9, 6, 6, 9, 6, 2, 3, 8, 8, 3, 8, 8, 4, 4, 3, 3]], "output": [[2, 6, 9, 2, 9, 8, 6, 8, 9, 9], [6, 6, 6, 9, 8, 9, 2, 6, 6, 9], [6, 6, 6, 9, 8, 9, 2, 6, 6, 9], [2, 6, 9, 2, 9, 8, 6, 8, 9, 9], [2, 6, 6, 6, 2, 6, 6, 8, 9, 9], [6, 9, 2, 6, 6, 8, 8, 6, 9, 9], [2, 8, 3, 2, 6, 6, 2, 9, 8, 4], [8, 2, 8, 3, 2, 6, 9, 6, 4, 8], [3, 8, 8, 3, 9, 6, 6, 6, 9, 5], [2, 3, 3, 8, 6, 2, 2, 6, 9, 9]]}, {"input": [[3, 3, 2, 2, 8, 9, 9, 8, 8, 5, 5, 5, 1, 3, 3, 1, 1, 3, 3, 1, 5, 7, 7, 7, 7, 7, 9, 8, 2, 2], [1, 1, 2, 1, 9, 8, 8, 9, 5, 2, 5, 5, 3, 1, 1, 9, 9, 1, 1, 3, 5, 7, 7, 7, 7, 7, 8, 9, 1, 2], [2, 2, 1, 3, 9, 8, 8, 9, 8, 5, 2, 5, 3, 1, 9, 2, 2, 9, 1, 3, 5, 7, 7, 7, 7, 7, 8, 9, 3, 1], [2, 9, 1, 3, 8, 9, 9, 8, 5, 8, 5, 8, 1, 9, 1, 9, 9, 1, 9, 1, 8, 7, 7, 7, 7, 7, 9, 8, 3, 1], [8, 3, 8, 1, 3, 3, 1, 2, 1, 3, 3, 1, 9, 4, 9, 8, 8, 9, 4, 9, 1, 7, 7, 7, 7, 7, 3, 3, 1, 8], [3, 8, 3, 8, 1, 1, 2, 2, 3, 1, 1, 9, 2, 8, 8, 9, 9, 8, 8, 2, 9, 7, 7, 7, 7, 7, 1, 1, 8, 3], [8, 3, 8, 3, 9, 2, 1, 3, 3, 1, 9, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 7, 7, 7, 7, 7, 2, 9, 3, 8], [1, 8, 3, 8, 2, 2, 1, 3, 1, 9, 2, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 2, 9, 1, 3, 1, 2, 2, 8, 3], [8, 5, 8, 5, 1, 3, 3, 1, 3, 2, 6, 2, 9, 9, 6, 9, 9, 6, 9, 9, 2, 6, 2, 3, 1, 3, 3, 1, 5, 8], [5, 2, 5, 8, 3, 1, 1, 9, 1, 1, 2, 2, 9, 9, 4, 6, 6, 4, 9, 9, 2, 2, 1, 1, 9, 1, 1, 3, 8, 5], [5, 5, 2, 5, 3, 1, 9, 2, 6, 3, 1, 2, 6, 4, 9, 9, 9, 9, 4, 6, 2, 1, 3, 6, 2, 9, 1, 3, 5, 2], [5, 5, 5, 8, 1, 9, 1, 9, 3, 6, 1, 3, 9, 6, 9, 9, 9, 9, 6, 9, 3, 1, 6, 3, 9, 1, 9, 1, 8, 5], [1, 3, 3, 1, 9, 2, 9, 9, 8, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 8, 9, 9, 2, 9, 1, 3], [3, 1, 1, 9, 4, 8, 9, 9, 4, 8, 2, 3, 1, 1, 2, 6, 6, 2, 1, 1, 3, 2, 8, 4, 9, 9, 8, 4, 9, 1], [3, 1, 9, 1, 9, 8, 8, 2, 3, 2, 8, 4, 6, 3, 1, 2, 2, 1, 3, 6, 4, 8, 2, 3, 2, 8, 8, 9, 1, 9], [1, 9, 2, 9, 8, 9, 4, 9, 2, 3, 4, 8, 3, 6, 1, 3, 3, 1, 6, 3, 8, 4, 3, 2, 9, 4, 9, 8, 9, 2], [1, 9, 2, 9, 8, 9, 4, 9, 2, 3, 4, 8, 3, 6, 1, 3, 3, 1, 6, 3, 8, 4, 3, 2, 9, 4, 9, 8, 9, 2], [3, 1, 9, 1, 9, 8, 8, 2, 3, 2, 8, 4, 6, 3, 1, 2, 2, 1, 3, 6, 4, 8, 2, 3, 2, 8, 8, 9, 1, 9], [3, 1, 1, 9, 4, 8, 9, 9, 4, 8, 2, 3, 1, 1, 2, 6, 6, 2, 1, 1, 3, 2, 8, 4, 9, 9, 8, 4, 9, 1], [1, 3, 3, 1, 9, 2, 9, 9, 8, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 8, 9, 9, 2, 9, 1, 3], [5, 5, 5, 8, 1, 9, 1, 9, 3, 6, 1, 3, 9, 6, 9, 9, 9, 9, 6, 9, 3, 1, 6, 3, 9, 1, 9, 1, 8, 5], [5, 5, 2, 5, 3, 1, 9, 2, 6, 3, 1, 2, 6, 4, 9, 9, 9, 9, 4, 6, 2, 1, 3, 6, 2, 9, 1, 3, 5, 2], [5, 2, 5, 8, 3, 1, 1, 9, 1, 1, 2, 2, 9, 9, 4, 6, 6, 4, 9, 9, 2, 2, 1, 1, 9, 1, 1, 3, 8, 5], [8, 5, 8, 5, 1, 3, 3, 1, 3, 2, 6, 2, 9, 9, 6, 9, 9, 6, 9, 9, 2, 6, 2, 3, 1, 3, 3, 1, 5, 8], [1, 8, 3, 8, 2, 2, 1, 3, 1, 9, 2, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 2, 9, 1, 3, 1, 2, 2, 8, 3], [8, 3, 8, 3, 9, 2, 1, 3, 3, 1, 9, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 9, 1, 3, 3, 1, 2, 9, 3, 8], [3, 8, 3, 8, 1, 1, 2, 2, 3, 1, 1, 9, 2, 8, 8, 9, 9, 8, 8, 2, 9, 1, 1, 3, 2, 2, 1, 1, 8, 3], [8, 3, 8, 1, 3, 3, 1, 2, 1, 3, 3, 1, 9, 4, 9, 8, 8, 9, 4, 9, 1, 3, 3, 1, 2, 1, 3, 3, 1, 8], [2, 9, 1, 3, 8, 9, 9, 8, 5, 8, 5, 8, 1, 9, 1, 9, 9, 1, 9, 1, 8, 5, 8, 5, 8, 9, 9, 8, 3, 1], [2, 2, 1, 3, 9, 8, 8, 9, 8, 5, 2, 5, 3, 1, 9, 2, 2, 9, 1, 3, 5, 2, 5, 8, 9, 8, 8, 9, 3, 1]], "output": [[5, 5, 8, 8, 9], [5, 2, 5, 9, 8], [2, 5, 8, 9, 8], [5, 8, 5, 8, 9], [3, 3, 1, 2, 1], [1, 1, 3, 2, 2], [9, 1, 3, 3, 1]]}, {"input": [[3, 1, 8, 8, 6, 8, 8, 6, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 6, 8, 8, 6, 8, 8], [2, 3, 8, 3, 8, 6, 1, 8, 8, 9, 9, 8, 2, 9, 8, 8, 8, 8, 9, 2, 8, 9, 9, 8, 8, 1, 6, 8, 3, 8], [1, 8, 3, 1, 8, 1, 6, 8, 4, 8, 9, 8, 9, 8, 9, 8, 8, 9, 8, 9, 8, 9, 8, 4, 8, 6, 1, 8, 1, 3], [8, 2, 2, 3, 6, 8, 8, 6, 8, 4, 8, 8, 9, 8, 9, 9, 9, 9, 8, 9, 8, 8, 4, 8, 6, 8, 8, 6, 3, 2], [3, 8, 8, 3, 3, 1, 3, 8, 9, 2, 9, 9, 9, 8, 9, 8, 8, 9, 8, 9, 9, 9, 2, 9, 8, 3, 1, 3, 3, 8], [8, 3, 1, 8, 2, 3, 8, 8, 9, 9, 8, 8, 8, 4, 8, 9, 9, 8, 4, 8, 8, 8, 9, 9, 8, 8, 3, 2, 8, 1], [8, 1, 3, 8, 2, 8, 3, 1, 9, 8, 9, 9, 9, 5, 4, 8, 8, 4, 5, 9, 9, 9, 8, 9, 1, 3, 8, 2, 8, 3], [3, 8, 8, 3, 8, 1, 2, 3, 9, 8, 8, 9, 5, 9, 8, 9, 9, 8, 9, 5, 9, 8, 8, 9, 3, 2, 1, 8, 3, 8], [8, 8, 4, 8, 9, 9, 9, 9, 2, 9, 8, 8, 5, 2, 5, 1, 1, 5, 2, 5, 8, 8, 9, 2, 9, 9, 9, 9, 8, 4], [8, 9, 8, 4, 2, 9, 8, 8, 8, 2, 8, 3, 2, 5, 4, 5, 5, 4, 5, 2, 3, 8, 2, 8, 8, 8, 9, 2, 4, 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8, 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], [8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [0, 8, 2, 8, 2, 3, 0, 8, 2, 8, 2, 3, 0, 8, 2, 8, 2, 3, 0, 8, 2, 8, 2, 3, 0, 8, 2, 8, 2], [0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8, 3, 0, 8, 8, 8, 8], [8, 8, 8, 8, 4, 3, 8, 8, 8, 8, 4, 3, 8, 8, 8, 8, 4, 3, 8, 8, 8, 8, 4, 3, 8, 8, 8, 8, 4]], "output": [[8, 8, 4, 8, 8], [8, 8, 8, 8, 8], [0, 8, 1, 8, 2], [1, 8, 8, 8, 8], [8, 8, 8, 8, 4]]}, {"input": [[0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 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], [0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 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], [0, 8, 2, 8, 4, 3, 0, 8, 8, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 0, 8, 2, 3, 8, 8, 8, 8, 8, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 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], [0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 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], [0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4, 3, 0, 8, 2, 8, 4], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8, 3, 4, 8, 6, 8, 8], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2, 3, 8, 8, 0, 8, 2]], "output": [[0, 8, 1, 8, 4], [8, 8, 8, 8, 8], [4, 8, 6, 8, 8], [8, 8, 8, 8, 8], [8, 8, 1, 8, 1]]}, {"input": [[0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8], [4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8], [8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8], [8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8], [0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 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], [0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8], [4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8], [8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8], [8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8], [0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 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], [0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8], [4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8], [8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8], [8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8], [0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 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], [0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8], [4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8], [8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8], [8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8], [0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 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], [0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 8, 8, 8, 3, 0, 8, 4, 8, 8, 3, 0, 8, 4, 8, 8], [4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8, 3, 4, 8, 8, 8, 8], [8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 2, 8, 8, 8, 3, 8, 2, 8, 8, 8], [8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 2, 8, 3, 8, 8, 8, 2, 8], [0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0, 3, 0, 8, 8, 8, 0]], "output": [[0, 8, 1, 8, 8], [1, 8, 8, 8, 8], [8, 1, 8, 8, 8], [8, 8, 8, 1, 8], [0, 8, 8, 8, 0]]}], "test": [{"input": [[2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8], [8, 0, 0, 8, 6, 3, 8, 0, 0, 8, 6, 3, 8, 0, 0, 8, 6, 3, 8, 0, 0, 8, 6, 3, 8, 0, 0, 8, 6], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8], [2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 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], [2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8, 3, 2, 8, 2, 8, 8], [8, 0, 0, 8, 6, 3, 8, 0, 0, 8, 6, 3, 8, 0, 0, 8, 6, 3, 8, 8, 8, 8, 8, 3, 8, 0, 0, 8, 6], [8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8], [8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8, 3, 8, 8, 4, 8, 8], [2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 4, 3, 2, 8, 8, 8, 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0, 8, 8, 0], [0, 8, 0, 0, 8], [8, 8, 8, 8, 8], [8, 0, 8, 8, 0]]]} diff --git a/models/recursive_reasoning/trm.py b/models/recursive_reasoning/trm.py deleted file mode 100644 index 5c3e39df..00000000 --- a/models/recursive_reasoning/trm.py +++ /dev/null @@ -1,297 +0,0 @@ -from typing import Tuple, List, Dict, Optional -from dataclasses import dataclass -import math -import torch -import copy -import torch.nn.functional as F -from torch import nn -from pydantic import BaseModel -import random -from models.common import trunc_normal_init_ -from models.layers import rms_norm, LinearSwish, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear -from models.sparse_embedding import CastedSparseEmbedding - -IGNORE_LABEL_ID = -100 - -@dataclass -class TinyRecursiveReasoningModel_ACTV1InnerCarry: - z_H: torch.Tensor - z_L: torch.Tensor - - -@dataclass -class TinyRecursiveReasoningModel_ACTV1Carry: - inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry - - steps: torch.Tensor - halted: torch.Tensor - - current_data: Dict[str, torch.Tensor] - - -class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): - batch_size: int - seq_len: int - puzzle_emb_ndim: int = 0 - num_puzzle_identifiers: int - vocab_size: int - - H_cycles: int - L_cycles: int - - H_layers: int # ignored - L_layers: int - - # Transformer config - hidden_size: int - expansion: float - num_heads: int - pos_encodings: str - - rms_norm_eps: float = 1e-5 - rope_theta: float = 10000.0 - - # Halting Q-learning config - halt_max_steps: int - halt_exploration_prob: float - - forward_dtype: str = "bfloat16" - - # Alexia: added - mlp_t: bool = False # use mlp on L instead of transformer - puzzle_emb_len: int = 16 # if non-zero, its specified to this value - no_ACT_continue: bool = True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense - -class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): - def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: - super().__init__() - - self.config = config - if self.config.mlp_t: - self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len - self.mlp_t = SwiGLU( - hidden_size=self.config.seq_len + self.puzzle_emb_len, # L - expansion=config.expansion, - ) - else: - self.self_attn = Attention( - hidden_size=config.hidden_size, - head_dim=config.hidden_size // config.num_heads, - num_heads=config.num_heads, - num_key_value_heads=config.num_heads, - causal=False - ) - self.mlp = SwiGLU( - hidden_size=config.hidden_size, - expansion=config.expansion, - ) - self.norm_eps = config.rms_norm_eps - - def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: - # B, L, D = hidden_states.shape - # Post Norm - if self.config.mlp_t: - hidden_states = hidden_states.transpose(1,2) - out = self.mlp_t(hidden_states) - hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) - hidden_states = hidden_states.transpose(1,2) - else: - # Self Attention - hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) - # Fully Connected - out = self.mlp(hidden_states) - hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) - return hidden_states - -class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): - def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): - super().__init__() - self.layers = torch.nn.ModuleList(layers) - - def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: - hidden_states = hidden_states + input_injection - for layer in self.layers: - hidden_states = layer(hidden_states=hidden_states, **kwargs) - return hidden_states - - -class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): - def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: - super().__init__() - self.config = config - self.forward_dtype = getattr(torch, self.config.forward_dtype) - - # I/O - - self.embed_scale = math.sqrt(self.config.hidden_size) - embed_init_std = 1.0 / self.embed_scale - - self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) - self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) - self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) - - self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len # ceil div - if self.config.puzzle_emb_ndim > 0: - # Zero init puzzle embeddings - self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, - batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) - - # LM Blocks - if self.config.pos_encodings == "rope": - self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, - max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, - base=self.config.rope_theta) - elif self.config.pos_encodings == "learned": - self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) - else: - pass - - # Reasoning Layers - self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule(layers=[TinyRecursiveReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) - - # Initial states - self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - - # Q head special init - # Init Q to (almost) zero for faster learning during bootstrapping - with torch.no_grad(): - self.q_head.weight.zero_() - self.q_head.bias.fill_(-5) # type: ignore - - def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): - # Token embedding - embedding = self.embed_tokens(input.to(torch.int32)) - - # Puzzle embeddings - if self.config.puzzle_emb_ndim > 0: - puzzle_embedding = self.puzzle_emb(puzzle_identifiers) - - pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] - if pad_count > 0: - puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) - - embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) - - # Position embeddings - if self.config.pos_encodings == "learned": - # scale by 1/sqrt(2) to maintain forward variance - embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) - - # Scale - return self.embed_scale * embedding - - def empty_carry(self, batch_size: int): - return TinyRecursiveReasoningModel_ACTV1InnerCarry( - z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - ) - - def reset_carry(self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry): - return TinyRecursiveReasoningModel_ACTV1InnerCarry( - z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), - z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), - ) - - def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: - seq_info = dict( - cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, - ) - - # Input encoding - input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) - - # Forward iterations - it = 0 - z_H, z_L = carry.z_H, carry.z_L - # H_cycles-1 without grad - with torch.no_grad(): - for _H_step in range(self.config.H_cycles-1): - for _L_step in range(self.config.L_cycles): - z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) - z_H = self.L_level(z_H, z_L, **seq_info) - # 1 with grad - for _L_step in range(self.config.L_cycles): - z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) - z_H = self.L_level(z_H, z_L, **seq_info) - - # LM Outputs - new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) # New carry no grad - output = self.lm_head(z_H)[:, self.puzzle_emb_len:] - q_logits = self.q_head(z_H[:, 0]).to(torch.float32) # Q-head; uses the first puzzle_emb position - return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) - - -class TinyRecursiveReasoningModel_ACTV1(nn.Module): - """ACT wrapper.""" - - def __init__(self, config_dict: dict): - super().__init__() - self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) - self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) - - @property - def puzzle_emb(self): - return self.inner.puzzle_emb - - def initial_carry(self, batch: Dict[str, torch.Tensor]): - batch_size = batch["inputs"].shape[0] - - return TinyRecursiveReasoningModel_ACTV1Carry( - inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. - - steps=torch.zeros((batch_size, ), dtype=torch.int32), - halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted - - current_data={k: torch.empty_like(v) for k, v in batch.items()} - ) - - def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: - - # Update data, carry (removing halted sequences) - new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) - - new_steps = torch.where(carry.halted, 0, carry.steps) - - new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} - - # Forward inner model - new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) - - outputs = { - "logits": logits, - "q_halt_logits": q_halt_logits, - "q_continue_logits": q_continue_logits - } - - with torch.no_grad(): - # Step - new_steps = new_steps + 1 - is_last_step = new_steps >= self.config.halt_max_steps - - halted = is_last_step - - # if training, and ACT is enabled - if self.training and (self.config.halt_max_steps > 1): - - # Halt signal - # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes - - if self.config.no_ACT_continue: - halted = halted | (q_halt_logits > 0) - else: - halted = halted | (q_halt_logits > q_continue_logits) - - # Exploration - min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) - halted = halted & (new_steps >= min_halt_steps) - - if not self.config.no_ACT_continue: - # Compute target Q - # NOTE: No replay buffer and target networks for computing target Q-value. - # As batch_size is large, there're many parallel envs. - # Similar concept as PQN https://arxiv.org/abs/2407.04811 - _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner(new_inner_carry, new_current_data) - outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) - - return TinyRecursiveReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/models/recursive_reasoning/trm_hier6.py b/models/recursive_reasoning/trm_hier6.py deleted file mode 100644 index c654474d..00000000 --- a/models/recursive_reasoning/trm_hier6.py +++ /dev/null @@ -1,323 +0,0 @@ -from typing import Tuple, List, Dict, Optional -from dataclasses import dataclass -import math -import torch -import copy -import torch.nn.functional as F -from torch import nn -from pydantic import BaseModel -import random -from models.common import trunc_normal_init_ -from models.layers import rms_norm, LinearSwish, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear -from models.sparse_embedding import CastedSparseEmbedding - -IGNORE_LABEL_ID = -100 - -@dataclass -class TinyRecursiveReasoningModel_ACTV1InnerCarry: - z_H: torch.Tensor - z_L1: torch.Tensor - z_L2: torch.Tensor - z_L3: torch.Tensor - z_L4: torch.Tensor - z_L5: torch.Tensor - z_L6: torch.Tensor - - - -@dataclass -class TinyRecursiveReasoningModel_ACTV1Carry: - inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry - - steps: torch.Tensor - halted: torch.Tensor - - current_data: Dict[str, torch.Tensor] - - -class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): - batch_size: int - seq_len: int - puzzle_emb_ndim: int = 0 - num_puzzle_identifiers: int - vocab_size: int - - H_cycles: int - L_cycles: int - - H_layers: int # ignored - L_layers: int - - # Transformer config - hidden_size: int - expansion: float - num_heads: int - pos_encodings: str - - rms_norm_eps: float = 1e-5 - rope_theta: float = 10000.0 - - # Halting Q-learning config - halt_max_steps: int - halt_exploration_prob: float - - forward_dtype: str = "bfloat16" - - # Alexia: added - mlp_t: bool = False # use mlp on L instead of transformer - puzzle_emb_len: int = 16 # if non-zero, its specified to this value - no_ACT_continue: bool = True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense - -class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): - def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: - super().