

'''simple docstring'''



from itertools import product







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      sides_number
     __SCREAMING_SNAKE_CASE     =      max_face_number * dice_number
     __SCREAMING_SNAKE_CASE     =      [0] * (max_total + 1)

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

     return totals_frequencies







def    a__       (  ):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      total_frequency_distribution(
         sides_number=4      ,    dice_number=9						)
     __SCREAMING_SNAKE_CASE     =      total_frequency_distribution(
         sides_number=6      ,    dice_number=6						)

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

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

     __SCREAMING_SNAKE_CASE     =      round(lowercase__      ,    ndigits=7						)

     return rounded_peter_win_probability


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










from __future__ import annotations


def        _UpperCamelCase							(      lowercase__      ):
						__SCREAMING_SNAKE_CASE						:     Dict					=		0.00
						__SCREAMING_SNAKE_CASE						:     List[str]					=		0
						for resistor in resistors:
												if resistor <= 0:
																		__SCREAMING_SNAKE_CASE						:     Any					=		F'''Resistor at index {index} has a negative or zero value!'''
																		raise ValueError(lowercase__      )
												first_sum += 1 / float(lowercase__      )
												index += 1
						return 1 / first_sum


def        _UpperCamelCase							(      lowercase__      ):
						__SCREAMING_SNAKE_CASE						:     Tuple					=		0.00
						__SCREAMING_SNAKE_CASE						:     int					=		0
						for resistor in resistors:
												sum_r += resistor
												if resistor < 0:
																		__SCREAMING_SNAKE_CASE						:     Tuple					=		F'''Resistor at index {index} has a negative value!'''
																		raise ValueError(lowercase__      )
												index += 1
						return sum_r


if __name__ == "__main__":
						import doctest

						doctest.testmod()
