





'''simple docstring'''







def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			str,			SCREAMING_SNAKE_CASE__      :			str   ) ->	Optional[int]:
						assert x is not None
						assert y is not None

						UpperCAmelCase_			:      str     						=  len(SCREAMING_SNAKE_CASE__   )
						UpperCAmelCase_			:      Optional[int]     						=  len(SCREAMING_SNAKE_CASE__   )

						# declaring the array for storing the dp values
						UpperCAmelCase_			:      Optional[int]     						=  [[0] * (n + 1) for _ in range(m + 1   )]  # noqa: E741

						for i in range(1,			m + 1   ):
												for j in range(1,			n + 1   ):
																		UpperCAmelCase_			:      Union[str, Any]     						=  1 if x[i - 1] == y[j - 1] else 0

																		UpperCAmelCase_			:      Any     						=  max(l[i - 1][j],			l[i][j - 1],			l[i - 1][j - 1] + match   )

						UpperCAmelCase_			:      Tuple     						=  ''''''
						UpperCAmelCase_						,       UpperCAmelCase_			:      List[str]     						=  m, n
						while i > 0 and j > 0:
												UpperCAmelCase_			:      List[str]     						=  1 if x[i - 1] == y[j - 1] else 0

												if l[i][j] == l[i - 1][j - 1] + match:
																		if match == 1:
																								UpperCAmelCase_			:      Dict     						=  x[i - 1] + seq
																		i -= 1
																		j -= 1
												elif l[i][j] == l[i - 1][j]:
																		i -= 1
												else:
																		j -= 1

						return l[m][n], seq


if __name__ == "__main__":
					snake_case_     :       Optional[int]						=  "AGGTAB"
					snake_case_     :       str						=  "GXTXAYB"
					snake_case_     :       Optional[Any]						=  4
					snake_case_     :       Optional[int]						=  "GTAB"

					snake_case_			,snake_case_     :       List[Any]						=  longest_common_subsequence(a, b)
					print("len =", ln, ", sub-sequence =", subseq)
					import doctest

					doctest.testmod()












'''simple docstring'''







snake_case_     :       int						=  {
    "Pillow": "Pillow",
    "accelerate": "accelerate>=0.11.0",
    "compel": "compel==0.1.8",
    "black": "black~=23.1",
    "datasets": "datasets",
    "filelock": "filelock",
    "flax": "flax>=0.4.1",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.13.2",
    "requests-mock": "requests-mock==1.10.0",
    "importlib_metadata": "importlib_metadata",
    "invisible-watermark": "invisible-watermark",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2",
    "jaxlib": "jaxlib>=0.1.65",
    "Jinja2": "Jinja2",
    "k-diffusion": "k-diffusion>=0.0.12",
    "torchsde": "torchsde",
    "note_seq": "note_seq",
    "librosa": "librosa",
    "numpy": "numpy",
    "omegaconf": "omegaconf",
    "parameterized": "parameterized",
    "protobuf": "protobuf>=3.20.3,<4",
    "pytest": "pytest",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "ruff": "ruff>=0.0.241",
    "safetensors": "safetensors",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "scipy": "scipy",
    "onnx": "onnx",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "tensorboard": "tensorboard",
    "torch": "torch>=1.4",
    "torchvision": "torchvision",
    "transformers": "transformers>=4.25.1",
    "urllib3": "urllib3<=2.0.0",
}