__init__() - - self.config = config - if self.config.mlp_t: - self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len - self.mlp_t = SwiGLU( - hidden_size=self.config.seq_len + self.puzzle_emb_len, # L - expansion=config.expansion, - ) - else: - self.self_attn = Attention( - hidden_size=config.hidden_size, - head_dim=config.hidden_size // config.num_heads, - num_heads=config.num_heads, - num_key_value_heads=config.num_heads, - causal=False - ) - self.mlp = SwiGLU( - hidden_size=config.hidden_size, - expansion=config.expansion, - ) - self.norm_eps = config.rms_norm_eps - - def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: - # B, L, D = hidden_states.shape - # Post Norm - if self.config.mlp_t: - hidden_states = hidden_states.transpose(1,2) - out = self.mlp_t(hidden_states) - hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) - hidden_states = hidden_states.transpose(1,2) - else: - # Self Attention - hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) - # Fully Connected - out = self.mlp(hidden_states) - hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) - return hidden_states - -class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): - def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): - super().__init__() - self.layers = torch.nn.ModuleList(layers) - - def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: - hidden_states = hidden_states + input_injection - for layer in self.layers: - hidden_states = layer(hidden_states=hidden_states, **kwargs) - return hidden_states - - -class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): - def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: - super().__init__() - self.config = config - self.forward_dtype = getattr(torch, self.config.forward_dtype) - - # I/O - - self.embed_scale = math.sqrt(self.config.hidden_size) - embed_init_std = 1.0 / self.embed_scale - - self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) - self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) - self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) - - self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len # ceil div - if self.config.puzzle_emb_ndim > 0: - # Zero init puzzle embeddings - self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, - batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) - - # LM Blocks - if self.config.pos_encodings == "rope": - self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, - max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, - base=self.config.rope_theta) - elif self.config.pos_encodings == "learned": - self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) - else: - pass - - # Reasoning Layers - self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule(layers=[TinyRecursiveReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) - - # Initial states - self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L1_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L2_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L3_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L4_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L5_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L6_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - - # Q head special init - # Init Q to (almost) zero for faster learning during bootstrapping - with torch.no_grad(): - self.q_head.weight.zero_() - self.q_head.bias.fill_(-5) # type: ignore - - def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): - # Token embedding - embedding = self.embed_tokens(input.to(torch.int32)) - - # Puzzle embeddings - if self.config.puzzle_emb_ndim > 0: - puzzle_embedding = self.puzzle_emb(puzzle_identifiers) - - pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] - if pad_count > 0: - puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) - - embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) - - # Position embeddings - if self.config.pos_encodings == "learned": - # scale by 1/sqrt(2) to maintain forward variance - embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) - - # Scale - return self.embed_scale * embedding - - def empty_carry(self, batch_size: int): - return TinyRecursiveReasoningModel_ACTV1InnerCarry( - z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L1=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L2=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L3=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L4=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L5=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L6=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - ) - - def reset_carry(self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry): - return TinyRecursiveReasoningModel_ACTV1InnerCarry( - z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), - z_L1=torch.where(reset_flag.view(-1, 1, 1), self.L1_init, carry.z_L1), - z_L2=torch.where(reset_flag.view(-1, 1, 1), self.L2_init, carry.z_L2), - z_L3=torch.where(reset_flag.view(-1, 1, 1), self.L3_init, carry.z_L3), - z_L4=torch.where(reset_flag.view(-1, 1, 1), self.L4_init, carry.z_L4), - z_L5=torch.where(reset_flag.view(-1, 1, 1), self.L5_init, carry.z_L5), - z_L6=torch.where(reset_flag.view(-1, 1, 1), self.L6_init, carry.z_L6), - ) - - - def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: - seq_info = dict( - cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, - ) - - # Input encoding - input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) - - # Forward iterations - it = 0 - z_H, z_L = carry.z_H, [carry.z_L1, carry.z_L2, carry.z_L3, carry.z_L4, carry.z_L5, carry.z_L6] - # H_cycles-1 without grad - with torch.no_grad(): - for _H_step in range(self.config.H_cycles-1): - for _L_step in range(self.config.L_cycles): - z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] - z_L[_L_step] = self.L_level(z_L_, z_H + input_embeddings, **seq_info) - z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] - z_H = self.L_level(z_H, z_L_, **seq_info) - # 1 with grad - for _L_step in range(self.config.L_cycles): - z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] - z_L[_L_step] = self.L_level(z_L_, z_H + input_embeddings, **seq_info) - z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] - z_H = self.L_level(z_H, z_L_, **seq_info) - - # LM Outputs - new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L1=z_L[0].detach(), z_L2=z_L[1].detach(), z_L3=z_L[2].detach(), z_L4=z_L[3].detach(), z_L5=z_L[4].detach(), z_L6=z_L[5].detach()) # New carry no grad - output = self.lm_head(z_H)[:, self.puzzle_emb_len:] - q_logits = self.q_head(z_H[:, 0]).to(torch.float32) # Q-head; uses the first puzzle_emb position - return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) - - -class TinyRecursiveReasoningModel_ACTV1(nn.Module): - """ACT wrapper.""" - - def __init__(self, config_dict: dict): - super().__init__() - self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) - self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) - - @property - def puzzle_emb(self): - return self.inner.puzzle_emb - - def initial_carry(self, batch: Dict[str, torch.Tensor]): - batch_size = batch["inputs"].shape[0] - - return TinyRecursiveReasoningModel_ACTV1Carry( - inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. - - steps=torch.zeros((batch_size, ), dtype=torch.int32), - halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted - - current_data={k: torch.empty_like(v) for k, v in batch.items()} - ) - - def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: - - # Update data, carry (removing halted sequences) - new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) - - new_steps = torch.where(carry.halted, 0, carry.steps) - - new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} - - # Forward inner model - new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) - - outputs = { - "logits": logits, - "q_halt_logits": q_halt_logits, - "q_continue_logits": q_continue_logits - } - - with torch.no_grad(): - # Step - new_steps = new_steps + 1 - is_last_step = new_steps >= self.config.halt_max_steps - - halted = is_last_step - - # if training, and ACT is enabled - if self.training and (self.config.halt_max_steps > 1): - - # Halt signal - # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes - - if self.config.no_ACT_continue: - halted = halted | (q_halt_logits > 0) - else: - halted = halted | (q_halt_logits > q_continue_logits) - - # Exploration - min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) - halted = halted & (new_steps >= min_halt_steps) - - if not self.config.no_ACT_continue: - # Compute target Q - # NOTE: No replay buffer and target networks for computing target Q-value. - # As batch_size is large, there're many parallel envs. - # Similar concept as PQN https://arxiv.org/abs/2407.04811 - _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner(new_inner_carry, new_current_data) - outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) - - return TinyRecursiveReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 00000000..923645a2 --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,30 @@ +[project] +name = "recursion" +version = "0.1.0" +description = "Improve RNN training" +readme = "README.md" +requires-python = ">=3.13" +dependencies = [ + "torch", + "adam-atan2-pytorch", + "einops", + "tqdm", + "coolname", + "pydantic", + "argdantic", + "wandb", + "omegaconf", + "hydra-core", + "huggingface_hub", + "packaging", + "ninja", + "wheel", + "setuptools", + "setuptools-scm", + "pydantic-core", + "huggingface_hub", + "numba", + "triton", + "pre-commit", + "torchjd>=0.8.0", +] diff --git a/requirements.txt b/requirements.txt deleted file mode 100644 index cea0f55f..00000000 --- a/requirements.txt +++ /dev/null @@ -1,20 +0,0 @@ -torch -adam-atan2 -einops -tqdm -coolname -pydantic -argdantic -wandb -omegaconf -hydra-core -huggingface_hub -packaging -ninja -wheel -setuptools -setuptools-scm -pydantic-core -huggingface_hub -numba -triton \ No newline at end of file diff --git a/specific_requirements.txt b/specific_requirements.txt deleted file mode 100644 index a9ea8062..00000000 --- a/specific_requirements.txt +++ /dev/null @@ -1,20 +0,0 @@ -torch==2.7.0+cu126 -adam-atan2==0.0.3 -einops==0.8.1 -tqdm==4.67.1 -coolname==2.2.0 -pydantic==2.11.7 -argdantic==1.3.3 -wandb==0.21.3 -omegaconf==2.3.0 -hydra-core==1.3.2 -huggingface_hub==0.34.4 -packaging==24.1 -ninja==1.13.0 -wheel==0.45.1 -setuptools==80.9.0 -setuptools-scm==9.2.0 -pydantic-core==2.33.2 -huggingface_hub==0.34.4 -numba==0.61.2 -triton==3.3.0 diff --git a/src/recursion/__init__.py b/src/recursion/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/src/recursion/custom_train.py b/src/recursion/custom_train.py new file mode 100644 index 00000000..ab7072ee --- /dev/null +++ b/src/recursion/custom_train.py @@ -0,0 +1,40 @@ +for i, (input, target) in enumerate(zip(input_sequence, target_sequence, strict=True)): + memories_wrt.append(memory.detach().requires_grad_(True)) + memory = model(input.unsqueeze(0).to(dtype=torch.float32), memories_wrt[-1]) + output = head(memory) + loss = criterion(output, target.unsqueeze(0).to(dtype=torch.float32)) + memories.append(memory) + transform = Accumulate() << Aggregate(aggregator, OrderedSet(list(model.parameters()))) + + print(f"{loss.item():.1e}") + + if (i + 1) % update_every == 0: + grad_output = torch.autograd.grad(loss, [memories[-1]], retain_graph=True) + + for j in range(update_every): + grads = torch.autograd.grad( + memories[-j - 1], + list(model.parameters()) + [memories_wrt[-j - 1]], + grad_outputs=grad_output, + ) + grads_wrt_params = grads[:-1] + grad_output = grads[-1] + + for param, grad in zip(model.parameters(), grads_wrt_params, strict=True): + param_to_gradients[param].append(grad) + + param_to_jacobian = { + param: torch.stack(gradients, dim=0) for param, gradients in param_to_gradients.items() + } + + optimizer.zero_grad() + transform(param_to_jacobian) # This stores the aggregated Jacobian in the .grad fields + optimizer.step() + + memories = [] + memories_wrt = [] + param_to_gradients = defaultdict(list) + + head_optimizer.zero_grad() + torch.autograd.backward(loss, inputs=list(head.parameters())) + head_optimizer.step() diff --git a/src/recursion/dataset/__init__.py b/src/recursion/dataset/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/dataset/build_arc_dataset.py b/src/recursion/dataset/build_arc_dataset.py similarity index 78% rename from dataset/build_arc_dataset.py rename to src/recursion/dataset/build_arc_dataset.py index c1442750..40a2f01e 100644 --- a/dataset/build_arc_dataset.py +++ b/src/recursion/dataset/build_arc_dataset.py @@ -1,15 +1,18 @@ -from typing import List, Tuple, Dict -from dataclasses import dataclass -import os -import json import hashlib -import numpy as np +import json +import os +from dataclasses import dataclass +from typing import Dict, List, Tuple +import numpy as np from argdantic import ArgParser from pydantic import BaseModel -from dataset.common import PuzzleDatasetMetadata, dihedral_transform, inverse_dihedral_transform - +from recursion.dataset.common import ( + PuzzleDatasetMetadata, + dihedral_transform, + inverse_dihedral_transform, +) cli = ArgParser() @@ -22,20 +25,21 @@ class DataProcessConfig(BaseModel): test_set_name2: str = "your_test_set" seed: int = 42 num_aug: int = 1000 - puzzle_identifiers_start: int = 1 # start > 1 to handle multiple datasets - + puzzle_identifiers_start: int = 1 # start > 1 to handle multiple datasets + + ARCMaxGridSize = 30 ARCAugmentRetriesFactor = 5 PuzzleIdSeparator = "|||" - + @dataclass class ARCPuzzle: id: str examples: List[Tuple[np.ndarray, np.ndarray]] - + def arc_grid_to_np(grid: List[List[int]]): arr = np.array(grid) @@ -60,7 +64,11 @@ def np_grid_to_seq_translational_augment(inp: np.ndarray, out: np.ndarray, do_tr result = [] for grid in [inp, out]: nrow, ncol = grid.shape - grid = np.pad(grid + 2, ((pad_r, ARCMaxGridSize - pad_r - nrow), (pad_c, ARCMaxGridSize - pad_c - ncol)), constant_values=0) + grid = np.pad( + grid + 2, + ((pad_r, ARCMaxGridSize - pad_r - nrow), (pad_c, ARCMaxGridSize - pad_c - ncol)), + constant_values=0, + ) # Add eos_row, eos_col = pad_r + nrow, pad_c + ncol @@ -78,9 +86,9 @@ def grid_hash(grid: np.ndarray): assert grid.ndim == 2 assert grid.dtype == np.uint8 - buffer = [x.to_bytes(1, byteorder='big') for x in grid.shape] + buffer = [x.to_bytes(1, byteorder="big") for x in grid.shape] buffer.append(grid.tobytes()) - + return hashlib.sha256(b"".join(buffer)).hexdigest() @@ -90,7 +98,7 @@ def puzzle_hash(puzzle: dict): for example_type, example in puzzle.items(): for input, label in example.examples: hashes.append(f"{grid_hash(input)}|{grid_hash(label)}") - + hashes.sort() return hashlib.sha256("|".join(hashes).encode()).hexdigest() @@ -98,13 +106,17 @@ def puzzle_hash(puzzle: dict): def aug(name: str): # Augment plan trans_id = np.random.randint(0, 8) - mapping = np.concatenate([np.arange(0, 1, dtype=np.uint8), np.random.permutation(np.arange(1, 10, dtype=np.uint8))]) # Permute colors, Excluding "0" (black) - - name_with_aug_repr = f"{name}{PuzzleIdSeparator}t{trans_id}{PuzzleIdSeparator}{''.join(str(x) for x in mapping)}" + mapping = np.concatenate( + [np.arange(0, 1, dtype=np.uint8), np.random.permutation(np.arange(1, 10, dtype=np.uint8))] + ) # Permute colors, Excluding "0" (black) + + name_with_aug_repr = ( + f"{name}{PuzzleIdSeparator}t{trans_id}{PuzzleIdSeparator}{''.join(str(x) for x in mapping)}" + ) def _map_grid(grid: np.ndarray): return dihedral_transform(mapping[grid], trans_id) - + return name_with_aug_repr, _map_grid @@ -116,24 +128,31 @@ def inverse_aug(name: str): trans_id, perm = name.split(PuzzleIdSeparator)[-2:] trans_id = int(trans_id[1:]) # Remove "t" letter inv_perm = np.argsort(list(perm)).astype(np.uint8) - + def _map_grid(grid: np.ndarray): return inv_perm[inverse_dihedral_transform(grid, trans_id)] - + return name.split(PuzzleIdSeparator)[0], _map_grid -def convert_single_arc_puzzle(results: dict, name: str, puzzle: dict, aug_count: int, dest_mapping: Dict[str, Tuple[str, str]]): +def convert_single_arc_puzzle( + results: dict, name: str, puzzle: dict, aug_count: int, dest_mapping: Dict[str, Tuple[str, str]] +): # Convert dests = set(dest_mapping.values()) converted = {dest: ARCPuzzle(name, []) for dest in dests} for example_type, examples in puzzle.items(): # Map to target split dest = dest_mapping[example_type] - converted[dest].examples.extend([(arc_grid_to_np(example["input"]), arc_grid_to_np(example["output"])) for example in examples]) + converted[dest].examples.extend( + [ + (arc_grid_to_np(example["input"]), arc_grid_to_np(example["output"])) + for example in examples + ] + ) group = [converted] - + # Augment if aug_count > 0: hashes = {puzzle_hash(converted)} @@ -142,17 +161,23 @@ def convert_single_arc_puzzle(results: dict, name: str, puzzle: dict, aug_count: aug_name, _map_grid = aug(name) # Check duplicate - augmented = {dest: ARCPuzzle(aug_name, [(_map_grid(input), _map_grid(label)) for (input, label) in puzzle.examples]) for dest, puzzle in converted.items()} + augmented = { + dest: ARCPuzzle( + aug_name, + [(_map_grid(input), _map_grid(label)) for (input, label) in puzzle.examples], + ) + for dest, puzzle in converted.items() + } h = puzzle_hash(augmented) if h not in hashes: hashes.add(h) group.append(augmented) - + if len(group) >= aug_count + 1: break - + if len(group) < aug_count + 1: - print (f"[Puzzle {name}] augmentation not full, only {len(group)}") + print(f"[Puzzle {name}] augmentation not full, only {len(group)}") # Append for dest in dests: @@ -169,9 +194,9 @@ def load_puzzles_arcagi(config: DataProcessConfig): test_examples_map = { config.test_set_name: [(1.0, ("test", "all"))], config.test_set_name2: [(1.0, ("test", "all"))], - "_default": [(1.0, ("train", "all"))] + "_default": [(1.0, ("train", "all"))], } - + test_puzzles = {} results = {} @@ -185,13 +210,13 @@ def load_puzzles_arcagi(config: DataProcessConfig): if os.path.isfile(sols_filename): with open(sols_filename, "r") as f: sols = json.load(f) - + for puzzle_id in puzzles.keys(): for idx, sol_grid in enumerate(sols[puzzle_id]): puzzles[puzzle_id]["test"][idx]["output"] = sol_grid else: # Fill with dummy - print (f"{subset_name} solutions not found, filling with dummy") + print(f"{subset_name} solutions not found, filling with dummy") for puzzle_id, puzzle in puzzles.items(): for example in puzzle["test"]: @@ -200,7 +225,7 @@ def load_puzzles_arcagi(config: DataProcessConfig): # Shuffle puzzles puzzles = list(puzzles.items()) np.random.shuffle(puzzles) - + # Assign by fraction for idx, (name, puzzle) in enumerate(puzzles): fraction = idx / len(puzzles) @@ -209,25 +234,31 @@ def load_puzzles_arcagi(config: DataProcessConfig): if fraction < f: test_examples_dest = dest break - + assert test_examples_dest is not None - + if test_examples_dest[0] == "test": test_puzzles[name] = puzzle - - convert_single_arc_puzzle(results, name, puzzle, config.num_aug, {"train": train_examples_dest, "test": test_examples_dest}) + + convert_single_arc_puzzle( + results, + name, + puzzle, + config.num_aug, + {"train": train_examples_dest, "test": test_examples_dest}, + ) total_puzzles += 1 - print (f"Total puzzles: {total_puzzles}") + print(f"Total puzzles: {total_puzzles}") return results, test_puzzles def convert_dataset(config: DataProcessConfig): np.random.seed(config.seed) - + # Read dataset data, test_puzzles = load_puzzles_arcagi(config) - + # Map global puzzle identifiers num_identifiers = config.puzzle_identifiers_start # 0 is blank, start at 1 identifier_map = {} @@ -238,12 +269,12 @@ def convert_dataset(config: DataProcessConfig): if puzzle.id not in identifier_map: identifier_map[puzzle.id] = num_identifiers num_identifiers += 1 - print (f"Total puzzle IDs (including ): {num_identifiers}") + print(f"Total puzzle IDs (including ): {num_identifiers}") # Save for split_name, split in data.items(): os.makedirs(os.path.join(config.output_dir, split_name), exist_ok=True) - + # Translational augmentations enable_translational_augment = split_name == "train" @@ -251,47 +282,60 @@ def convert_dataset(config: DataProcessConfig): total_examples = 0 total_puzzles = 0 total_groups = 0 - - for subset_name, subset in split.items(): # "all" is the only subset + + for subset_name, subset in split.items(): # "all" is the only subset # Construct subset - results = {k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"]} + results = { + k: [] + for k in [ + "inputs", + "labels", + "puzzle_identifiers", + "puzzle_indices", + "group_indices", + ] + } results["puzzle_indices"].append(0) results["group_indices"].append(0) - + example_id = 0 puzzle_id = 0 - + for group in subset: for puzzle in group: # Push puzzle no_aug_id = np.random.randint(0, len(puzzle.examples)) for _idx_ex, (inp, out) in enumerate(puzzle.examples): - inp, out = np_grid_to_seq_translational_augment(inp, out, do_translation=enable_translational_augment and _idx_ex != no_aug_id) - + inp, out = np_grid_to_seq_translational_augment( + inp, + out, + do_translation=enable_translational_augment and _idx_ex != no_aug_id, + ) + results["inputs"].append(inp) results["labels"].append(out) example_id += 1 - + total_examples += 1 results["puzzle_indices"].append(example_id) results["puzzle_identifiers"].append(identifier_map[puzzle.id]) - + puzzle_id += 1 total_puzzles += 1 - + # Push group results["group_indices"].append(puzzle_id) total_groups += 1 - + for k, v in results.items(): if k in {"inputs", "labels"}: v = np.stack(v, 0) else: v = np.array(v, dtype=np.int32) - + np.save(os.path.join(config.output_dir, split_name, f"{subset_name}__{k}.npy"), v) - + # Metadata metadata = PuzzleDatasetMetadata( seq_len=ARCMaxGridSize * ARCMaxGridSize, @@ -303,18 +347,18 @@ def convert_dataset(config: DataProcessConfig): total_groups=total_groups, mean_puzzle_examples=total_examples / total_puzzles, total_puzzles=total_puzzles, - sets=list(split.keys()) + sets=list(split.keys()), ) # Save metadata as JSON. with open(os.path.join(config.output_dir, split_name, "dataset.json"), "w") as f: json.dump(metadata.model_dump(), f) - + # Save IDs mapping with open(os.path.join(config.output_dir, "identifiers.json"), "w") as f: ids_mapping = {v: k for k, v in identifier_map.items()} json.dump([ids_mapping.get(i, "") for i in range(num_identifiers)], f) - + # Save Test Puzzles with open(os.path.join(config.output_dir, "test_puzzles.json"), "w") as f: json.dump(test_puzzles, f) @@ -327,15 +371,3 @@ def main(config: DataProcessConfig): if __name__ == "__main__": cli() - - - - - - - - - - - - diff --git a/dataset/build_maze_dataset.py b/src/recursion/dataset/build_maze_dataset.py similarity index 93% rename from dataset/build_maze_dataset.py rename to src/recursion/dataset/build_maze_dataset.py index 7ebe2672..dc34f0e1 100644 --- a/dataset/build_maze_dataset.py +++ b/src/recursion/dataset/build_maze_dataset.py @@ -1,17 +1,15 @@ -from typing import Optional -import math -import os import csv import json -import numpy as np +import math +import os +from typing import Optional +import numpy as np from argdantic import ArgParser +from recursion.dataset.common import PuzzleDatasetMetadata, dihedral_transform +from huggingface_hub import hf_hub_download from pydantic import BaseModel from tqdm import tqdm -from huggingface_hub import hf_hub_download - -from common import PuzzleDatasetMetadata, dihedral_transform - CHARSET = "# SGo" @@ -33,7 +31,7 @@ def convert_subset(set_name: str, config: DataProcessConfig): grid_size = None inputs = [] labels = [] - + with open(hf_hub_download(config.source_repo, f"{set_name}.csv", repo_type="dataset"), newline="") as csvfile: # type: ignore reader = csv.reader(csvfile) next(reader) # Skip header @@ -44,7 +42,7 @@ def convert_subset(set_name: str, config: DataProcessConfig): if grid_size is None: n = int(len(q) ** 0.5) grid_size = (n, n) - + inputs.append(np.frombuffer(q.encode(), dtype=np.uint8).reshape(grid_size)) labels.append(np.frombuffer(a.encode(), dtype=np.uint8).reshape(grid_size)) @@ -58,13 +56,15 @@ def convert_subset(set_name: str, config: DataProcessConfig): labels = [labels[i] for i in indices] # Generate dataset - results = {k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"]} + results = { + k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"] + } puzzle_id = 0 example_id = 0 - + results["puzzle_indices"].append(0) results["group_indices"].append(0) - + for inp, out in zip(tqdm(inputs), labels): # Dihedral transformations for augmentation for aug_idx in range(8 if (set_name == "train" and config.aug) else 1): @@ -72,29 +72,28 @@ def convert_subset(set_name: str, config: DataProcessConfig): results["labels"].append(dihedral_transform(out, aug_idx)) example_id += 1 puzzle_id += 1 - + results["puzzle_indices"].append(example_id) results["puzzle_identifiers"].append(0) - + # Push group results["group_indices"].append(puzzle_id) - + # Char mappings assert len(all_chars - set(CHARSET)) == 0 - + char2id = np.zeros(256, np.uint8) char2id[np.array(list(map(ord, CHARSET)))] = np.arange(len(CHARSET)) + 1 # To Numpy def _seq_to_numpy(seq): arr = np.vstack([char2id[s.reshape(-1)] for s in seq]) - + return arr - + results = { "inputs": _seq_to_numpy(results["inputs"]), "labels": _seq_to_numpy(results["labels"]), - "group_indices": np.array(results["group_indices"], dtype=np.int32), "puzzle_indices": np.array(results["puzzle_indices"], dtype=np.int32), "puzzle_identifiers": np.array(results["puzzle_identifiers"], dtype=np.int32), @@ -111,20 +110,20 @@ def _seq_to_numpy(seq): total_groups=len(results["group_indices"]) - 1, mean_puzzle_examples=1, total_puzzles=len(results["group_indices"]) - 1, - sets=["all"] + sets=["all"], ) # Save metadata as JSON. save_dir = os.path.join(config.output_dir, set_name) os.makedirs(save_dir, exist_ok=True) - + with open(os.path.join(save_dir, "dataset.json"), "w") as f: json.dump(metadata.model_dump(), f) - + # Save data for k, v in results.items(): np.save(os.path.join(save_dir, f"all__{k}.npy"), v) - + # Save IDs mapping (for visualization only) with open(os.path.join(config.output_dir, "identifiers.json"), "w") as f: json.dump([""], f) diff --git a/dataset/build_sudoku_dataset.py b/src/recursion/dataset/build_sudoku_dataset.py similarity index 90% rename from dataset/build_sudoku_dataset.py rename to src/recursion/dataset/build_sudoku_dataset.py index 796b1280..e9991409 100644 --- a/dataset/build_sudoku_dataset.py +++ b/src/recursion/dataset/build_sudoku_dataset.py @@ -1,16 +1,14 @@ -from typing import Optional -import os import csv import json -import numpy as np +import os +from typing import Optional +import numpy as np from argdantic import ArgParser +from recursion.dataset.common import PuzzleDatasetMetadata +from huggingface_hub import hf_hub_download from pydantic import BaseModel from tqdm import tqdm -from huggingface_hub import hf_hub_download - -from common import PuzzleDatasetMetadata - cli = ArgParser() @@ -27,7 +25,7 @@ class DataProcessConfig(BaseModel): def shuffle_sudoku(board: np.ndarray, solution: np.ndarray): # Create a random digit mapping: a permutation of 1..9, with zero (blank) unchanged digit_map = np.pad(np.random.permutation(np.arange(1, 10)), (1, 0)) - + # Randomly decide whether to transpose. transpose_flag = np.random.rand() < 0.5 @@ -61,16 +59,21 @@ def convert_subset(set_name: str, config: DataProcessConfig): # Read CSV inputs = [] labels = [] - - with open(hf_hub_download(config.source_repo, f"{set_name}.csv", repo_type="dataset"), newline="") as csvfile: + + with open( + hf_hub_download(config.source_repo, f"{set_name}.csv", repo_type="dataset"), newline="" + ) as csvfile: reader = csv.reader(csvfile) next(reader) # Skip header for source, q, a, rating in reader: if (config.min_difficulty is None) or (int(rating) >= config.min_difficulty): assert len(q) == 81 and len(a) == 81 - - inputs.append(np.frombuffer(q.replace('.', '0').encode(), dtype=np.uint8).reshape(9, 9) - ord('0')) - labels.append(np.frombuffer(a.encode(), dtype=np.uint8).reshape(9, 9) - ord('0')) + + inputs.append( + np.frombuffer(q.replace(".", "0").encode(), dtype=np.uint8).reshape(9, 9) + - ord("0") + ) + labels.append(np.frombuffer(a.encode(), dtype=np.uint8).reshape(9, 9) - ord("0")) # If subsample_size is specified for the training set, # randomly sample the desired number of examples. @@ -84,13 +87,15 @@ def convert_subset(set_name: str, config: DataProcessConfig): # Generate dataset num_augments = config.num_aug if set_name == "train" else 0 - results = {k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"]} + results = { + k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"] + } puzzle_id = 0 example_id = 0 - + results["puzzle_indices"].append(0) results["group_indices"].append(0) - + for orig_inp, orig_out in zip(tqdm(inputs), labels): for aug_idx in range(1 + num_augments): # First index is not augmented @@ -104,24 +109,23 @@ def convert_subset(set_name: str, config: DataProcessConfig): results["labels"].append(out) example_id += 1 puzzle_id += 1 - + results["puzzle_indices"].append(example_id) results["puzzle_identifiers"].append(0) - + # Push group results["group_indices"].append(puzzle_id) - + # To Numpy def _seq_to_numpy(seq): arr = np.concatenate(seq).reshape(len(seq), -1) - + assert np.all((arr >= 0) & (arr <= 9)) return arr + 1 - + results = { "inputs": _seq_to_numpy(results["inputs"]), "labels": _seq_to_numpy(results["labels"]), - "group_indices": np.array(results["group_indices"], dtype=np.int32), "puzzle_indices": np.array(results["puzzle_indices"], dtype=np.int32), "puzzle_identifiers": np.array(results["puzzle_identifiers"], dtype=np.int32), @@ -138,20 +142,20 @@ def _seq_to_numpy(seq): total_groups=len(results["group_indices"]) - 1, mean_puzzle_examples=1, total_puzzles=len(results["group_indices"]) - 1, - sets=["all"] + sets=["all"], ) # Save metadata as JSON. save_dir = os.path.join(config.output_dir, set_name) os.makedirs(save_dir, exist_ok=True) - + with open(os.path.join(save_dir, "dataset.json"), "w") as f: json.dump(metadata.model_dump(), f) - + # Save data for k, v in results.items(): np.save(os.path.join(save_dir, f"all__{k}.npy"), v) - + # Save IDs mapping (for visualization only) with open(os.path.join(config.output_dir, "identifiers.json"), "w") as f: json.dump([""], f) diff --git a/dataset/common.py b/src/recursion/dataset/common.py similarity index 85% rename from dataset/common.py rename to src/recursion/dataset/common.py index 5ff91bbc..dd9be839 100644 --- a/dataset/common.py +++ b/src/recursion/dataset/common.py @@ -1,8 +1,7 @@ from typing import List, Optional -import pydantic import numpy as np - +import pydantic # Global list mapping each dihedral transform id to its inverse. # Index corresponds to the original tid, and the value is its inverse. @@ -24,7 +23,7 @@ class PuzzleDatasetMetadata(pydantic.BaseModel): def dihedral_transform(arr: np.ndarray, tid: int) -> np.ndarray: """8 dihedral symmetries by rotate, flip and mirror""" - + if tid == 0: return arr # identity elif tid == 1: @@ -34,16 +33,16 @@ def dihedral_transform(arr: np.ndarray, tid: int) -> np.ndarray: elif tid == 3: return np.rot90(arr, k=3) elif tid == 4: - return np.fliplr(arr) # horizontal flip + return np.fliplr(arr) # horizontal flip elif tid == 5: - return np.flipud(arr) # vertical flip + return np.flipud(arr) # vertical flip elif tid == 6: - return arr.T # transpose (reflection along main diagonal) + return arr.T # transpose (reflection along main diagonal) elif tid == 7: return np.fliplr(np.rot90(arr, k=1)) # anti-diagonal reflection else: return arr - - + + def inverse_dihedral_transform(arr: np.ndarray, tid: int) -> np.ndarray: return dihedral_transform(arr, DIHEDRAL_INVERSE[tid]) diff --git a/src/recursion/evaluators/__init__.py b/src/recursion/evaluators/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/evaluators/arc.py b/src/recursion/evaluators/arc.py similarity index 75% rename from evaluators/arc.py rename to src/recursion/evaluators/arc.py index 3003cbff..4bdc4f73 100644 --- a/evaluators/arc.py +++ b/src/recursion/evaluators/arc.py @@ -1,24 +1,25 @@ -from typing import Dict, Sequence, Optional -import os import json +import os +from typing import Dict, Optional, Sequence -import torch import numpy as np -from numba import njit +import torch import torch.distributed as dist +from numba import njit + +from recursion.dataset.build_arc_dataset import arc_grid_to_np, grid_hash, inverse_aug +from recursion.dataset.common import PuzzleDatasetMetadata -from dataset.build_arc_dataset import inverse_aug, grid_hash, arc_grid_to_np -from dataset.common import PuzzleDatasetMetadata @njit def _crop(grid: np.ndarray): - """Find maximum-sized rectangle without any EOS token inside. """ + """Find maximum-sized rectangle without any EOS token inside.""" grid = grid.reshape(30, 30) max_area = 0 max_size = (0, 0) nr, nc = grid.shape - + num_c = nc for num_r in range(1, nr + 1): # Scan for maximum c @@ -27,23 +28,26 @@ def _crop(grid: np.ndarray): if (x < 2) | (x > 11): num_c = c - 1 break - + area = num_r * num_c if area > max_area: max_area = area max_size = (num_r, num_c) - return (grid[:max_size[0], :max_size[1]] - 2).astype(np.uint8) + return (grid[: max_size[0], : max_size[1]] - 2).astype(np.uint8) class ARC: required_outputs = {"inputs", "puzzle_identifiers", "q_halt_logits", "preds"} - - def __init__(self, data_path: str, - eval_metadata: PuzzleDatasetMetadata, - submission_K: int = 2, - pass_Ks: Sequence[int] = (1, 2, 5, 10, 100, 1000), - aggregated_voting: bool = True): + + def __init__( + self, + data_path: str, + eval_metadata: PuzzleDatasetMetadata, + submission_K: int = 2, + pass_Ks: Sequence[int] = (1, 2, 5, 10, 100, 1000), + aggregated_voting: bool = True, + ): super().