





'''simple docstring'''

from math import sqrt





def lowerCamelCase						(     __lowerCamelCase :    int = 100_0000    )						->int:
    _SCREAMING_SNAKE_CASE									=			0
    _SCREAMING_SNAKE_CASE									=			0
    _SCREAMING_SNAKE_CASE									=			42

    while num_cuboids <= limit:
        max_cuboid_size += 1
        for sum_shortest_sides in range(2					,       2 * max_cuboid_size + 1    ):
            if sqrt(sum_shortest_sides**2 + max_cuboid_size**2    ).is_integer():
                num_cuboids += (
                    min(__lowerCamelCase					,       sum_shortest_sides // 2    )
                    - max(1					,       sum_shortest_sides - max_cuboid_size    )
                    + 1
                )

    return max_cuboid_size


if __name__ == "__main__":
      print(f"""{solution() = }""")










'''simple docstring'''




lowercase__    :      Dict						=    {
    '''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''',
}