__lowercase											=      {
    '''Pillow''': '''Pillow<10.0.0''',
    '''accelerate''': '''accelerate>=0.20.3''',
    '''av''': '''av==9.2.0''',
    '''beautifulsoup4''': '''beautifulsoup4''',
    '''black''': '''black~=23.1''',
    '''codecarbon''': '''codecarbon==1.2.0''',
    '''cookiecutter''': '''cookiecutter==1.7.3''',
    '''dataclasses''': '''dataclasses''',
    '''datasets''': '''datasets!=2.5.0''',
    '''decord''': '''decord==0.6.0''',
    '''deepspeed''': '''deepspeed>=0.9.3''',
    '''diffusers''': '''diffusers''',
    '''dill''': '''dill<0.3.5''',
    '''evaluate''': '''evaluate>=0.2.0''',
    '''fairscale''': '''fairscale>0.3''',
    '''faiss-cpu''': '''faiss-cpu''',
    '''fastapi''': '''fastapi''',
    '''filelock''': '''filelock''',
    '''flax''': '''flax>=0.4.1,<=0.7.0''',
    '''ftfy''': '''ftfy''',
    '''fugashi''': '''fugashi>=1.0''',
    '''GitPython''': '''GitPython<3.1.19''',
    '''hf-doc-builder''': '''hf-doc-builder>=0.3.0''',
    '''huggingface-hub''': '''huggingface-hub>=0.14.1,<1.0''',
    '''importlib_metadata''': '''importlib_metadata''',
    '''ipadic''': '''ipadic>=1.0.0,<2.0''',
    '''isort''': '''isort>=5.5.4''',
    '''jax''': '''jax>=0.2.8,!=0.3.2,<=0.4.13''',
    '''jaxlib''': '''jaxlib>=0.1.65,<=0.4.13''',
    '''jieba''': '''jieba''',
    '''kenlm''': '''kenlm''',
    '''keras-nlp''': '''keras-nlp>=0.3.1''',
    '''librosa''': '''librosa''',
    '''nltk''': '''nltk''',
    '''natten''': '''natten>=0.14.6''',
    '''numpy''': '''numpy>=1.17''',
    '''onnxconverter-common''': '''onnxconverter-common''',
    '''onnxruntime-tools''': '''onnxruntime-tools>=1.4.2''',
    '''onnxruntime''': '''onnxruntime>=1.4.0''',
    '''opencv-python''': '''opencv-python''',
    '''optuna''': '''optuna''',
    '''optax''': '''optax>=0.0.8,<=0.1.4''',
    '''packaging''': '''packaging>=20.0''',
    '''parameterized''': '''parameterized''',
    '''phonemizer''': '''phonemizer''',
    '''protobuf''': '''protobuf''',
    '''psutil''': '''psutil''',
    '''pyyaml''': '''pyyaml>=5.1''',
    '''pydantic''': '''pydantic<2''',
    '''pytest''': '''pytest>=7.2.0''',
    '''pytest-timeout''': '''pytest-timeout''',
    '''pytest-xdist''': '''pytest-xdist''',
    '''python''': '''python>=3.8.0''',
    '''ray[tune]''': '''ray[tune]''',
    '''regex''': '''regex!=2019.12.17''',
    '''requests''': '''requests''',
    '''rhoknp''': '''rhoknp>=1.1.0,<1.3.1''',
    '''rjieba''': '''rjieba''',
    '''rouge-score''': '''rouge-score!=0.0.7,!=0.0.8,!=0.1,!=0.1.1''',
    '''ruff''': '''ruff>=0.0.241,<=0.0.259''',
    '''sacrebleu''': '''sacrebleu>=1.4.12,<2.0.0''',
    '''sacremoses''': '''sacremoses''',
    '''safetensors''': '''safetensors>=0.3.1''',
    '''sagemaker''': '''sagemaker>=2.31.0''',
    '''scikit-learn''': '''scikit-learn''',
    '''sentencepiece''': '''sentencepiece>=0.1.91,!=0.1.92''',
    '''sigopt''': '''sigopt''',
    '''starlette''': '''starlette''',
    '''sudachipy''': '''sudachipy>=0.6.6''',
    '''sudachidict_core''': '''sudachidict_core>=20220729''',
    '''tensorflow-cpu''': '''tensorflow-cpu>=2.6,<2.14''',
    '''tensorflow''': '''tensorflow>=2.6,<2.14''',
    '''tensorflow-text''': '''tensorflow-text<2.14''',
    '''tf2onnx''': '''tf2onnx''',
    '''timeout-decorator''': '''timeout-decorator''',
    '''timm''': '''timm''',
    '''tokenizers''': '''tokenizers>=0.11.1,!=0.11.3,<0.14''',
    '''torch''': '''torch>=1.9,!=1.12.0''',
    '''torchaudio''': '''torchaudio''',
    '''torchvision''': '''torchvision''',
    '''pyctcdecode''': '''pyctcdecode>=0.4.0''',
    '''tqdm''': '''tqdm>=4.27''',
    '''unidic''': '''unidic>=1.0.2''',
    '''unidic_lite''': '''unidic_lite>=1.0.7''',
    '''urllib3''': '''urllib3<2.0.0''',
    '''uvicorn''': '''uvicorn''',
}