__init__() self.pass_Ks = pass_Ks self.submission_K = submission_K @@ -55,17 +59,17 @@ def __init__(self, data_path: str, self.identifier_map = json.load(f) with open(os.path.join(data_path, "test_puzzles.json"), "r") as f: self.test_puzzles = json.load(f) - + # States self._local_hmap = {} self._local_preds = {} - + def begin_eval(self): if not self.aggregated_voting: # Clear previous predictions self._local_hmap = {} self._local_preds = {} - + def update_batch(self, batch: Dict[str, torch.Tensor], preds: Dict[str, torch.Tensor]): # Collect required outputs to CPU outputs = {} @@ -78,7 +82,7 @@ def update_batch(self, batch: Dict[str, torch.Tensor], preds: Dict[str, torch.Te q_values = v.to(torch.float64).sigmoid().cpu() else: outputs[k] = v.cpu() - + assert q_values is not None # Remove padding from outputs @@ -86,29 +90,44 @@ def update_batch(self, batch: Dict[str, torch.Tensor], preds: Dict[str, torch.Te outputs = {k: v[mask] for k, v in outputs.items()} # Get predictions - for identifier, input, pred, q in zip(outputs["puzzle_identifiers"].numpy(), outputs["inputs"].numpy(), outputs["preds"].numpy(), q_values.numpy()): + for identifier, input, pred, q in zip( + outputs["puzzle_identifiers"].numpy(), + outputs["inputs"].numpy(), + outputs["preds"].numpy(), + q_values.numpy(), + ): name = self.identifier_map[identifier] orig_name, _inverse_fn = inverse_aug(name) - + input_hash = grid_hash(_inverse_fn(_crop(input))) - + pred = _inverse_fn(_crop(pred)) - assert np.all((pred >= 0) & (pred <= 9)), f"Puzzle {name}'s prediction out of 0-9 range." # Sanity check + assert np.all( + (pred >= 0) & (pred <= 9) + ), f"Puzzle {name}'s prediction out of 0-9 range." # Sanity check # Store into local state pred_hash = grid_hash(pred) self._local_hmap[pred_hash] = pred - + self._local_preds.setdefault(orig_name, {}) self._local_preds[orig_name].setdefault(input_hash, []) self._local_preds[orig_name][input_hash].append((pred_hash, float(q))) - - def result(self, save_path: Optional[str], rank: int, world_size: int, group: Optional[torch.distributed.ProcessGroup] = None) -> Optional[Dict[str, float]]: + + def result( + self, + save_path: Optional[str], + rank: int, + world_size: int, + group: Optional[torch.distributed.ProcessGroup] = None, + ) -> Optional[Dict[str, float]]: # Gather predictions to rank 0 for voting global_hmap_preds = [None for _ in range(world_size)] if rank == 0 else None - dist.gather_object((self._local_hmap, self._local_preds), global_hmap_preds, dst=0, group=group) - + dist.gather_object( + (self._local_hmap, self._local_preds), global_hmap_preds, dst=0, group=group + ) + # Rank 0 logic if rank != 0: return @@ -123,21 +142,21 @@ def result(self, save_path: Optional[str], rank: int, world_size: int, group: Op for pair in puzzle["test"]: input_hash = grid_hash(arc_grid_to_np(pair["input"])) label_hash = grid_hash(arc_grid_to_np(pair["output"])) - + p_map = {} for hmap, preds in global_hmap_preds: # type: ignore for h, q in preds.get(name, {}).get(input_hash, {}): p_map.setdefault(h, [0, 0]) p_map[h][0] += 1 p_map[h][1] += q - + if not len(p_map): - print (f"Puzzle {name} has no predictions.") + print(f"Puzzle {name} has no predictions.") continue for h, stats in p_map.items(): stats[1] /= stats[0] - + p_map = sorted(p_map.items(), key=lambda kv: kv[1], reverse=True) # vote for different Ks @@ -145,22 +164,24 @@ def result(self, save_path: Optional[str], rank: int, world_size: int, group: Op ok = False for h, stats in p_map[:k]: ok |= h == label_hash - + num_test_correct[i] += ok - + # Query grids pred_grids = [] - for h, stats in p_map[:self.submission_K]: + for h, stats in p_map[: self.submission_K]: for hmap, preds in global_hmap_preds: # type: ignore if h in hmap: pred_grids.append(hmap[h]) break - + # Pad to K while len(pred_grids) < self.submission_K: pred_grids.append(pred_grids[0]) - - submission[name].append({f"attempt_{i + 1}": grid.tolist() for i, grid in enumerate(pred_grids)}) + + submission[name].append( + {f"attempt_{i + 1}": grid.tolist() for i, grid in enumerate(pred_grids)} + ) # Total correctness for i in range(len(self.pass_Ks)): @@ -172,6 +193,8 @@ def result(self, save_path: Optional[str], rank: int, world_size: int, group: Op json.dump(submission, f) # Final result - all_results = {f"ARC/pass@{k}": correct[i] / len(self.test_puzzles) for i, k in enumerate(self.pass_Ks)} + all_results = { + f"ARC/pass@{k}": correct[i] / len(self.test_puzzles) for i, k in enumerate(self.pass_Ks) + } - return all_results \ No newline at end of file + return all_results diff --git a/src/recursion/models/__init__.py b/src/recursion/models/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/models/common.py b/src/recursion/models/common.py similarity index 71% rename from models/common.py rename to src/recursion/models/common.py index 1a045051..825618ad 100644 --- a/models/common.py +++ b/src/recursion/models/common.py @@ -1,10 +1,11 @@ import math import torch -from torch import nn -def trunc_normal_init_(tensor: torch.Tensor, std: float = 1.0, lower: float = -2.0, upper: float = 2.0): +def trunc_normal_init_( + tensor: torch.Tensor, std: float = 1.0, lower: float = -2.0, upper: float = 2.0 +): # NOTE: PyTorch nn.init.trunc_normal_ is not mathematically correct, the std dev is not actually the std dev of initialized tensor # This function is a PyTorch version of jax truncated normal init (default init method in flax) # https://github.com/jax-ml/jax/blob/main/jax/_src/random.py#L807-L848 @@ -20,9 +21,11 @@ def trunc_normal_init_(tensor: torch.Tensor, std: float = 1.0, lower: float = -2 z = (b - a) / 2 c = (2 * math.pi) ** -0.5 - pdf_u = c * math.exp(-0.5 * lower ** 2) - pdf_l = c * math.exp(-0.5 * upper ** 2) - comp_std = std / math.sqrt(1 - (upper * pdf_u - lower * pdf_l) / z - ((pdf_u - pdf_l) / z) ** 2) + pdf_u = c * math.exp(-0.5 * lower**2) + pdf_l = c * math.exp(-0.5 * upper**2) + comp_std = std / math.sqrt( + 1 - (upper * pdf_u - lower * pdf_l) / z - ((pdf_u - pdf_l) / z) ** 2 + ) tensor.uniform_(a, b) tensor.erfinv_() diff --git a/models/ema.py b/src/recursion/models/ema.py similarity index 88% rename from models/ema.py rename to src/recursion/models/ema.py index 2e529333..9af64cc2 100644 --- a/models/ema.py +++ b/src/recursion/models/ema.py @@ -1,6 +1,8 @@ import copy + import torch.nn as nn + class EMAHelper(object): def __init__(self, mu=0.999): self.mu = mu @@ -18,7 +20,9 @@ def update(self, module): module = module.module for name, param in module.named_parameters(): if param.requires_grad: - self.shadow[name].data = (1. - self.mu) * param.data + self.mu * self.shadow[name].data + self.shadow[name].data = (1.0 - self.mu) * param.data + self.mu * self.shadow[ + name + ].data def ema(self, module): if isinstance(module, nn.DataParallel): @@ -37,4 +41,3 @@ def state_dict(self): def load_state_dict(self, state_dict): self.shadow = state_dict - diff --git a/models/layers.py b/src/recursion/models/layers.py similarity index 73% rename from models/layers.py rename to src/recursion/models/layers.py index 705bcaf2..f90f0d6a 100644 --- a/models/layers.py +++ b/src/recursion/models/layers.py @@ -1,18 +1,18 @@ from typing import Tuple + import einops import torch -from torch import nn import torch.nn.functional as F +from torch import nn -#try: +# try: # from flash_attn_interface import flash_attn_func # type: ignore[import] -#except ImportError: +# except ImportError: # # Fallback to FlashAttention 2 # from flash_attn import flash_attn_func # type: ignore[import] from torch.nn.functional import scaled_dot_product_attention -from models.common import trunc_normal_init_ - +from recursion.models.common import trunc_normal_init_ CosSin = Tuple[torch.Tensor, torch.Tensor] @@ -42,30 +42,31 @@ def apply_rotary_pos_emb(q: torch.Tensor, k: torch.Tensor, cos: torch.Tensor, si class CastedLinear(nn.Module): - def __init__(self, - in_features: int, - out_features: int, - bias: bool): + def __init__(self, in_features: int, out_features: int, bias: bool): super().__init__() # Truncated LeCun normal init self.weight = nn.Parameter( - trunc_normal_init_(torch.empty((out_features, in_features)), std=1.0 / (in_features ** 0.5)) + trunc_normal_init_( + torch.empty((out_features, in_features)), std=1.0 / (in_features**0.5) + ) ) self.bias = None if bias: # Zero init bias - self.bias = nn.Parameter(torch.zeros((out_features, ))) + self.bias = nn.Parameter(torch.zeros((out_features,))) def forward(self, input: torch.Tensor) -> torch.Tensor: - return F.linear(input, self.weight.to(input.dtype), bias=self.bias.to(input.dtype) if self.bias is not None else None) + return F.linear( + input, + self.weight.to(input.dtype), + bias=self.bias.to(input.dtype) if self.bias is not None else None, + ) class CastedEmbedding(nn.Module): - def __init__(self, - num_embeddings: int, - embedding_dim: int, - init_std: float, - cast_to: torch.dtype): + def __init__( + self, num_embeddings: int, embedding_dim: int, init_std: float, cast_to: torch.dtype + ): super().__init__() self.cast_to = cast_to @@ -73,7 +74,7 @@ def __init__(self, self.embedding_weight = nn.Parameter( trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std) ) - + def forward(self, input: torch.Tensor) -> torch.Tensor: return F.embedding(input, self.embedding_weight.to(self.cast_to)) @@ -83,7 +84,9 @@ def __init__(self, dim, max_position_embeddings, base, device=None): super().__init__() # RoPE - inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2, dtype=torch.float32, device=device) / dim)) + inv_freq = 1.0 / ( + base ** (torch.arange(0, dim, 2, dtype=torch.float32, device=device) / dim) + ) t = torch.arange(max_position_embeddings, dtype=torch.float32, device=device) freqs = torch.outer(t, inv_freq) @@ -107,7 +110,11 @@ def __init__(self, hidden_size, head_dim, num_heads, num_key_value_heads, causal self.num_key_value_heads = num_key_value_heads self.causal = causal - self.qkv_proj = CastedLinear(self.hidden_size, (self.num_heads + 2 * self.num_key_value_heads) * self.head_dim, bias=False) + self.qkv_proj = CastedLinear( + self.hidden_size, + (self.num_heads + 2 * self.num_key_value_heads) * self.head_dim, + bias=False, + ) self.o_proj = CastedLinear(self.output_size, self.hidden_size, bias=False) def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: @@ -117,10 +124,12 @@ def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: qkv = self.qkv_proj(hidden_states) # Split head - qkv = qkv.view(batch_size, seq_len, self.num_heads + 2 * self.num_key_value_heads, self.head_dim) - query = qkv[:, :, :self.num_heads] - key = qkv[:, :, self.num_heads: self.num_heads + self.num_key_value_heads] - value = qkv[:, :, self.num_heads + self.num_key_value_heads:] + qkv = qkv.view( + batch_size, seq_len, self.num_heads + 2 * self.num_key_value_heads, self.head_dim + ) + query = qkv[:, :, : self.num_heads] + key = qkv[:, :, self.num_heads : self.num_heads + self.num_key_value_heads] + value = qkv[:, :, self.num_heads + self.num_key_value_heads :] # RoPE if cos_sin is not None: @@ -128,12 +137,17 @@ def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: query, key = apply_rotary_pos_emb(query, key, cos, sin) # flash attn - query, key, value = map(lambda t: einops.rearrange(t, 'B S H D -> B H S D'), (query, key, value)) # needed for scaled_dot_product_attention but not flash_attn_func - attn_output = scaled_dot_product_attention(query=query, key=key, value=value, is_causal=self.causal) - attn_output = einops.rearrange(attn_output, 'B H S D -> B S H D') + query, key, value = map( + lambda t: einops.rearrange(t, "B S H D -> B H S D"), (query, key, value) + ) # needed for scaled_dot_product_attention but not flash_attn_func + attn_output = scaled_dot_product_attention( + query=query, key=key, value=value, is_causal=self.causal + ) + attn_output = einops.rearrange(attn_output, "B H S D -> B S H D") attn_output = attn_output.reshape(batch_size, seq_len, self.output_size) # type: ignore return self.o_proj(attn_output) + class LinearSwish(nn.Module): def __init__(self, hidden_size: int, reverse=False): super().__init__() @@ -154,12 +168,13 @@ def __init__(self, hidden_size: int, expansion: float): inter = _find_multiple(round(expansion * hidden_size * 2 / 3), 256) self.gate_up_proj = CastedLinear(hidden_size, inter * 2, bias=False) - self.down_proj = CastedLinear(inter, hidden_size, bias=False) + self.down_proj = CastedLinear(inter, hidden_size, bias=False) def forward(self, x): gate, up = self.gate_up_proj(x).chunk(2, dim=-1) return self.down_proj(F.silu(gate) * up) + def rms_norm(hidden_states: torch.Tensor, variance_epsilon: float) -> torch.Tensor: input_dtype = hidden_states.dtype hidden_states = hidden_states.to(torch.float32) diff --git a/models/losses.py b/src/recursion/models/losses.py similarity index 53% rename from models/losses.py rename to src/recursion/models/losses.py index 2597cd67..471e0150 100644 --- a/models/losses.py +++ b/src/recursion/models/losses.py @@ -1,33 +1,30 @@ -from typing import Any, Tuple, Dict, Sequence, Optional +from typing import Any, Dict, Optional, Sequence, Tuple import torch import torch.nn.functional as F from torch import nn -import math IGNORE_LABEL_ID = -100 def s(x, epsilon=1e-30): - return torch.where( - x<0, - 1/(1-x+ epsilon), - x + 1 - ) + return torch.where(x < 0, 1 / (1 - x + epsilon), x + 1) def log_stablemax(x, dim=-1): s_x = s(x) - return torch.log(s_x/torch.sum(s_x, dim=dim, keepdim=True)) + return torch.log(s_x / torch.sum(s_x, dim=dim, keepdim=True)) def stablemax_cross_entropy(logits, labels, ignore_index: int = -100, valid_mask=None): logprobs = log_stablemax(logits.to(torch.float64), dim=-1) if valid_mask is None: - valid_mask = (labels != ignore_index) + valid_mask = labels != ignore_index transformed_labels = torch.where(valid_mask, labels, 0) - prediction_logprobs = torch.gather(logprobs, index=transformed_labels.to(torch.long).unsqueeze(-1), dim=-1).squeeze(-1) + prediction_logprobs = torch.gather( + logprobs, index=transformed_labels.to(torch.long).unsqueeze(-1), dim=-1 + ).squeeze(-1) return -torch.where(valid_mask, prediction_logprobs, 0) @@ -35,7 +32,12 @@ def stablemax_cross_entropy(logits, labels, ignore_index: int = -100, valid_mask def softmax_cross_entropy(logits, labels, ignore_index: int = -100): # Cast logits to f32 # Flatten logits - return F.cross_entropy(logits.to(torch.float32).view(-1, logits.shape[-1]), labels.to(torch.long).view(-1), ignore_index=ignore_index, reduction="none").view(labels.shape) + return F.cross_entropy( + logits.to(torch.float32).view(-1, logits.shape[-1]), + labels.to(torch.long).view(-1), + ignore_index=ignore_index, + reduction="none", + ).view(labels.shape) class ACTLossHead(nn.Module): @@ -43,7 +45,7 @@ def __init__(self, model: nn.Module, loss_type: str): super().__init__() self.model = model self.loss_fn = globals()[loss_type] - + def initial_carry(self, *args, **kwargs): return self.model.initial_carry(*args, **kwargs) # type: ignore @@ -52,7 +54,9 @@ def forward( return_keys: Sequence[str], # Model args **model_kwargs, - ) -> Tuple[Any, torch.Tensor, Dict[str, torch.Tensor], Optional[Dict[str, torch.Tensor]], torch.Tensor]: + ) -> Tuple[ + Any, torch.Tensor, Dict[str, torch.Tensor], Optional[Dict[str, torch.Tensor]], torch.Tensor + ]: # Model logits # B x SeqLen x D new_carry, outputs = self.model(**model_kwargs) @@ -63,41 +67,59 @@ def forward( outputs["preds"] = torch.argmax(outputs["logits"], dim=-1) # Correctness - mask = (labels != IGNORE_LABEL_ID) + mask = labels != IGNORE_LABEL_ID loss_counts = mask.sum(-1) loss_divisor = loss_counts.clamp_min(1).unsqueeze(-1) # Avoid NaNs in division is_correct = mask & (torch.argmax(outputs["logits"], dim=-1) == labels) seq_is_correct = is_correct.sum(-1) == loss_counts - + # Metrics (halted) valid_metrics = new_carry.halted & (loss_counts > 0) metrics = { "count": valid_metrics.sum(), - - "accuracy": torch.where(valid_metrics, (is_correct.to(torch.float32) / loss_divisor).sum(-1), 0).sum(), + "accuracy": torch.where( + valid_metrics, (is_correct.to(torch.float32) / loss_divisor).sum(-1), 0 + ).sum(), "exact_accuracy": (valid_metrics & seq_is_correct).sum(), - - "q_halt_accuracy": (valid_metrics & ((outputs["q_halt_logits"] >= 0) == seq_is_correct)).sum(), - "steps": torch.where(valid_metrics, new_carry.steps, 0).sum(), + "q_halt_accuracy": ( + valid_metrics & ((outputs["q_halt_logits"] >= 0) == seq_is_correct) + ).sum(), + "steps": torch.where(valid_metrics, new_carry.steps, 0).sum(), } # Losses - lm_loss = (self.loss_fn(outputs["logits"], labels, ignore_index=IGNORE_LABEL_ID, valid_mask=mask) / loss_divisor).sum() - q_halt_loss = F.binary_cross_entropy_with_logits(outputs["q_halt_logits"], seq_is_correct.to(outputs["q_halt_logits"].dtype), reduction="sum") - metrics.update({ - "lm_loss": lm_loss.detach(), - "q_halt_loss": q_halt_loss.detach(), - }) + lm_loss = ( + self.loss_fn(outputs["logits"], labels, ignore_index=IGNORE_LABEL_ID, valid_mask=mask) + / loss_divisor + ).sum() + q_halt_loss = F.binary_cross_entropy_with_logits( + outputs["q_halt_logits"], + seq_is_correct.to(outputs["q_halt_logits"].dtype), + reduction="sum", + ) + metrics.update( + { + "lm_loss": lm_loss.detach(), + "q_halt_loss": q_halt_loss.detach(), + } + ) # Q continue (bootstrapping target loss); Alexia: This fits Q-learning, but seems totally unecessary q_continue_loss = 0 if "target_q_continue" in outputs: - q_continue_loss = F.binary_cross_entropy_with_logits(outputs["q_continue_logits"], outputs["target_q_continue"], reduction="sum") + q_continue_loss = F.binary_cross_entropy_with_logits( + outputs["q_continue_logits"], outputs["target_q_continue"], reduction="sum" + ) metrics["q_continue_loss"] = q_continue_loss.detach() # Filter outputs for return detached_outputs = {k: outputs[k].detach() for k in return_keys if k in outputs} - return new_carry, lm_loss + 0.5 * (q_halt_loss + q_continue_loss), metrics, detached_outputs, new_carry.halted.all() - + return ( + new_carry, + lm_loss + 0.5 * (q_halt_loss + q_continue_loss), + metrics, + detached_outputs, + new_carry.halted.all(), + ) diff --git a/src/recursion/models/recursive_reasoning/__init__.py b/src/recursion/models/recursive_reasoning/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/models/recursive_reasoning/hrm.py b/src/recursion/models/recursive_reasoning/hrm.py similarity index 57% rename from models/recursive_reasoning/hrm.py rename to src/recursion/models/recursive_reasoning/hrm.py index 9a1a5037..73c87b39 100644 --- a/models/recursive_reasoning/hrm.py +++ b/src/recursion/models/recursive_reasoning/hrm.py @@ -1,14 +1,24 @@ -from typing import Tuple, List, Dict, Optional -from dataclasses import dataclass import math +from dataclasses import dataclass +from typing import Dict, List, Tuple + import torch import torch.nn.functional as F -from torch import nn from pydantic import BaseModel +from torch import nn + +from recursion.models.common import trunc_normal_init_ +from recursion.models.layers import ( + Attention, + CastedEmbedding, + CastedLinear, + CosSin, + RotaryEmbedding, + SwiGLU, + rms_norm, +) +from recursion.models.sparse_embedding import CastedSparseEmbedding -from models.common import trunc_normal_init_ -from models.layers import rms_norm, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear -from models.sparse_embedding import CastedSparseEmbedding @dataclass class HierarchicalReasoningModel_ACTV1InnerCarry: @@ -19,10 +29,10 @@ class HierarchicalReasoningModel_ACTV1InnerCarry: @dataclass class HierarchicalReasoningModel_ACTV1Carry: inner_carry: HierarchicalReasoningModel_ACTV1InnerCarry - + steps: torch.Tensor halted: torch.Tensor - + current_data: Dict[str, torch.Tensor] @@ -47,7 +57,7 @@ class HierarchicalReasoningModel_ACTV1Config(BaseModel): rms_norm_eps: float = 1e-5 rope_theta: float = 10000.0 - + # Halting Q-learning config halt_max_steps: int halt_exploration_prob: float @@ -55,7 +65,8 @@ class HierarchicalReasoningModel_ACTV1Config(BaseModel): forward_dtype: str = "bfloat16" # Alexia: added - mlp_t: bool=False # use mlp on L instead of transformer + mlp_t: bool = False # use mlp on L instead of transformer + class HierarchicalReasoningModel_ACTV1Block(nn.Module): def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: @@ -65,7 +76,7 @@ def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: if self.config.mlp_t: self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) self.mlp_t = SwiGLU( - hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L expansion=config.expansion, ) else: @@ -74,7 +85,7 @@ def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: head_dim=config.hidden_size // config.num_heads, num_heads=config.num_heads, num_key_value_heads=config.num_heads, - causal=False + causal=False, ) self.mlp = SwiGLU( hidden_size=config.hidden_size, @@ -86,25 +97,31 @@ def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: # B, L, D = hidden_states.shape # Post Norm if self.config.mlp_t: - hidden_states = hidden_states.transpose(1,2) + hidden_states = hidden_states.transpose(1, 2) out = self.mlp_t(hidden_states) hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) - hidden_states = hidden_states.transpose(1,2) + hidden_states = hidden_states.transpose(1, 2) else: # Self Attention - hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + hidden_states = rms_norm( + hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), + variance_epsilon=self.norm_eps, + ) # Fully Connected out = self.mlp(hidden_states) hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) return hidden_states + class HierarchicalReasoningModel_ACTV1ReasoningModule(nn.Module): def __init__(self, layers: List[HierarchicalReasoningModel_ACTV1Block]): super().