




_lowerCamelCase      			=						{
    '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',
}











from __future__ import annotations

from fractions import Fraction




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						int	,					__UpperCamelCase      :						int				)  ->							bool:
    return (
        num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
    )




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						int				)  ->							list[str]:
    UpperCAmelCase_										=					[]
    UpperCAmelCase_										=					11
    UpperCAmelCase_										=					int('''1''' + '''0''' * digit_len				)
    for num in range(__UpperCamelCase	,					__UpperCamelCase				):
        while den <= 99:
            if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                if is_digit_cancelling(__UpperCamelCase	,					__UpperCamelCase				):
                    solutions.append(f'{num}/{den}'				)
            den += 1
        num += 1
        UpperCAmelCase_										=					10
    return solutions




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						int = 2				)  ->							int:
    UpperCAmelCase_										=					1.0
    for fraction in fraction_list(__UpperCamelCase				):
        UpperCAmelCase_										=					Fraction(__UpperCamelCase				)
        result *= frac.denominator / frac.numerator
    return int(__UpperCamelCase				)


if __name__ == "__main__":
 print(solution())





