


'''simple docstring'''



from __future__ import annotations

from fractions import Fraction







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__					):
			return (
			    num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
			)







def     _UpperCamelCase      (		UpperCamelCase__					):
			UpperCAmelCase__  :					Dict        =     []
			UpperCAmelCase__  :					Dict        =     1_1
			UpperCAmelCase__  :					List[str]        =     int("""1""" + """0""" * digit_len					)
			for num in range(UpperCamelCase__ ,      UpperCamelCase__					):
						while den <= 9_9:
									if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
												if is_digit_cancelling(UpperCamelCase__ ,      UpperCamelCase__					):
															solutions.append(f'''{num}/{den}'''					)
									den += 1
						num += 1
						UpperCAmelCase__  :					int        =     1_0
			return solutions







def     _UpperCamelCase      (		UpperCamelCase__ = 2					):
			UpperCAmelCase__  :					Any        =     1.0
			for fraction in fraction_list(UpperCamelCase__					):
						UpperCAmelCase__  :					Any        =     Fraction(UpperCamelCase__					)
						result *= frac.denominator / frac.numerator
			return int(UpperCamelCase__					)


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



'''simple docstring'''



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


__A	={
    'configuration_encodec': [
        'ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'EncodecConfig',
    ],
    'feature_extraction_encodec': ['EncodecFeatureExtractor'],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__A	=[
		    'ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST',
		    'EncodecModel',
		    'EncodecPreTrainedModel',
		]

if TYPE_CHECKING:
		from .configuration_encodec import (
		    ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP,
		    EncodecConfig,
		)
		from .feature_extraction_encodec import EncodecFeatureExtractor

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_encodec import (
				    ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST,
				    EncodecModel,
				    EncodecPreTrainedModel,
				)

else:
		import sys

		__A	=_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)