__init__() self.layers = torch.nn.ModuleList(layers) - def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + def forward( + self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs + ) -> torch.Tensor: # Input injection (add) hidden_states = hidden_states + input_injection # Layers @@ -121,36 +138,73 @@ def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: self.forward_dtype = getattr(torch, self.config.forward_dtype) # I/O - self.embed_scale = math.sqrt(self.config.hidden_size) + self.embed_scale = math.sqrt(self.config.hidden_size) embed_init_std = 1.0 / self.embed_scale - self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) - self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) - self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + self.embed_tokens = CastedEmbedding( + self.config.vocab_size, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) # ceil div if self.config.puzzle_emb_ndim > 0: # Zero init puzzle embeddings - self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, - batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + self.puzzle_emb = CastedSparseEmbedding( + self.config.num_puzzle_identifiers, + self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, + init_std=0, + cast_to=self.forward_dtype, + ) # LM Blocks if self.config.pos_encodings == "rope": - self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, - max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, - base=self.config.rope_theta) + self.rotary_emb = RotaryEmbedding( + dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta, + ) elif self.config.pos_encodings == "learned": - self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.embed_pos = CastedEmbedding( + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) else: pass # Reasoning Layers - self.H_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.H_layers)]) - self.L_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + self.H_level = HierarchicalReasoningModel_ACTV1ReasoningModule( + layers=[ + HierarchicalReasoningModel_ACTV1Block(self.config) + for _i in range(self.config.H_layers) + ] + ) + self.L_level = HierarchicalReasoningModel_ACTV1ReasoningModule( + layers=[ + HierarchicalReasoningModel_ACTV1Block(self.config) + for _i in range(self.config.L_layers) + ] + ) # Initial states - self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) - self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.H_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) # Q head special init # Init Q to (almost) zero for faster learning during bootstrapping @@ -165,34 +219,58 @@ def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tenso # Puzzle embeddings if self.config.puzzle_emb_ndim > 0: puzzle_embedding = self.puzzle_emb(puzzle_identifiers) - + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] if pad_count > 0: puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) - embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + embedding = torch.cat( + ( + puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), + embedding, + ), + dim=-2, + ) # Position embeddings if self.config.pos_encodings == "learned": # scale by 1/sqrt(2) to maintain forward variance - embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + embedding = 0.707106781 * ( + embedding + self.embed_pos.embedding_weight.to(self.forward_dtype) + ) # Scale return self.embed_scale * embedding def empty_carry(self, batch_size: int): return HierarchicalReasoningModel_ACTV1InnerCarry( - z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), - z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_H=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), ) - - def reset_carry(self, reset_flag: torch.Tensor, carry: HierarchicalReasoningModel_ACTV1InnerCarry): + + def reset_carry( + self, reset_flag: torch.Tensor, carry: HierarchicalReasoningModel_ACTV1InnerCarry + ): return HierarchicalReasoningModel_ACTV1InnerCarry( z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), ) - def forward(self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + def forward( + self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor] + ) -> Tuple[ + HierarchicalReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor] + ]: seq_info = dict( cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, ) @@ -205,7 +283,10 @@ def forward(self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict z_H, z_L = carry.z_H, carry.z_L for _H_step in range(self.config.H_cycles): for _L_step in range(self.config.L_cycles): - if not ((_H_step == self.config.H_cycles - 1) and (_L_step == self.config.L_cycles - 1)): + if not ( + (_H_step == self.config.H_cycles - 1) + and (_L_step == self.config.L_cycles - 1) + ): z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) if not (_H_step == self.config.H_cycles - 1): z_H = self.H_level(z_H, z_L, **seq_info) @@ -215,12 +296,14 @@ def forward(self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict z_H = self.H_level(z_H, z_L, **seq_info) # LM Outputs - new_carry = HierarchicalReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) # New carry no grad - output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + new_carry = HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=z_H.detach(), z_L=z_L.detach() + ) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len :] # Q head q_logits = self.q_head(z_H[:, 0]).to(torch.float32) - + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) @@ -240,36 +323,43 @@ def initial_carry(self, batch: Dict[str, torch.Tensor]): batch_size = batch["inputs"].shape[0] return HierarchicalReasoningModel_ACTV1Carry( - inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. - - steps=torch.zeros((batch_size, ), dtype=torch.int32), - halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted - - current_data={k: torch.empty_like(v) for k, v in batch.items()} + inner_carry=self.inner.empty_carry( + batch_size + ), # Empty is expected, it will be reseted in first pass as all sequences are halted. + steps=torch.zeros((batch_size,), dtype=torch.int32), + halted=torch.ones((batch_size,), dtype=torch.bool), # Default to halted + current_data={k: torch.empty_like(v) for k, v in batch.items()}, ) - - def forward(self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + def forward( + self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor] + ) -> Tuple[HierarchicalReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: # Update data, carry (removing halted sequences) new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) - + new_steps = torch.where(carry.halted, 0, carry.steps) - new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + new_current_data = { + k: torch.where(carry.halted.view((-1,) + (1,) * (batch[k].ndim - 1)), batch[k], v) + for k, v in carry.current_data.items() + } # Forward inner model - new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner( + new_inner_carry, new_current_data + ) outputs = { "logits": logits, "q_halt_logits": q_halt_logits, - "q_continue_logits": q_continue_logits + "q_continue_logits": q_continue_logits, } - + with torch.no_grad(): # Step new_steps = new_steps + 1 is_last_step = new_steps >= self.config.halt_max_steps - + halted = is_last_step # if training, and ACT is enabled @@ -279,7 +369,9 @@ def forward(self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, halted = halted | (q_halt_logits > q_continue_logits) # Exploration - min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + min_halt_steps = ( + torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob + ) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) halted = halted & (new_steps >= min_halt_steps) @@ -287,8 +379,21 @@ def forward(self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, # NOTE: No replay buffer and target networks for computing target Q-value. # As batch_size is large, there're many parallel envs. # Similar concept as PQN https://arxiv.org/abs/2407.04811 - next_q_halt_logits, next_q_continue_logits = self.inner(new_inner_carry, new_current_data)[-1] - - outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) - - return HierarchicalReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs + next_q_halt_logits, next_q_continue_logits = self.inner( + new_inner_carry, new_current_data + )[-1] + + outputs["target_q_continue"] = torch.sigmoid( + torch.where( + is_last_step, + next_q_halt_logits, + torch.maximum(next_q_halt_logits, next_q_continue_logits), + ) + ) + + return ( + HierarchicalReasoningModel_ACTV1Carry( + new_inner_carry, new_steps, halted, new_current_data + ), + outputs, + ) diff --git a/models/recursive_reasoning/transformers_baseline.py b/src/recursion/models/recursive_reasoning/transformers_baseline.py similarity index 88% rename from models/recursive_reasoning/transformers_baseline.py rename to src/recursion/models/recursive_reasoning/transformers_baseline.py index 7a08acca..ddbd2e56 100644 --- a/models/recursive_reasoning/transformers_baseline.py +++ b/src/recursion/models/recursive_reasoning/transformers_baseline.py @@ -13,18 +13,26 @@ """ -from typing import Tuple, List, Dict, Optional -from dataclasses import dataclass import math +from dataclasses import dataclass +from typing import Dict, List, Tuple import torch import torch.nn.functional as F -from torch import nn from pydantic import BaseModel +from torch import nn -from models.common import trunc_normal_init_ -from models.layers import rms_norm, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear -from models.sparse_embedding import CastedSparseEmbedding +from recursion.models.common import trunc_normal_init_ +from recursion.models.layers import ( + Attention, + CastedEmbedding, + CastedLinear, + CosSin, + RotaryEmbedding, + SwiGLU, + rms_norm, +) +from recursion.models.sparse_embedding import CastedSparseEmbedding @dataclass @@ -65,7 +73,9 @@ class Model_ACTV2Config(BaseModel): # Halting Q-learning config halt_max_steps: int halt_exploration_prob: float - act_enabled: bool = True # If False, always run halt_max_steps (no early stopping during training) + act_enabled: bool = ( + True # If False, always run halt_max_steps (no early stopping during training) + ) act_inference: bool = False # If True, use adaptive computation during inference forward_dtype: str = "bfloat16" @@ -96,7 +106,9 @@ def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: variance_epsilon=self.norm_eps, ) # Fully Connected - hidden_states = rms_norm(hidden_states + self.mlp(hidden_states), variance_epsilon=self.norm_eps) + hidden_states = rms_norm( + hidden_states + self.mlp(hidden_states), variance_epsilon=self.norm_eps + ) return hidden_states @@ -106,7 +118,9 @@ def __init__(self, layers: List[Model_ACTV2Block]): self.layers = torch.nn.ModuleList(layers) - def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + def forward( + self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs + ) -> torch.Tensor: # Input injection (add) hidden_states = hidden_states + input_injection # Layers @@ -170,7 +184,9 @@ def __init__(self, config: Model_ACTV2Config) -> None: # Initial states self.H_init = nn.Buffer( - trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), persistent=True, ) @@ -193,13 +209,19 @@ def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tenso puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) embedding = torch.cat( - (puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2 + ( + puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), + embedding, + ), + dim=-2, ) # Position embeddings if self.config.pos_encodings == "learned": # scale by 1/sqrt(2) to maintain forward variance - embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + embedding = 0.707106781 * ( + embedding + self.embed_pos.embedding_weight.to(self.forward_dtype) + ) # Scale return self.embed_scale * embedding @@ -289,7 +311,11 @@ def forward( new_inner_carry, new_current_data ) - outputs = {"logits": logits, "q_halt_logits": q_halt_logits, "q_continue_logits": q_continue_logits} + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits, + } with torch.no_grad(): # Step @@ -337,6 +363,4 @@ def forward( ) ) - return Model_ACTV2Carry( - new_inner_carry, new_steps, halted, new_current_data - ), outputs + return Model_ACTV2Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/src/recursion/models/recursive_reasoning/trm.py b/src/recursion/models/recursive_reasoning/trm.py new file mode 100644 index 00000000..34372bb4 --- /dev/null +++ b/src/recursion/models/recursive_reasoning/trm.py @@ -0,0 +1,378 @@ +import math +from dataclasses import dataclass +from typing import Dict, List, Tuple + +import torch +import torch.nn.functional as F +from pydantic import BaseModel +from torch import nn + +from recursion.models.common import trunc_normal_init_ +from recursion.models.layers import ( + Attention, + CastedEmbedding, + CastedLinear, + CosSin, + RotaryEmbedding, + SwiGLU, + rms_norm, +) +from recursion.models.sparse_embedding import CastedSparseEmbedding + +IGNORE_LABEL_ID = -100 + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L: torch.Tensor + memories_wrt: list[torch.Tensor] + memories: list[torch.Tensor] + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1Carry: + inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int # ignored + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + # Alexia: added + mlp_t: bool = False # use mlp on L instead of transformer + puzzle_emb_len: int = 16 # if non-zero, its specified to this value + no_ACT_continue: bool = ( + True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + ) + + +class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.config = config + if self.config.mlp_t: + self.puzzle_emb_len = ( + -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + if self.config.puzzle_emb_len == 0 + else self.config.puzzle_emb_len + ) + self.mlp_t = SwiGLU( + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + expansion=config.expansion, + ) + else: + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False, + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # B, L, D = hidden_states.shape + # Post Norm + if self.config.mlp_t: + hidden_states = hidden_states.transpose(1, 2) + out = self.mlp_t(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + hidden_states = hidden_states.transpose(1, 2) + else: + # Self Attention + hidden_states = rms_norm( + hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), + variance_epsilon=self.norm_eps, + ) + # Fully Connected + out = self.mlp(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): + super().__init__() + self.layers = torch.nn.ModuleList(layers) + + def forward( + self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs + ) -> torch.Tensor: + hidden_states = hidden_states + input_injection + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding( + self.config.vocab_size, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = ( + -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + if self.config.puzzle_emb_len == 0 + else self.config.puzzle_emb_len + ) # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding( + self.config.num_puzzle_identifiers, + self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, + init_std=0, + cast_to=self.forward_dtype, + ) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding( + dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta, + ) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding( + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + else: + pass + + # Reasoning Layers + self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule( + layers=[ + TinyRecursiveReasoningModel_ACTV1Block(self.config) + for _i in range(self.config.L_layers) + ] + ) + + # Initial states + self.H_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat( + ( + puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), + embedding, + ), + dim=-2, + ) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * ( + embedding + self.embed_pos.embedding_weight.to(self.forward_dtype) + ) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ).requires_grad_(True), + z_L=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + memories_wrt=[], + memories=[], + ) + + def reset_carry( + self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + ): + if torch.any(reset_flag): + memories_wrt = [] + memories = [] + else: + memories_wrt = carry.memories_wrt + memories = carry.memories + + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + memories_wrt=memories_wrt, + memories=memories, + ) + + def forward( + self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor] + ) -> Tuple[ + TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor] + ]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + # shape: [batch_size, 97, 512] (97 tokens of dim 512) + + # Forward iterations + z_H, z_L = carry.z_H, carry.z_L + z_H = self.L_level(z_L, z_H + input_embeddings, **seq_info) + + # LM Outputs + next_z_H = z_H.detach().requires_grad_(True) + new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=next_z_H, + z_L=z_L.detach(), # TODO: osef + memories_wrt=carry.memories_wrt + [carry.z_H], + memories=carry.memories + [z_H], + ) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len :] + q_logits = self.q_head(z_H[:, 0]).to( + torch.float32 + ) # Q-head; uses the first puzzle_emb position + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class TinyRecursiveReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) + self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return TinyRecursiveReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry( + batch_size + ), # Empty is expected, it will be reseted in first pass as all sequences are halted. + steps=torch.zeros((batch_size,), dtype=torch.int32), + halted=torch.ones((batch_size,), dtype=torch.bool), # Default to halted + current_data={k: torch.empty_like(v) for k, v in batch.items()}, + ) + + def forward( + self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor] + ) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = { + k: torch.where(carry.halted.view((-1,) + (1,) * (batch[k].ndim - 1)), batch[k], v) + for k, v in carry.current_data.items() + } + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner( + new_inner_carry, new_current_data + ) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits, + } + + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + halted = is_last_step + + return ( + TinyRecursiveReasoningModel_ACTV1Carry( + new_inner_carry, new_steps, halted, new_current_data + ), + outputs, + ) diff --git a/src/recursion/models/recursive_reasoning/trm_hier6.py b/src/recursion/models/recursive_reasoning/trm_hier6.py new file mode 100644 index 00000000..48a56b17 --- /dev/null +++ b/src/recursion/models/recursive_reasoning/trm_hier6.py @@ -0,0 +1,491 @@ +import math +from dataclasses import dataclass +from typing import Dict, List, Tuple + +import torch +import torch.nn.functional as F +from pydantic import BaseModel +from torch import nn + +from recursion.models.common import trunc_normal_init_ +from recursion.models.layers import ( + Attention, + CastedEmbedding, + CastedLinear, + CosSin, + RotaryEmbedding, + SwiGLU, + rms_norm, +) +from recursion.models.sparse_embedding import CastedSparseEmbedding + +IGNORE_LABEL_ID = -100 + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L1: torch.Tensor + z_L2: torch.Tensor + z_L3: torch.Tensor + z_L4: torch.Tensor + z_L5: torch.Tensor + z_L6: torch.Tensor + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1Carry: + inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int # ignored + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + # Alexia: added + mlp_t: bool = False # use mlp on L instead of transformer + puzzle_emb_len: int = 16 # if non-zero, its specified to this value + no_ACT_continue: bool = ( + True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + ) + + +class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.config = config + if self.config.mlp_t: + self.puzzle_emb_len = ( + -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + if self.config.puzzle_emb_len == 0 + else self.config.puzzle_emb_len + ) + self.mlp_t = SwiGLU( + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + expansion=config.expansion, + ) + else: + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False, + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # B, L, D = hidden_states.shape + # Post Norm + if self.config.mlp_t: + hidden_states = hidden_states.transpose(1, 2) + out = self.mlp_t(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + hidden_states = hidden_states.transpose(1, 2) + else: + # Self Attention + hidden_states = rms_norm( + hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), + variance_epsilon=self.norm_eps, + ) + # Fully Connected + out = self.mlp(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): + super().