




from itertools import product



def        __lowercase       (				_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     )			->       list[int]:


      '''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(_SCREAMING_SNAKE_CASE			,						max_face_number + 1     )
      for dice_numbers in product(_SCREAMING_SNAKE_CASE			,						repeat=_SCREAMING_SNAKE_CASE     ):
            SCREAMING_SNAKE_CASE		=						sum(_SCREAMING_SNAKE_CASE     )
            totals_frequencies[total] += 1

      return totals_frequencies



def        __lowercase       (				)			->       float:


      '''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(_SCREAMING_SNAKE_CASE			,						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(_SCREAMING_SNAKE_CASE			,						ndigits=7     )

      return rounded_peter_win_probability


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









from __future__ import annotations



def        __lowercase       (				_SCREAMING_SNAKE_CASE     )			->       list[int]:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						2
      SCREAMING_SNAKE_CASE		=						[]
      while i * i <= n:
            if n % i:
                  i += 1
            else:
                  n //= i
                  factors.append(_SCREAMING_SNAKE_CASE     )
      if n > 1:
            factors.append(_SCREAMING_SNAKE_CASE     )
      return factors


if __name__ == "__main__":
      import doctest

      doctest.testmod()