def lowerCamelCase						(     SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    __UpperCamelCase  :Optional[int]    						=	generate_pascal_triangle(SCREAMING_SNAKE_CASE			)
    for row_idx in range(SCREAMING_SNAKE_CASE			):
        # Print left spaces
        for _ in range(num_rows - row_idx - 1			):
            print(end=''' '''			)
        # Print row values
        for col_idx in range(row_idx + 1			):
            if col_idx != row_idx:
                print(triangle[row_idx][col_idx]						,    end=''' '''			)
            else:
                print(triangle[row_idx][col_idx]						,    end=''''''			)
        print()



def lowerCamelCase						(     SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    if not isinstance(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			):
        raise TypeError('''The input value of \'num_rows\' should be \'int\''''			)

    if num_rows == 0:
        return []
    elif num_rows < 0:
        raise ValueError(
            '''The input value of \'num_rows\' should be greater than or equal to 0'''			)

    __UpperCamelCase  :list[list[int]]    						=	[]
    for current_row_idx in range(SCREAMING_SNAKE_CASE			):
        __UpperCamelCase  :List[Any]    						=	populate_current_row(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			)
        triangle.append(SCREAMING_SNAKE_CASE			)
    return triangle



def lowerCamelCase						(     SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    __UpperCamelCase  :int    						=	[-1] * (current_row_idx + 1)
    # first and last elements of current row are equal to 1
    __UpperCamelCase						, __UpperCamelCase  :int    						=	1, 1
    for current_col_idx in range(1						,    SCREAMING_SNAKE_CASE			):
        calculate_current_element(
            SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			)
    return current_row



def lowerCamelCase						(     SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    ):
    '''simple docstring'''







    __UpperCamelCase  :Dict    						=	triangle[current_row_idx - 1][current_col_idx - 1]
    __UpperCamelCase  :List[Any]    						=	triangle[current_row_idx - 1][current_col_idx]
    __UpperCamelCase  :List[Any]    						=	above_to_left_elt + above_to_right_elt



def lowerCamelCase						(     SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    if not isinstance(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			):
        raise TypeError('''The input value of \'num_rows\' should be \'int\''''			)

    if num_rows == 0:
        return []
    elif num_rows < 0:
        raise ValueError(
            '''The input value of \'num_rows\' should be greater than or equal to 0'''			)

    __UpperCamelCase  :list[list[int]]    						=	[[1]]

    for row_index in range(1						,    SCREAMING_SNAKE_CASE			):
        __UpperCamelCase  :Optional[Any]    						=	[0] + result[-1] + [0]
        __UpperCamelCase  :Any    						=	row_index + 1
        # Calculate the number of distinct elements in a row
        __UpperCamelCase  :Optional[Any]    						=	sum(divmod(SCREAMING_SNAKE_CASE						,    2			)			)
        __UpperCamelCase  :Union[str, Any]    						=	[
            temp_row[i - 1] + temp_row[i] for i in range(1						,    distinct_elements + 1			)
        ]
        __UpperCamelCase  :List[Any]    						=	row_first_half[: (row_index + 1) // 2]
        row_second_half.reverse()
        __UpperCamelCase  :List[str]    						=	row_first_half + row_second_half
        result.append(SCREAMING_SNAKE_CASE			)

    return result



def lowerCamelCase						(     ):
    '''simple docstring'''







    from collections.abc import Callable
    from timeit import timeit

    def benchmark_a_function(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			) -> None:
        __UpperCamelCase  :List[str]    						=	f"""{func.__name__}({value})"""
        __UpperCamelCase  :Optional[int]    						=	timeit(f"""__main__.{call}"""						,    setup='''import __main__'''			)
        # print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
        print(f"""{call:38} -- {timing:.4f} seconds"""			)

    for value in range(15			):  # (1, 7, 14):
        for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
            benchmark_a_function(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			)
        print()


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    benchmark()