__init__() + self.layers = torch.nn.ModuleList(layers) + + def forward( + self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs + ) -> torch.Tensor: + hidden_states = hidden_states + input_injection + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding( + self.config.vocab_size, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = ( + -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + if self.config.puzzle_emb_len == 0 + else self.config.puzzle_emb_len + ) # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding( + self.config.num_puzzle_identifiers, + self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, + init_std=0, + cast_to=self.forward_dtype, + ) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding( + dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta, + ) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding( + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + else: + pass + + # Reasoning Layers + self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule( + layers=[ + TinyRecursiveReasoningModel_ACTV1Block(self.config) + for _i in range(self.config.L_layers) + ] + ) + + # Initial states + self.H_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L1_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L2_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L3_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L4_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L5_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + self.L6_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat( + ( + puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), + embedding, + ), + dim=-2, + ) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * ( + embedding + self.embed_pos.embedding_weight.to(self.forward_dtype) + ) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L1=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L2=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L3=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L4=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L5=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + z_L6=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + ) + + def reset_carry( + self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + ): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L1=torch.where(reset_flag.view(-1, 1, 1), self.L1_init, carry.z_L1), + z_L2=torch.where(reset_flag.view(-1, 1, 1), self.L2_init, carry.z_L2), + z_L3=torch.where(reset_flag.view(-1, 1, 1), self.L3_init, carry.z_L3), + z_L4=torch.where(reset_flag.view(-1, 1, 1), self.L4_init, carry.z_L4), + z_L5=torch.where(reset_flag.view(-1, 1, 1), self.L5_init, carry.z_L5), + z_L6=torch.where(reset_flag.view(-1, 1, 1), self.L6_init, carry.z_L6), + ) + + def forward( + self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor] + ) -> Tuple[ + TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor] + ]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + z_H, z_L = carry.z_H, [ + carry.z_L1, + carry.z_L2, + carry.z_L3, + carry.z_L4, + carry.z_L5, + carry.z_L6, + ] + # H_cycles-1 without grad + with torch.no_grad(): + for _H_step in range(self.config.H_cycles - 1): + for _L_step in range(self.config.L_cycles): + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_L[_L_step] = self.L_level(z_L_, z_H + input_embeddings, **seq_info) + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_H = self.L_level(z_H, z_L_, **seq_info) + # 1 with grad + for _L_step in range(self.config.L_cycles): + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_L[_L_step] = self.L_level(z_L_, z_H + input_embeddings, **seq_info) + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_H = self.L_level(z_H, z_L_, **seq_info) + + # LM Outputs + new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=z_H.detach(), + z_L1=z_L[0].detach(), + z_L2=z_L[1].detach(), + z_L3=z_L[2].detach(), + z_L4=z_L[3].detach(), + z_L5=z_L[4].detach(), + z_L6=z_L[5].detach(), + ) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len :] + q_logits = self.q_head(z_H[:, 0]).to( + torch.float32 + ) # Q-head; uses the first puzzle_emb position + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class TinyRecursiveReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) + self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return TinyRecursiveReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry( + batch_size + ), # Empty is expected, it will be reseted in first pass as all sequences are halted. + steps=torch.zeros((batch_size,), dtype=torch.int32), + halted=torch.ones((batch_size,), dtype=torch.bool), # Default to halted + current_data={k: torch.empty_like(v) for k, v in batch.items()}, + ) + + def forward( + self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor] + ) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = { + k: torch.where(carry.halted.view((-1,) + (1,) * (batch[k].ndim - 1)), batch[k], v) + for k, v in carry.current_data.items() + } + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner( + new_inner_carry, new_current_data + ) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits, + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + + if self.config.no_ACT_continue: + halted = halted | (q_halt_logits > 0) + else: + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = ( + torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob + ) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + halted = halted & (new_steps >= min_halt_steps) + + if not self.config.no_ACT_continue: + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner( + new_inner_carry, new_current_data + ) + outputs["target_q_continue"] = torch.sigmoid( + torch.where( + is_last_step, + next_q_halt_logits, + torch.maximum(next_q_halt_logits, next_q_continue_logits), + ) + ) + + return ( + TinyRecursiveReasoningModel_ACTV1Carry( + new_inner_carry, new_steps, halted, new_current_data + ), + outputs, + ) diff --git a/models/recursive_reasoning/trm_singlez.py b/src/recursion/models/recursive_reasoning/trm_singlez.py similarity index 57% rename from models/recursive_reasoning/trm_singlez.py rename to src/recursion/models/recursive_reasoning/trm_singlez.py index e5e1a7d3..f3f26330 100644 --- a/models/recursive_reasoning/trm_singlez.py +++ b/src/recursion/models/recursive_reasoning/trm_singlez.py @@ -1,31 +1,39 @@ -from typing import Tuple, List, Dict, Optional -from dataclasses import dataclass import math +from dataclasses import dataclass +from typing import Dict, List, Tuple + import torch -import copy import torch.nn.functional as F -from torch import nn from pydantic import BaseModel -import random -from models.common import trunc_normal_init_ -from models.layers import rms_norm, LinearSwish, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear -from models.sparse_embedding import CastedSparseEmbedding +from torch import nn + +from recursion.models.common import trunc_normal_init_ +from recursion.models.layers import ( + Attention, + CastedEmbedding, + CastedLinear, + CosSin, + RotaryEmbedding, + SwiGLU, + rms_norm, +) +from recursion.models.sparse_embedding import CastedSparseEmbedding IGNORE_LABEL_ID = -100 + @dataclass class TinyRecursiveReasoningModel_ACTV1InnerCarry: z_L: torch.Tensor - @dataclass class TinyRecursiveReasoningModel_ACTV1Carry: inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry - + steps: torch.Tensor halted: torch.Tensor - + current_data: Dict[str, torch.Tensor] @@ -39,7 +47,7 @@ class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): H_cycles: int L_cycles: int - H_layers: int # ignored + H_layers: int # ignored L_layers: int # Transformer config @@ -50,7 +58,7 @@ class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): rms_norm_eps: float = 1e-5 rope_theta: float = 10000.0 - + # Halting Q-learning config halt_max_steps: int halt_exploration_prob: float @@ -58,9 +66,12 @@ class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): forward_dtype: str = "bfloat16" # Alexia: added - mlp_t: bool = False # use mlp on L instead of transformer - puzzle_emb_len: int = 16 # if non-zero, its specified to this value - no_ACT_continue: bool = True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + mlp_t: bool = False # use mlp on L instead of transformer + puzzle_emb_len: int = 16 # if non-zero, its specified to this value + no_ACT_continue: bool = ( + True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + ) + class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: @@ -68,9 +79,13 @@ def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: self.config = config if self.config.mlp_t: - self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len + self.puzzle_emb_len = ( + -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + if self.config.puzzle_emb_len == 0 + else self.config.puzzle_emb_len + ) self.mlp_t = SwiGLU( - hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L expansion=config.expansion, ) else: @@ -79,7 +94,7 @@ def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: head_dim=config.hidden_size // config.num_heads, num_heads=config.num_heads, num_key_value_heads=config.num_heads, - causal=False + causal=False, ) self.mlp = SwiGLU( hidden_size=config.hidden_size, @@ -91,18 +106,22 @@ def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: # B, L, D = hidden_states.shape # Post Norm if self.config.mlp_t: - hidden_states = hidden_states.transpose(1,2) + hidden_states = hidden_states.transpose(1, 2) out = self.mlp_t(hidden_states) hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) - hidden_states = hidden_states.transpose(1,2) + hidden_states = hidden_states.transpose(1, 2) else: # Self Attention - hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + hidden_states = rms_norm( + hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), + variance_epsilon=self.norm_eps, + ) # Fully Connected out = self.mlp(hidden_states) hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) return hidden_states + class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): super().__init__() @@ -125,31 +144,62 @@ def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: self.embed_scale = math.sqrt(self.config.hidden_size) embed_init_std = 1.0 / self.embed_scale - self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) - self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) - self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) - - self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len # ceil div + self.embed_tokens = CastedEmbedding( + self.config.vocab_size, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = ( + -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + if self.config.puzzle_emb_len == 0 + else self.config.puzzle_emb_len + ) # ceil div if self.config.puzzle_emb_ndim > 0: # Zero init puzzle embeddings - self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, - batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + self.puzzle_emb = CastedSparseEmbedding( + self.config.num_puzzle_identifiers, + self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, + init_std=0, + cast_to=self.forward_dtype, + ) # LM Blocks if self.config.pos_encodings == "rope": - self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, - max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, - base=self.config.rope_theta) + self.rotary_emb = RotaryEmbedding( + dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta, + ) elif self.config.pos_encodings == "learned": - self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.embed_pos = CastedEmbedding( + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) else: pass # Reasoning Layers - self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule(layers=[TinyRecursiveReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule( + layers=[ + TinyRecursiveReasoningModel_ACTV1Block(self.config) + for _i in range(self.config.L_layers) + ] + ) # Initial states - self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L_init = nn.Buffer( + trunc_normal_init_( + torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1 + ), + persistent=True, + ) # Q head special init # Init Q to (almost) zero for faster learning during bootstrapping @@ -164,32 +214,51 @@ def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tenso # Puzzle embeddings if self.config.puzzle_emb_ndim > 0: puzzle_embedding = self.puzzle_emb(puzzle_identifiers) - + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] if pad_count > 0: puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) - embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + embedding = torch.cat( + ( + puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), + embedding, + ), + dim=-2, + ) # Position embeddings if self.config.pos_encodings == "learned": # scale by 1/sqrt(2) to maintain forward variance - embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + embedding = 0.707106781 * ( + embedding + self.embed_pos.embedding_weight.to(self.forward_dtype) + ) # Scale return self.embed_scale * embedding def empty_carry(self, batch_size: int): return TinyRecursiveReasoningModel_ACTV1InnerCarry( - z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), ) - - def reset_carry(self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry): + + def reset_carry( + self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + ): return TinyRecursiveReasoningModel_ACTV1InnerCarry( z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), ) - def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + def forward( + self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor] + ) -> Tuple[ + TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor] + ]: seq_info = dict( cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, ) @@ -198,11 +267,10 @@ def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dic input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) # Forward iterations - it = 0 z_L = carry.z_L # H_cycles-1 without grad with torch.no_grad(): - for _H_step in range(self.config.H_cycles-1): + for _H_step in range(self.config.H_cycles - 1): for _L_step in range(self.config.L_cycles): z_L = self.L_level(z_L + input_embeddings, **seq_info) z_L = self.L_level(z_L, **seq_info) @@ -213,9 +281,13 @@ def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dic z_out = z_L # LM Outputs - new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry(z_L=z_L.detach()) # New carry no grad - output = self.lm_head(z_out)[:, self.puzzle_emb_len:] - q_logits = self.q_head(z_out[:, 0]).to(torch.float32) # Q-head; uses the first puzzle_emb position + new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_L=z_L.detach() + ) # New carry no grad + output = self.lm_head(z_out)[:, self.puzzle_emb_len :] + q_logits = self.q_head(z_out[:, 0]).to( + torch.float32 + ) # Q-head; uses the first puzzle_emb position return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) @@ -235,37 +307,44 @@ def initial_carry(self, batch: Dict[str, torch.Tensor]): batch_size = batch["inputs"].shape[0] return TinyRecursiveReasoningModel_ACTV1Carry( - inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. - - steps=torch.zeros((batch_size, ), dtype=torch.int32), - halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted - - current_data={k: torch.empty_like(v) for k, v in batch.items()} + inner_carry=self.inner.empty_carry( + batch_size + ), # Empty is expected, it will be reseted in first pass as all sequences are halted. + steps=torch.zeros((batch_size,), dtype=torch.int32), + halted=torch.ones((batch_size,), dtype=torch.bool), # Default to halted + current_data={k: torch.empty_like(v) for k, v in batch.items()}, ) - - def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + def forward( + self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor] + ) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: # Update data, carry (removing halted sequences) new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) - + new_steps = torch.where(carry.halted, 0, carry.steps) - new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + new_current_data = { + k: torch.where(carry.halted.view((-1,) + (1,) * (batch[k].ndim - 1)), batch[k], v) + for k, v in carry.current_data.items() + } # Forward inner model - new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner( + new_inner_carry, new_current_data + ) outputs = { "logits": logits, "q_halt_logits": q_halt_logits, - "q_continue_logits": q_continue_logits + "q_continue_logits": q_continue_logits, } with torch.no_grad(): # Step new_steps = new_steps + 1 is_last_step = new_steps >= self.config.halt_max_steps - + halted = is_last_step # if training, and ACT is enabled @@ -273,14 +352,16 @@ def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str # Halt signal # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes - + if self.config.no_ACT_continue: halted = halted | (q_halt_logits > 0) else: halted = halted | (q_halt_logits > q_continue_logits) # Exploration - min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + min_halt_steps = ( + torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob + ) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) halted = halted & (new_steps >= min_halt_steps) if not self.config.no_ACT_continue: @@ -288,7 +369,20 @@ def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str # NOTE: No replay buffer and target networks for computing target Q-value. # As batch_size is large, there're many parallel envs. # Similar concept as PQN https://arxiv.org/abs/2407.04811 - _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner(new_inner_carry, new_current_data) - outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) - - return TinyRecursiveReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs + _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner( + new_inner_carry, new_current_data + ) + outputs["target_q_continue"] = torch.sigmoid( + torch.where( + is_last_step, + next_q_halt_logits, + torch.maximum(next_q_halt_logits, next_q_continue_logits), + ) + ) + + return ( + TinyRecursiveReasoningModel_ACTV1Carry( + new_inner_carry, new_steps, halted, new_current_data + ), + outputs, + ) diff --git a/models/sparse_embedding.py b/src/recursion/models/sparse_embedding.py similarity index 76% rename from models/sparse_embedding.py rename to src/recursion/models/sparse_embedding.py index f369205e..8028d15a 100644 --- a/models/sparse_embedding.py +++ b/src/recursion/models/sparse_embedding.py @@ -1,27 +1,37 @@ from typing import Union import torch -from torch import nn import torch.distributed as dist +from torch import nn from torch.optim.optimizer import Optimizer, ParamsT -from models.common import trunc_normal_init_ +from recursion.models.common import trunc_normal_init_ class CastedSparseEmbedding(nn.Module): - def __init__(self, num_embeddings: int, embedding_dim: int, batch_size: int, init_std: float, cast_to: torch.dtype): + def __init__( + self, + num_embeddings: int, + embedding_dim: int, + batch_size: int, + init_std: float, + cast_to: torch.dtype, + ): super().