

from itertools import product

def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int					, lowerCAmelCase:					int	)				->    list[int]:
				_UpperCAmelCase    :						Union[str, Any]							=      sides_number
				_UpperCAmelCase    :						Dict							=      max_face_number * dice_number
				_UpperCAmelCase    :						List[str]							=      [0] * (max_total + 1)

				_UpperCAmelCase    :						str							=      1
				_UpperCAmelCase    :						Optional[Any]							=      range(lowerCAmelCase					, max_face_number + 1	)
				for dice_numbers in product(lowerCAmelCase					, repeat=lowerCAmelCase	):
								_UpperCAmelCase    :						Union[str, Any]							=      sum(lowerCAmelCase	)
								totals_frequencies[total] += 1

				return totals_frequencies

def 							__SCREAMING_SNAKE_CASE							(			)				->    float:
				_UpperCAmelCase    :						Optional[Any]							=      total_frequency_distribution(
				    sides_number=4					, dice_number=9	)
				_UpperCAmelCase    :						str							=      total_frequency_distribution(
				    sides_number=6					, dice_number=6	)

				_UpperCAmelCase    :						Optional[Any]							=      0
				_UpperCAmelCase    :						int							=      9
				_UpperCAmelCase    :						Any							=      4 * 9
				_UpperCAmelCase    :						Any							=      6
				for peter_total in range(lowerCAmelCase					, max_peter_total + 1	):
								peter_wins_count += peter_totals_frequencies[peter_total] * sum(
								    colin_totals_frequencies[min_colin_total:peter_total]	)

				_UpperCAmelCase    :						str							=      (4**9) * (6**6)
				_UpperCAmelCase    :						str							=      peter_wins_count / total_games_number

				_UpperCAmelCase    :						Dict							=      round(lowerCAmelCase					, ndigits=7	)

				return rounded_peter_win_probability


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





def 							__SCREAMING_SNAKE_CASE							(			lowerCAmelCase:					int	)				->    int:
				if not isinstance(lowerCAmelCase					, lowerCAmelCase	):
								raise TypeError("Input value must be an 'int' type"	)

				_UpperCAmelCase    :						List[Any]							=      0
				while number:
								position += 1
								number >>= 1

				return position


if __name__ == "__main__":
					import doctest

					doctest.testmod()


