




from __future__ import annotations

from fractions import Fraction





def      __a     (       _UpperCamelCase:   int ,						_UpperCamelCase:   int   )						->			bool:

     """simple docstring"""




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





def      __a     (       _UpperCamelCase:   int   )						->			list[str]:

     """simple docstring"""




     _snake_case							=				[]
     _snake_case							=				11
     _snake_case							=				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
          _snake_case							=				10
     return solutions





def      __a     (       _UpperCamelCase:   int = 2   )						->			int:

     """simple docstring"""




     _snake_case							=				1.0
     for fraction in fraction_list(_UpperCamelCase   ):
          _snake_case							=				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_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase_						:      List[Any]       =						{
    '''configuration_convbert''': ['''CONVBERT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''ConvBertConfig''', '''ConvBertOnnxConfig'''],
    '''tokenization_convbert''': ['''ConvBertTokenizer'''],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_						:      Optional[Any]       =						['''ConvBertTokenizerFast''']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_						:      Optional[int]       =						[
       '''CONVBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''ConvBertForMaskedLM''',
       '''ConvBertForMultipleChoice''',
       '''ConvBertForQuestionAnswering''',
       '''ConvBertForSequenceClassification''',
       '''ConvBertForTokenClassification''',
       '''ConvBertLayer''',
       '''ConvBertModel''',
       '''ConvBertPreTrainedModel''',
       '''load_tf_weights_in_convbert''',
   ]


try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase_						:      Tuple       =						[
       '''TF_CONVBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''TFConvBertForMaskedLM''',
       '''TFConvBertForMultipleChoice''',
       '''TFConvBertForQuestionAnswering''',
       '''TFConvBertForSequenceClassification''',
       '''TFConvBertForTokenClassification''',
       '''TFConvBertLayer''',
       '''TFConvBertModel''',
       '''TFConvBertPreTrainedModel''',
   ]


if TYPE_CHECKING:
   from .configuration_convbert import CONVBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, ConvBertConfig, ConvBertOnnxConfig
   from .tokenization_convbert import ConvBertTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_convbert_fast import ConvBertTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_convbert import (
          CONVBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
          ConvBertForMaskedLM,
          ConvBertForMultipleChoice,
          ConvBertForQuestionAnswering,
          ConvBertForSequenceClassification,
          ConvBertForTokenClassification,
          ConvBertLayer,
          ConvBertModel,
          ConvBertPreTrainedModel,
          load_tf_weights_in_convbert,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_convbert import (
          TF_CONVBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFConvBertForMaskedLM,
          TFConvBertForMultipleChoice,
          TFConvBertForQuestionAnswering,
          TFConvBertForSequenceClassification,
          TFConvBertForTokenClassification,
          TFConvBertLayer,
          TFConvBertModel,
          TFConvBertPreTrainedModel,
      )


else:
   import sys

   UpperCamelCase_						:      Tuple       =						_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