__init__() self.cast_to = cast_to # Real Weights # Truncated LeCun normal init self.weights = nn.Buffer( - trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std), persistent=True + trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std), + persistent=True, ) # Local weights and IDs # Local embeddings, with gradient, not persistent - self.local_weights = nn.Buffer(torch.zeros(batch_size, embedding_dim, requires_grad=True), persistent=False) + self.local_weights = nn.Buffer( + torch.zeros(batch_size, embedding_dim, requires_grad=True), persistent=False + ) # Local embedding IDs, not persistent self.local_ids = nn.Buffer(torch.zeros(batch_size, dtype=torch.int32), persistent=False) @@ -29,7 +39,7 @@ def forward(self, inputs: torch.Tensor) -> torch.Tensor: if not self.training: # Test mode, no gradient return self.weights[inputs].to(self.cast_to) - + # Training mode, fill puzzle embedding from weights with torch.no_grad(): self.local_weights.copy_(self.weights[inputs]) @@ -42,7 +52,6 @@ class CastedSparseEmbeddingSignSGD_Distributed(Optimizer): def __init__( self, params: ParamsT, - world_size: int, lr: Union[float, torch.Tensor] = 1e-3, weight_decay: float = 1e-2, @@ -52,11 +61,7 @@ def __init__( if not 0.0 <= weight_decay: raise ValueError(f"Invalid weight_decay value: {weight_decay}") - defaults = dict( - lr=lr, - weight_decay=weight_decay, - world_size=world_size - ) + defaults = dict(lr=lr, weight_decay=weight_decay, world_size=world_size) super().__init__(params, defaults) @torch.no_grad @@ -66,7 +71,7 @@ def step(self, closure=None): # type: ignore local_weights_grad = None local_ids = None weights = None - + assert len(group["params"]) == 3 for p in group["params"]: if p.requires_grad: @@ -77,10 +82,10 @@ def step(self, closure=None): # type: ignore weights = p else: assert False - + assert local_ids is not None assert weights is not None - + # Apply SignSGD # Adam ≈ SignSGD if gradient is very sparse if local_weights_grad is not None: @@ -88,10 +93,9 @@ def step(self, closure=None): # type: ignore local_weights_grad, local_ids, weights, - lr=group["lr"], weight_decay=group["weight_decay"], - world_size=group["world_size"] + world_size=group["world_size"], ) @@ -99,28 +103,31 @@ def _sparse_emb_signsgd_dist( local_weights_grad: torch.Tensor, local_ids: torch.Tensor, weights: torch.Tensor, - lr: float, weight_decay: float, - world_size: int + world_size: int, ) -> None: N, D = local_weights_grad.shape - + # All-gather all_weights_grad = local_weights_grad all_ids = local_ids if world_size > 1: - all_weights_grad = torch.empty((world_size * N, D), dtype=local_weights_grad.dtype, device=local_weights_grad.device) - all_ids = torch.empty(world_size * N, dtype=local_ids.dtype, device=local_ids.device) - + all_weights_grad = torch.empty( + (world_size * N, D), dtype=local_weights_grad.dtype, device=local_weights_grad.device + ) + all_ids = torch.empty(world_size * N, dtype=local_ids.dtype, device=local_ids.device) + dist.all_gather_into_tensor(all_weights_grad, local_weights_grad) - dist.all_gather_into_tensor(all_ids, local_ids) + dist.all_gather_into_tensor(all_ids, local_ids) # Unique grad_ids, inv = all_ids.unique(return_inverse=True) - grad = torch.zeros((grad_ids.shape[0], D), dtype=all_weights_grad.dtype, device=all_weights_grad.device) + grad = torch.zeros( + (grad_ids.shape[0], D), dtype=all_weights_grad.dtype, device=all_weights_grad.device + ) grad.scatter_add_(0, inv.unsqueeze(-1).expand(-1, D), all_weights_grad) # SignSGD with decoupled weight decay diff --git a/pretrain.py b/src/recursion/pretrain.py similarity index 63% rename from pretrain.py rename to src/recursion/pretrain.py index b9072e25..0be1eb8f 100644 --- a/pretrain.py +++ b/src/recursion/pretrain.py @@ -1,37 +1,69 @@ -from typing import Optional, Any, Sequence, List -from dataclasses import dataclass -import os +import copy import math -import yaml +import os import shutil -import copy +from collections import defaultdict +from dataclasses import dataclass +from typing import Any, List, Optional, Sequence +import coolname +import hydra +import pydantic import torch import torch.distributed as dist +import tqdm +import yaml +from adam_atan2_pytorch import AdamAtan2 +from omegaconf import DictConfig from torch import nn +from torch.nn.functional import cosine_similarity from torch.utils.data import DataLoader +from torchjd.aggregation import UPGrad +from torchjd.autojac._transform import Accumulate, Aggregate, OrderedSet -import tqdm import wandb -import coolname -import hydra -import pydantic -from omegaconf import DictConfig -from adam_atan2 import AdamATan2 +from recursion.models.ema import EMAHelper +from recursion.models.sparse_embedding import CastedSparseEmbeddingSignSGD_Distributed +from recursion.puzzle_dataset import PuzzleDataset, PuzzleDatasetConfig, PuzzleDatasetMetadata +from recursion.utils.functions import get_model_source_path, load_model_class + +global_step = 0 + + +def print_gramian(_, inputs, __): + if not dist.is_initialized() or dist.get_rank() == 0: + # print(inputs[0]) + diag = torch.diag(inputs[0]).sqrt() + outer = diag.unsqueeze(0) * diag.unsqueeze(1) + scaled_gramian = inputs[0].clone() / outer + + wandb.log( + { + "gramian_min": inputs[0].min(), + "gramian_mean": inputs[0].mean(), + "gramian_median": inputs[0].median(), + "min_gramian_scaled": scaled_gramian.min(), + }, + step=global_step, + ) -from puzzle_dataset import PuzzleDataset, PuzzleDatasetConfig, PuzzleDatasetMetadata -from utils.functions import load_model_class, get_model_source_path -from models.sparse_embedding import CastedSparseEmbeddingSignSGD_Distributed -from models.ema import EMAHelper + +def log_gd_similarity(_, inputs: tuple[torch.Tensor, ...], aggregation: torch.Tensor) -> None: + """Prints the cosine similarity between the aggregation and the average gradient.""" + if not dist.is_initialized() or dist.get_rank() == 0: + matrix = inputs[0] + gd_output = matrix.mean(dim=0) + similarity = cosine_similarity(aggregation, gd_output, dim=0) + wandb.log({"gd_similarity": similarity.item()}, step=global_step) class LossConfig(pydantic.BaseModel): - model_config = pydantic.ConfigDict(extra='allow') + model_config = pydantic.ConfigDict(extra="allow") name: str class ArchConfig(pydantic.BaseModel): - model_config = pydantic.ConfigDict(extra='allow') + model_config = pydantic.ConfigDict(extra="allow") name: str loss: LossConfig @@ -76,12 +108,13 @@ class PretrainConfig(pydantic.BaseModel): seed: int = 0 checkpoint_every_eval: bool = False eval_interval: Optional[int] = None - min_eval_interval: Optional[int] = 0 # when to start eval + min_eval_interval: Optional[int] = 0 # when to start eval eval_save_outputs: List[str] = [] - ema: bool = False # use Exponential-Moving-Average - ema_rate: float = 0.999 # EMA-rate - freeze_weights: bool = False # If True, freeze weights and only learn the embeddings + ema: bool = False # use Exponential-Moving-Average + ema_rate: float = 0.999 # EMA-rate + freeze_weights: bool = False # If True, freeze weights and only learn the embeddings + @dataclass class TrainState: @@ -95,32 +128,41 @@ class TrainState: def create_dataloader(config: PretrainConfig, split: str, rank: int, world_size: int, **kwargs): - dataset = PuzzleDataset(PuzzleDatasetConfig( - seed=config.seed, - dataset_paths=config.data_paths_test if len(config.data_paths_test)>0 and split=="test" else config.data_paths, - rank=rank, - num_replicas=world_size, - **kwargs - ), split=split) + dataset = PuzzleDataset( + PuzzleDatasetConfig( + seed=config.seed, + dataset_paths=( + config.data_paths_test + if len(config.data_paths_test) > 0 and split == "test" + else config.data_paths + ), + rank=rank, + num_replicas=world_size, + **kwargs, + ), + split=split, + ) dataloader = DataLoader( dataset, batch_size=None, num_workers=1, prefetch_factor=8, pin_memory=True, - persistent_workers=True + persistent_workers=True, ) return dataloader, dataset.metadata -def create_model(config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, rank: int, world_size: int): +def create_model( + config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, rank: int, world_size: int +): model_cfg = dict( **config.arch.__pydantic_extra__, # type: ignore batch_size=config.global_batch_size // world_size, vocab_size=train_metadata.vocab_size, seq_len=train_metadata.seq_len, num_puzzle_identifiers=train_metadata.num_puzzle_identifiers, - causal=False # Non-autoregressive + causal=False, # Non-autoregressive ) # Instantiate model with loss head @@ -147,88 +189,105 @@ def create_model(config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, # Optimizers and lr if config.arch.puzzle_emb_ndim == 0: optimizers = [ - AdamATan2( + AdamAtan2( model.parameters(), - lr=0, # Needs to be set by scheduler + lr=0.0001, # Needs to be set by scheduler weight_decay=config.weight_decay, - betas=(config.beta1, config.beta2) + betas=(config.beta1, config.beta2), ) ] - optimizer_lrs = [ - config.lr - ] + optimizer_lrs = [config.lr] elif config.freeze_weights: optimizers = [ CastedSparseEmbeddingSignSGD_Distributed( model.model.puzzle_emb.buffers(), # type: ignore - lr=0, # Needs to be set by scheduler + lr=0.0001, # Needs to be set by scheduler weight_decay=config.puzzle_emb_weight_decay, - world_size=world_size + world_size=world_size, ) ] - optimizer_lrs = [ - config.puzzle_emb_lr - ] + optimizer_lrs = [config.puzzle_emb_lr] else: optimizers = [ CastedSparseEmbeddingSignSGD_Distributed( model.model.puzzle_emb.buffers(), # type: ignore - lr=0, # Needs to be set by scheduler + lr=0.0001, # Needs to be set by scheduler weight_decay=config.puzzle_emb_weight_decay, - world_size=world_size + world_size=world_size, ), - AdamATan2( + AdamAtan2( model.parameters(), - lr=0, # Needs to be set by scheduler + lr=0.0001, # Needs to be set by scheduler weight_decay=config.weight_decay, - betas=(config.beta1, config.beta2) - ) - ] - optimizer_lrs = [ - config.puzzle_emb_lr, - config.lr + betas=(config.beta1, config.beta2), + ), ] + optimizer_lrs = [config.puzzle_emb_lr, config.lr] return model, optimizers, optimizer_lrs + def mix_weights_direct(device, alpha, net, nets): sd = [] for i in range(len(nets)): sd += [nets[i].state_dict()] sd_alpha = {} for k in sd[0].keys(): - comb_net = alpha[0]*sd[0][k].to(device) - for i in range(1,len(nets)): - comb_net += alpha[i]*sd[i][k].to(device) - sd_alpha[k] = comb_net + comb_net = alpha[0] * sd[0][k].to(device) + for i in range(1, len(nets)): + comb_net += alpha[i] * sd[i][k].to(device) + sd_alpha[k] = comb_net net.load_state_dict(sd_alpha) return net + def cosine_schedule_with_warmup_lr_lambda( - current_step: int, *, base_lr: float, num_warmup_steps: int, num_training_steps: int, min_ratio: float = 0.0, num_cycles: float = 0.5 + current_step: int, + *, + base_lr: float, + num_warmup_steps: int, + num_training_steps: int, + min_ratio: float = 0.0, + num_cycles: float = 0.5, ): if current_step < num_warmup_steps: return base_lr * float(current_step) / float(max(1, num_warmup_steps)) - progress = float(current_step - num_warmup_steps) / float(max(1, num_training_steps - num_warmup_steps)) - return base_lr * (min_ratio + max(0.0, (1 - min_ratio) * 0.5 * (1.0 + math.cos(math.pi * float(num_cycles) * 2.0 * progress)))) + progress = float(current_step - num_warmup_steps) / float( + max(1, num_training_steps - num_warmup_steps) + ) + return base_lr * ( + min_ratio + + max( + 0.0, + (1 - min_ratio) * 0.5 * (1.0 + math.cos(math.pi * float(num_cycles) * 2.0 * progress)), + ) + ) -def init_train_state(config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, rank: int, world_size: int): +def init_train_state( + config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, rank: int, world_size: int +): # Estimated total training steps - total_steps = int(config.epochs * train_metadata.total_groups * train_metadata.mean_puzzle_examples / config.global_batch_size) + total_steps = int( + config.epochs + * train_metadata.total_groups + * train_metadata.mean_puzzle_examples + / config.global_batch_size + ) # Model - model, optimizers, optimizer_lrs = create_model(config, train_metadata, rank=rank, world_size=world_size) + model, optimizers, optimizer_lrs = create_model( + config, train_metadata, rank=rank, world_size=world_size + ) return TrainState( step=0, total_steps=total_steps, - model=model, optimizers=optimizers, optimizer_lrs=optimizer_lrs, - carry=None + carry=None, ) @@ -238,7 +297,10 @@ def save_train_state(config: PretrainConfig, train_state: TrainState): return os.makedirs(config.checkpoint_path, exist_ok=True) - torch.save(train_state.model.state_dict(), os.path.join(config.checkpoint_path, f"step_{train_state.step}")) + torch.save( + train_state.model.state_dict(), + os.path.join(config.checkpoint_path, f"step_{train_state.step}"), + ) def load_checkpoint(model: nn.Module, config: PretrainConfig): @@ -254,7 +316,9 @@ def load_checkpoint(model: nn.Module, config: PretrainConfig): if puzzle_emb_name in state_dict: puzzle_emb = state_dict[puzzle_emb_name] if puzzle_emb.shape != expected_shape: - print(f"Resetting puzzle embedding as shape is different. Found {puzzle_emb.shape}, Expected {expected_shape}") + print( + f"Resetting puzzle embedding as shape is different. Found {puzzle_emb.shape}, Expected {expected_shape}" + ) # Re-initialize using mean state_dict[puzzle_emb_name] = ( torch.mean(puzzle_emb, dim=0, keepdim=True).expand(expected_shape).contiguous() @@ -268,13 +332,12 @@ def compute_lr(base_lr: float, config: PretrainConfig, train_state: TrainState): base_lr=base_lr, num_warmup_steps=round(config.lr_warmup_steps), num_training_steps=train_state.total_steps, - min_ratio=config.lr_min_ratio + min_ratio=config.lr_min_ratio, ) - def create_evaluators(config: PretrainConfig, eval_metadata: PuzzleDatasetMetadata) -> List[Any]: - data_paths =config.data_paths_test if len(config.data_paths_test)>0 else config.data_paths + data_paths = config.data_paths_test if len(config.data_paths_test) > 0 else config.data_paths # Initialize evaluators evaluators = [] for cfg in config.evaluators: @@ -286,8 +349,21 @@ def create_evaluators(config: PretrainConfig, eval_metadata: PuzzleDatasetMetada return evaluators -def train_batch(config: PretrainConfig, train_state: TrainState, batch: Any, global_batch_size: int, rank: int, world_size: int): + +UPDATE_EVERY = 8 + + +def train_batch( + config: PretrainConfig, + train_state: TrainState, + batch: Any, + global_batch_size: int, + rank: int, + world_size: int, +): + global global_step train_state.step += 1 + global_step = train_state.step if train_state.step > train_state.total_steps: # At most train_total_steps return @@ -300,24 +376,62 @@ def train_batch(config: PretrainConfig, train_state: TrainState, batch: Any, glo train_state.carry = train_state.model.initial_carry(batch) # type: ignore # Forward - train_state.carry, loss, metrics, _, _ = train_state.model(carry=train_state.carry, batch=batch, return_keys=[]) + train_state.carry, loss, metrics, _, _ = train_state.model( + carry=train_state.carry, batch=batch, return_keys=[] + ) - ((1 / global_batch_size) * loss).backward() + current_step = train_state.carry.steps[0].item() # Something between 1 and 16 + if current_step > 0 and (current_step % UPDATE_EVERY == 0): + memories = train_state.carry.inner_carry.memories + memories_wrt = train_state.carry.inner_carry.memories_wrt + rec_model = train_state.model.model.inner.L_level + + grad_output = torch.autograd.grad( + (1 / global_batch_size) * loss, [memories[-1]], retain_graph=True + ) + param_to_gradients = defaultdict(list) + + for j in range(UPDATE_EVERY): + grads = torch.autograd.grad( + memories[-j - 1], + list(rec_model.parameters()) + [memories_wrt[-j - 1]], + grad_outputs=grad_output, + ) + grads_wrt_params = grads[:-1] + grad_output = grads[-1] + + for param, grad in zip(rec_model.parameters(), grads_wrt_params, strict=True): + param_to_gradients[param].append(grad) + + param_to_jacobian = { + param: torch.stack(gradients, dim=0) for param, gradients in param_to_gradients.items() + } + aggregator = UPGrad() + aggregator.weighting.weighting.weighting.register_forward_hook(print_gramian) + aggregator.register_forward_hook(log_gd_similarity) + transform = Accumulate() << Aggregate(aggregator, OrderedSet(list(rec_model.parameters()))) + transform(param_to_jacobian) # This stores the aggregated Jacobian in the .grad fields + + # Reset memories + train_state.carry.inner_carry.memories_wrt = [] + train_state.carry.inner_carry.memories = [] + + # ((1 / global_batch_size) * loss).backward() # Allreduce if world_size > 1: for param in train_state.model.parameters(): if param.grad is not None: dist.all_reduce(param.grad) - + # Apply optimizer - lr_this_step = None + lr_this_step = None for optim, base_lr in zip(train_state.optimizers, train_state.optimizer_lrs): lr_this_step = compute_lr(base_lr, config, train_state) for param_group in optim.param_groups: - param_group['lr'] = lr_this_step - + param_group["lr"] = lr_this_step + optim.step() optim.zero_grad() @@ -325,7 +439,9 @@ def train_batch(config: PretrainConfig, train_state: TrainState, batch: Any, glo if len(metrics): assert not any(v.requires_grad for v in metrics.values()) - metric_keys = list(sorted(metrics.keys())) # Sort keys to guarantee all processes use the same order. + metric_keys = list( + sorted(metrics.keys()) + ) # Sort keys to guarantee all processes use the same order. # Reduce and reconstruct metric_values = torch.stack([metrics[k] for k in metric_keys]) if world_size > 1: @@ -334,14 +450,18 @@ def train_batch(config: PretrainConfig, train_state: TrainState, batch: Any, glo if rank == 0: metric_values = metric_values.cpu().numpy() reduced_metrics = {k: metric_values[i] for i, k in enumerate(metric_keys)} - + # Postprocess count = max(reduced_metrics["count"], 1) # Avoid NaNs - reduced_metrics = {f"train/{k}": v / (global_batch_size if k.endswith("loss") else count) for k, v in reduced_metrics.items()} + reduced_metrics = { + f"train/{k}": v / (global_batch_size if k.endswith("loss") else count) + for k, v in reduced_metrics.items() + } reduced_metrics["train/lr"] = lr_this_step return reduced_metrics + def evaluate( config: PretrainConfig, train_state: TrainState, @@ -370,12 +490,12 @@ def evaluate( carry = None processed_batches = 0 - + for set_name, batch, global_batch_size in eval_loader: processed_batches += 1 if rank == 0: print(f"Processing batch {processed_batches}: {set_name}") - + # To device batch = {k: v.cuda() for k, v in batch.items()} with torch.device("cuda"): @@ -429,7 +549,8 @@ def evaluate( # Each rank save predictions independently os.makedirs(os.path.dirname(config.checkpoint_path), exist_ok=True) torch.save( - save_preds, os.path.join(config.checkpoint_path, f"step_{train_state.step}_all_preds.