


'''simple docstring'''






from __future__ import annotations

from fractions import Fraction





def lowerCamelCase__     (		__lowerCamelCase			:				int			,       __lowerCamelCase			:				int				):







   '''simple docstring'''




   return (
       num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
   )





def lowerCamelCase__     (		__lowerCamelCase			:				int				):







   '''simple docstring'''




   _UpperCAmelCase  :  Optional[int]				       =[]
   _UpperCAmelCase  :  Union[str, Any]				       =1_1
   _UpperCAmelCase  :  Union[str, Any]				       =int('1' + '0' * digit_len				)
   for num in range(__lowerCamelCase			,       __lowerCamelCase				):
      while den <= 9_9:
         if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
            if is_digit_cancelling(__lowerCamelCase			,       __lowerCamelCase				):
               solutions.append(f"{num}/{den}"				)
         den += 1
      num += 1
      _UpperCAmelCase  :  Optional[int]				       =1_0
   return solutions





def lowerCamelCase__     (		__lowerCamelCase			:				int = 2				):







   '''simple docstring'''




   _UpperCAmelCase  :  Any				       =1.0
   for fraction in fraction_list(__lowerCamelCase				):
      _UpperCAmelCase  :  List[str]				       =Fraction(__lowerCamelCase				)
      result *= frac.denominator / frac.numerator
   return int(__lowerCamelCase				)


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





'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase				={
    'configuration_table_transformer': [
        'TABLE_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'TableTransformerConfig',
        'TableTransformerOnnxConfig',
    ]
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowercase				=[
     'TABLE_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'TableTransformerForObjectDetection',
     'TableTransformerModel',
     'TableTransformerPreTrainedModel',
 ]


if TYPE_CHECKING:
 from .configuration_table_transformer import (
     TABLE_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
     TableTransformerConfig,
     TableTransformerOnnxConfig,
 )

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_table_transformer import (
      TABLE_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TableTransformerForObjectDetection,
      TableTransformerModel,
      TableTransformerPreTrainedModel,
  )

else:
 import sys

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

