


from itertools import product
def 							_UpperCAmelCase				(UpperCamelCase__     :  int				,							UpperCamelCase__     :  int						):
       _A      :       Dict				    = sides_number
       _A      :       Any				    = max_face_number * dice_number
       _A      :       Optional[int]				    = [0] * (max_total + 1)

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

       return totals_frequencies
def 							_UpperCAmelCase				():
       _A      :       Any				    = total_frequency_distribution(
           sides_number=4				,							dice_number=9						)
       _A      :       Tuple				    = total_frequency_distribution(
           sides_number=6				,							dice_number=6						)

       _A      :       Any				    = 0
       _A      :       int				    = 9
       _A      :       List[str]				    = 4 * 9
       _A      :       Dict				    = 6
       for peter_total in range(UpperCamelCase__				,							max_peter_total + 1						):
              peter_wins_count += peter_totals_frequencies[peter_total] * sum(
                  colin_totals_frequencies[min_colin_total:peter_total]						)

       _A      :       Dict				    = (4**9) * (6**6)
       _A      :       List[str]				    = peter_wins_count / total_games_number

       _A      :       Dict				    = round(UpperCamelCase__				,							ndigits=7						)

       return rounded_peter_win_probability


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

"""simple docstring"""






from ..utils import DummyObject, requires_backends





class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   str							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   List[Any]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   Optional[Any]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   int							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   List[str]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   Optional[Any]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)