{rank}") + save_preds, + os.path.join(config.checkpoint_path, f"step_{train_state.step}_all_preds.{rank}"), ) del save_preds @@ -457,11 +578,13 @@ def evaluate( # Run evaluators if rank == 0: print(f"\nRunning {len(evaluators)} evaluator(s)...") - + for i, evaluator in enumerate(evaluators): if rank == 0: - print(f"Running evaluator {i+1}/{len(evaluators)}: {evaluator.__class__.__name__}") - + print( + f"Running evaluator {i + 1}/{len(evaluators)}: {evaluator.__class__.__name__}" + ) + # Path for saving evaluator_save_path = None if config.checkpoint_path is not None: @@ -472,19 +595,22 @@ def evaluate( os.makedirs(evaluator_save_path, exist_ok=True) # Run and log - metrics = evaluator.result(evaluator_save_path, rank=rank, world_size=world_size, group=cpu_group) + metrics = evaluator.result( + evaluator_save_path, rank=rank, world_size=world_size, group=cpu_group + ) if rank == 0 and metrics is not None: if reduced_metrics is None: reduced_metrics = {} reduced_metrics.update(metrics) print(f" Completed {evaluator.__class__.__name__}") - + if rank == 0: print("All evaluators completed!") return reduced_metrics + def save_code_and_config(config: PretrainConfig): if config.checkpoint_path is None or wandb.run is None: return @@ -494,7 +620,7 @@ def save_code_and_config(config: PretrainConfig): # Copy code code_list = [ get_model_source_path(config.arch.name), - get_model_source_path(config.arch.loss.name) + get_model_source_path(config.arch.loss.name), ] for code_file in code_list: if code_file is not None: @@ -522,7 +648,9 @@ def load_synced_config(hydra_config: DictConfig, rank: int, world_size: int) -> if config.run_name is None: config.run_name = f"{config.arch.name.split('@')[-1]} {coolname.generate_slug(2)}" if config.checkpoint_path is None: - config.checkpoint_path = os.path.join("checkpoints", config.project_name, config.run_name) + config.checkpoint_path = os.path.join( + "checkpoints", config.project_name, config.run_name + ) objects = [config] @@ -532,7 +660,7 @@ def load_synced_config(hydra_config: DictConfig, rank: int, world_size: int) -> return objects[0] # type: ignore -@hydra.main(config_path="config", config_name="cfg_pretrain", version_base=None) +@hydra.main(config_path="../../config", config_name="cfg_pretrain", version_base=None) def launch(hydra_config: DictConfig): RANK = 0 WORLD_SIZE = 1 @@ -547,11 +675,12 @@ def launch(hydra_config: DictConfig): WORLD_SIZE = dist.get_world_size() torch.cuda.set_device(int(os.environ["LOCAL_RANK"])) - + # CPU GLOO process group CPU_PROCESS_GROUP = dist.new_group(backend="gloo") assert ( - dist.get_rank(CPU_PROCESS_GROUP) == RANK and dist.get_world_size(CPU_PROCESS_GROUP) == WORLD_SIZE + dist.get_rank(CPU_PROCESS_GROUP) == RANK + and dist.get_world_size(CPU_PROCESS_GROUP) == WORLD_SIZE ) # Load sync'ed config @@ -561,23 +690,47 @@ def launch(hydra_config: DictConfig): torch.random.manual_seed(config.seed + RANK) # Dataset - train_epochs_per_iter = config.eval_interval if config.eval_interval is not None else config.epochs + train_epochs_per_iter = ( + config.eval_interval if config.eval_interval is not None else config.epochs + ) total_iters = config.epochs // train_epochs_per_iter - assert config.epochs % train_epochs_per_iter == 0, "Eval interval must be a divisor of total epochs." - - train_loader, train_metadata = create_dataloader(config, "train", test_set_mode=False, epochs_per_iter=train_epochs_per_iter, global_batch_size=config.global_batch_size, rank=RANK, world_size=WORLD_SIZE) - try: - eval_loader, eval_metadata = create_dataloader(config, "test", test_set_mode=True, epochs_per_iter=1, global_batch_size=config.global_batch_size, rank=RANK, world_size=WORLD_SIZE) - except: - print("NO EVAL DATA FOUND") - eval_loader = eval_metadata = None - - try: - evaluators = create_evaluators(config, eval_metadata) - except: - print("No evaluator found") - evaluators = [] + assert ( + config.epochs % train_epochs_per_iter == 0 + ), "Eval interval must be a divisor of total epochs." + + train_loader, train_metadata = create_dataloader( + config, + "train", + test_set_mode=False, + epochs_per_iter=train_epochs_per_iter, + global_batch_size=config.global_batch_size, + rank=RANK, + world_size=WORLD_SIZE, + ) + # try: + eval_loader, eval_metadata = create_dataloader( + config, + "test", + test_set_mode=True, + epochs_per_iter=1, + global_batch_size=config.global_batch_size, + rank=RANK, + world_size=WORLD_SIZE, + ) + # Bare exception: keep this commented until we know what exception can be raised, and we catch + # this one specifically. + # except: + # print("NO EVAL DATA FOUND") + # eval_loader = eval_metadata = None + + # try: + evaluators = create_evaluators(config, eval_metadata) + # Bare exception: keep this commented until we know what exception can be raised, and we catch + # this one specifically. + # except: + # print("No evaluator found") + # evaluators = [] # Train state train_state = init_train_state(config, train_metadata, rank=RANK, world_size=WORLD_SIZE) @@ -591,20 +744,22 @@ def launch(hydra_config: DictConfig): wandb.log({"num_params": sum(x.numel() for x in train_state.model.parameters())}, step=0) save_code_and_config(config) if config.ema: - print('Setup EMA') + print("Setup EMA") ema_helper = EMAHelper(mu=config.ema_rate) ema_helper.register(train_state.model) # Training Loop for _iter_id in range(total_iters): - print (f"[Rank {RANK}, World Size {WORLD_SIZE}]: Epoch {_iter_id * train_epochs_per_iter}") + print(f"[Rank {RANK}, World Size {WORLD_SIZE}]: Epoch {_iter_id * train_epochs_per_iter}") - ############ Train Iter + # Train Iter if RANK == 0: print("TRAIN") train_state.model.train() for set_name, batch, global_batch_size in train_loader: - metrics = train_batch(config, train_state, batch, global_batch_size, rank=RANK, world_size=WORLD_SIZE) + metrics = train_batch( + config, train_state, batch, global_batch_size, rank=RANK, world_size=WORLD_SIZE + ) if RANK == 0 and metrics is not None: wandb.log(metrics, step=train_state.step) @@ -613,7 +768,7 @@ def launch(hydra_config: DictConfig): ema_helper.update(train_state.model) if _iter_id >= config.min_eval_interval: - ############ Evaluation + # Evaluation if RANK == 0: print("EVALUATE") if config.ema: @@ -623,19 +778,21 @@ def launch(hydra_config: DictConfig): else: train_state_eval = train_state train_state_eval.model.eval() - metrics = evaluate(config, - train_state_eval, - eval_loader, - eval_metadata, + metrics = evaluate( + config, + train_state_eval, + eval_loader, + eval_metadata, evaluators, - rank=RANK, + rank=RANK, world_size=WORLD_SIZE, - cpu_group=CPU_PROCESS_GROUP) + cpu_group=CPU_PROCESS_GROUP, + ) if RANK == 0 and metrics is not None: wandb.log(metrics, step=train_state.step) - - ############ Checkpointing + + # Checkpointing if RANK == 0: print("SAVE CHECKPOINT") if RANK == 0 and (config.checkpoint_every_eval or (_iter_id == total_iters - 1)): diff --git a/puzzle_dataset.py b/src/recursion/puzzle_dataset.py similarity index 69% rename from puzzle_dataset.py rename to src/recursion/puzzle_dataset.py index 16cf2928..e56cef3e 100644 --- a/puzzle_dataset.py +++ b/src/recursion/puzzle_dataset.py @@ -1,19 +1,24 @@ -import os import json -from typing import Tuple, List, Dict, Optional +import os +from typing import List + import numpy as np import pydantic - import torch from torch.utils.data import IterableDataset, get_worker_info -from models.losses import IGNORE_LABEL_ID -from dataset.common import PuzzleDatasetMetadata +from recursion.dataset.common import PuzzleDatasetMetadata +from recursion.models.losses import IGNORE_LABEL_ID -from argdantic import ArgParser -from pydantic import BaseModel -def _sample_batch(rng: np.random.Generator, group_order: np.ndarray, puzzle_indices: np.ndarray, group_indices: np.ndarray, start_index: int, global_batch_size: int): +def _sample_batch( + rng: np.random.Generator, + group_order: np.ndarray, + puzzle_indices: np.ndarray, + group_indices: np.ndarray, + start_index: int, + global_batch_size: int, +): # Pack examples into a full batch batch = [] batch_puzzle_indices = [] @@ -49,6 +54,7 @@ class PuzzleDatasetConfig(pydantic.BaseModel): rank: int num_replicas: int + class PuzzleDataset(IterableDataset): def __init__(self, config: PuzzleDatasetConfig, split: str = "train"): super().__init__() @@ -85,7 +91,9 @@ def __init__(self, config: PuzzleDatasetConfig, split: str = "train"): assert prev_blank_identifier_id == current_metadata.blank_identifier_id assert prev_sets == current_metadata.sets assert prev_num_identifiers == current_metadata.num_puzzle_identifiers - mean_puzzle_examples += current_metadata.mean_puzzle_examples*current_metadata.total_puzzles + mean_puzzle_examples += ( + current_metadata.mean_puzzle_examples * current_metadata.total_puzzles + ) total_puzzles += current_metadata.total_puzzles total_groups += current_metadata.total_groups num_identifiers += current_metadata.num_puzzle_identifiers @@ -101,11 +109,13 @@ def __init__(self, config: PuzzleDatasetConfig, split: str = "train"): total_groups=total_groups, mean_puzzle_examples=mean_puzzle_examples, total_puzzles=total_puzzles, - sets=prev_sets + sets=prev_sets, ) # Checks - assert self.config.global_batch_size % self.config.num_replicas == 0, f"Global batch size {self.config.global_batch_size} must be multiples of nodes {self.config.num_replicas}." + assert ( + self.config.global_batch_size % self.config.num_replicas == 0 + ), f"Global batch size {self.config.global_batch_size} must be multiples of nodes {self.config.num_replicas}." self.local_batch_size = self.config.global_batch_size // self.config.num_replicas # State @@ -123,27 +133,28 @@ def _lazy_load_dataset(self): field_mmap_modes = { "inputs": "r", "labels": "r", - # Keep indices in memory "puzzle_identifiers": None, "puzzle_indices": None, - "group_indices": None + "group_indices": None, } # Load data self._data = {} - for set_name in self.metadata.sets: # Load subset + for set_name in self.metadata.sets: # Load subset for i, dataset_path in enumerate(self.config.dataset_paths): if i > 0: set_name_ = set_name + str(i) else: set_name_ = set_name self._data[set_name_] = { - field_name: np.load(os.path.join(dataset_path, self.split, f"{set_name}__{field_name}.npy"), mmap_mode=mmap_mode) + field_name: np.load( + os.path.join(dataset_path, self.split, f"{set_name}__{field_name}.npy"), + mmap_mode=mmap_mode, + ) for field_name, mmap_mode in field_mmap_modes.items() } - def _collate_batch(self, batch): # Convert dtype batch = {k: v.astype(np.int32) for k, v in batch.items()} @@ -158,13 +169,18 @@ def _collate_batch(self, batch): pad_values = { "inputs": self.metadata.pad_id, "labels": IGNORE_LABEL_ID, - "puzzle_identifiers": self.metadata.blank_identifier_id + "puzzle_identifiers": self.metadata.blank_identifier_id, + } + batch = { + k: np.pad( + v, ((0, pad_size),) + ((0, 0),) * (v.ndim - 1), constant_values=pad_values[k] + ) + for k, v in batch.items() } - batch = {k: np.pad(v, ((0, pad_size), ) + ((0, 0), ) * (v.ndim - 1), constant_values=pad_values[k]) for k, v in batch.items()} # To tensor return {k: torch.from_numpy(v) for k, v in batch.items()} - + def _iter_test(self): for set_i, (set_name, dataset) in enumerate(self._data.items()): # type: ignore total_examples = len(dataset["inputs"]) @@ -174,27 +190,36 @@ def _iter_test(self): while start_index < total_examples: # Compute indices end_index = min(total_examples, start_index + self.config.global_batch_size) - + local_start = start_index + self.config.rank * self.local_batch_size - local_end = min(start_index + (self.config.rank + 1) * self.local_batch_size, end_index) - + local_end = min( + start_index + (self.config.rank + 1) * self.local_batch_size, end_index + ) + # Get batch of examples, and also puzzle IDs puzzle_indices = [] - puzzle_index = np.searchsorted(dataset["puzzle_indices"], local_start, side="right") - 1 + puzzle_index = ( + np.searchsorted(dataset["puzzle_indices"], local_start, side="right") - 1 + ) for i in range(local_start, local_end): - while puzzle_index + 1 < len(dataset["puzzle_indices"]) and i >= dataset["puzzle_indices"][puzzle_index + 1]: + while ( + puzzle_index + 1 < len(dataset["puzzle_indices"]) + and i >= dataset["puzzle_indices"][puzzle_index + 1] + ): puzzle_index += 1 puzzle_indices.append(puzzle_index) - - batch = self._collate_batch({ - "inputs": dataset["inputs"][local_start: local_end], - "labels": dataset["labels"][local_start: local_end], - "puzzle_identifiers": dataset["puzzle_identifiers"][puzzle_indices] - }) + + batch = self._collate_batch( + { + "inputs": dataset["inputs"][local_start:local_end], + "labels": dataset["labels"][local_start:local_end], + "puzzle_identifiers": dataset["puzzle_identifiers"][puzzle_indices], + } + ) yield set_name, batch, end_index - start_index - + # Advance to next batch start_index += self.config.global_batch_size @@ -206,9 +231,14 @@ def _iter_train(self): # Randomly shuffle groups rng = np.random.Generator(np.random.Philox(seed=self.config.seed + self._iters)) - group_order = np.concatenate([rng.permutation(dataset["group_indices"].size - 1) for _i in range(self.config.epochs_per_iter)]) + group_order = np.concatenate( + [ + rng.permutation(dataset["group_indices"].size - 1) + for _i in range(self.config.epochs_per_iter) + ] + ) start_index = 0 - + while start_index < group_order.size: start_index, batch_indices, batch_puzzle_indices = _sample_batch( rng, @@ -220,31 +250,44 @@ def _iter_train(self): ) # Select current rank and collate - global_effective_batch_size = batch_puzzle_indices.size # Global effective batch size, excluding pads + global_effective_batch_size = ( + batch_puzzle_indices.size + ) # Global effective batch size, excluding pads # Drop last batch if global_effective_batch_size < self.config.global_batch_size: break - batch_indices = batch_indices [self.config.rank * self.local_batch_size: (self.config.rank + 1) * self.local_batch_size] - batch_puzzle_indices = batch_puzzle_indices[self.config.rank * self.local_batch_size: (self.config.rank + 1) * self.local_batch_size] - batch = self._collate_batch({ - "inputs": dataset["inputs"][batch_indices], - "labels": dataset["labels"][batch_indices], - "puzzle_identifiers": dataset["puzzle_identifiers"][batch_puzzle_indices] - }) + batch_indices = batch_indices[ + self.config.rank + * self.local_batch_size : (self.config.rank + 1) + * self.local_batch_size + ] + batch_puzzle_indices = batch_puzzle_indices[ + self.config.rank + * self.local_batch_size : (self.config.rank + 1) + * self.local_batch_size + ] + batch = self._collate_batch( + { + "inputs": dataset["inputs"][batch_indices], + "labels": dataset["labels"][batch_indices], + "puzzle_identifiers": dataset["puzzle_identifiers"][batch_puzzle_indices], + } + ) yield set_name, batch, global_effective_batch_size - + def __iter__(self): worker_info = get_worker_info() - assert worker_info is None or worker_info.num_workers == 1, "Multithreaded data loading is not currently supported." - + assert ( + worker_info is None or worker_info.num_workers == 1 + ), "Multithreaded data loading is not currently supported." + self._lazy_load_dataset() - + # Iterate using specified mode if self.config.test_set_mode: yield from self._iter_test() else: yield from self._iter_train() - diff --git a/src/recursion/utils/__init__.py b/src/recursion/utils/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/utils/functions.py b/src/recursion/utils/functions.py similarity index 51% rename from utils/functions.py rename to src/recursion/utils/functions.py index b1236360..125c2fe6 100644 --- a/utils/functions.py +++ b/src/recursion/utils/functions.py @@ -2,18 +2,18 @@ import inspect -def load_model_class(identifier: str, prefix: str = "models."): - module_path, class_name = identifier.split('@') +def load_model_class(identifier: str, prefix: str = "recursion.models."): + module_path, class_name = identifier.split("@") # Import the module module = importlib.import_module(prefix + module_path) cls = getattr(module, class_name) - + return cls -def get_model_source_path(identifier: str, prefix: str = "models."): - module_path, class_name = identifier.split('@') +def get_model_source_path(identifier: str, prefix: str = "recursion.models."): + module_path, class_name = identifier.split("@") module = importlib.import_module(prefix + module_path) return inspect.getsourcefile(module)