from __future__ import annotations

from fractions import Fraction




def       _snake_case	(   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       _snake_case	(   lowerCAmelCase							:   int	):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    []
		SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    1_1
		SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    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
				SCREAMING_SNAKE_CASE_  :		List[Any]				      =    1_0
		return solutions




def       _snake_case	(   lowerCAmelCase							:   int = 2	):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		int				      =    1.0
		for fraction in fraction_list(__lowerCamelCase	):
				SCREAMING_SNAKE_CASE_  :		Tuple				      =    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


lowerCAmelCase					:     int												={
    '''configuration_bigbird_pegasus''': [
        '''BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''BigBirdPegasusConfig''',
        '''BigBirdPegasusOnnxConfig''',
    ],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase					:     Any												=[
     '''BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''BigBirdPegasusForCausalLM''',
     '''BigBirdPegasusForConditionalGeneration''',
     '''BigBirdPegasusForQuestionAnswering''',
     '''BigBirdPegasusForSequenceClassification''',
     '''BigBirdPegasusModel''',
     '''BigBirdPegasusPreTrainedModel''',
 ]


if TYPE_CHECKING:
 from .configuration_bigbird_pegasus import (
     BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP,
     BigBirdPegasusConfig,
     BigBirdPegasusOnnxConfig,
 )

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_bigbird_pegasus import (
      BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
      BigBirdPegasusForCausalLM,
      BigBirdPegasusForConditionalGeneration,
      BigBirdPegasusForQuestionAnswering,
      BigBirdPegasusForSequenceClassification,
      BigBirdPegasusModel,
      BigBirdPegasusPreTrainedModel,
  )


else:
 import sys

 lowerCAmelCase					:     Dict												=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


