from itertools import product




def       __lowerCAmelCase      (						A_   : int						,	A_   : int					):
  __UpperCAmelCase						    =       sides_number
  __UpperCAmelCase						    =       max_face_number * dice_number
  __UpperCAmelCase						    =       [0] * (max_total + 1)

  __UpperCAmelCase						    =       1
  __UpperCAmelCase						    =       range(_A						,	max_face_number + 1					)
  for dice_numbers in product(_A						,	repeat=_A					):
    __UpperCAmelCase						    =       sum(_A					)
    totals_frequencies[total] += 1

  return totals_frequencies




def       __lowerCAmelCase      (						):
  __UpperCAmelCase						    =       total_frequency_distribution(
      sides_number=4						,	dice_number=9					)
  __UpperCAmelCase						    =       total_frequency_distribution(
      sides_number=6						,	dice_number=6					)

  __UpperCAmelCase						    =       0
  __UpperCAmelCase						    =       9
  __UpperCAmelCase						    =       4 * 9
  __UpperCAmelCase						    =       6
  for peter_total in range(_A						,	max_peter_total + 1					):
    peter_wins_count += peter_totals_frequencies[peter_total] * sum(
        colin_totals_frequencies[min_colin_total:peter_total]					)

  __UpperCAmelCase						    =       (4**9) * (6**6)
  __UpperCAmelCase						    =       peter_wins_count / total_games_number

  __UpperCAmelCase						    =       round(_A						,	ndigits=7					)

  return rounded_peter_win_probability


if __name__ == "__main__":
       print(F"{solution() = }")




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


a_							=      {
    """configuration_squeezebert""": [
        """SQUEEZEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """SqueezeBertConfig""",
        """SqueezeBertOnnxConfig""",
    ],
    """tokenization_squeezebert""": ["""SqueezeBertTokenizer"""],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a_							=      ["""SqueezeBertTokenizerFast"""]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a_							=      [
           """SQUEEZEBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
           """SqueezeBertForMaskedLM""",
           """SqueezeBertForMultipleChoice""",
           """SqueezeBertForQuestionAnswering""",
           """SqueezeBertForSequenceClassification""",
           """SqueezeBertForTokenClassification""",
           """SqueezeBertModel""",
           """SqueezeBertModule""",
           """SqueezeBertPreTrainedModel""",
       ]


if TYPE_CHECKING:
       from .configuration_squeezebert import (
           SQUEEZEBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
           SqueezeBertConfig,
           SqueezeBertOnnxConfig,
       )
       from .tokenization_squeezebert import SqueezeBertTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_squeezebert_fast import SqueezeBertTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_squeezebert import (
                  SQUEEZEBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
                  SqueezeBertForMaskedLM,
                  SqueezeBertForMultipleChoice,
                  SqueezeBertForQuestionAnswering,
                  SqueezeBertForSequenceClassification,
                  SqueezeBertForTokenClassification,
                  SqueezeBertModel,
                  SqueezeBertModule,
                  SqueezeBertPreTrainedModel,
              )

else:
       import sys

       a_							=      _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



