



"""simple docstring"""
from __future__ import annotations

from fractions import Fraction


def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase ,  __lowerCAmelCase							) ->						int:







  '''simple docstring'''


  return (
      num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
  )


def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase							) ->						Union[str, Any]:







  '''simple docstring'''


  lowercase_								= []
  lowercase_								= 11
  lowercase_								= int("""1""" + """0""" * digit_len							)
  for num in range(_lowercase ,  _lowercase							):
    while den <= 99:
      if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
        if is_digit_cancelling(_lowercase ,  _lowercase							):
          solutions.append(F'''{num}/{den}'''							)
      den += 1
    num += 1
    lowercase_								= 10
  return solutions


def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase = 2							) ->						Optional[Any]:







  '''simple docstring'''


  lowercase_								= 1.0
  for fraction in fraction_list(_lowercase							):
    lowercase_								= Fraction(_lowercase							)
    result *= frac.denominator / frac.numerator
  return int(_lowercase							)


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






"""simple docstring"""
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase						:		Any			= {"configuration_xglm": ["XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP", "XGLMConfig"]}

try:
       if not is_sentencepiece_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase						:		List[str]			= ["XGLMTokenizer"]

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase						:		Dict			= ["XGLMTokenizerFast"]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase						:		Tuple			= [
           "XGLM_PRETRAINED_MODEL_ARCHIVE_LIST",
           "XGLMForCausalLM",
           "XGLMModel",
           "XGLMPreTrainedModel",
       ]


try:
       if not is_flax_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase						:		int			= [
           "FlaxXGLMForCausalLM",
           "FlaxXGLMModel",
           "FlaxXGLMPreTrainedModel",
       ]


try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase						:		List[str]			= [
           "TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST",
           "TFXGLMForCausalLM",
           "TFXGLMModel",
           "TFXGLMPreTrainedModel",
       ]


if TYPE_CHECKING:
       from .configuration_xglm import XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XGLMConfig

       try:
              if not is_sentencepiece_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_xglm import XGLMTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_xglm_fast import XGLMTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_xglm import XGLM_PRETRAINED_MODEL_ARCHIVE_LIST, XGLMForCausalLM, XGLMModel, XGLMPreTrainedModel

       try:
              if not is_flax_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel, FlaxXGLMPreTrainedModel

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_xglm import (
                  TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST,
                  TFXGLMForCausalLM,
                  TFXGLMModel,
                  TFXGLMPreTrainedModel,
              )


else:
       import sys

       UpperCAmelCase						:		Any			= _LazyModule(__name__, globals()["__file__"], _import_structure)

