from itertools import product

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: int  ):


      '''simple docstring'''



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

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

      return totals_frequencies

def     _SCREAMING_SNAKE_CASE    (							):


      '''simple docstring'''



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

      lowerCamelCase_	  =					0
      lowerCamelCase_	  =					9
      lowerCamelCase_	  =					4 * 9
      lowerCamelCase_	  =					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]  )

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

      lowerCamelCase_	  =					round(lowercase			,							ndigits=7  )

      return rounded_peter_win_probability


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









from __future__ import annotations

from fractions import Fraction

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: int  ):


      '''simple docstring'''



      return (
          num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
      )

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int  ):


      '''simple docstring'''



      lowerCamelCase_	  =					[]
      lowerCamelCase_	  =					11
      lowerCamelCase_	  =					int('1' + '0' * digit_len  )
      for num in range(lowercase			,							lowercase  ):
            while den <= 99:
                  if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                        if is_digit_cancelling(lowercase			,							lowercase  ):
                              solutions.append(f"""{num}/{den}"""  )
                  den += 1
            num += 1
            lowerCamelCase_	  =					10
      return solutions

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int = 2  ):


      '''simple docstring'''



      lowerCamelCase_	  =					1.0
      for fraction in fraction_list(lowercase  ):
            lowerCamelCase_	  =					Fraction(lowercase  )
            result *= frac.denominator / frac.numerator
      return int(lowercase  )


if __name__ == "__main__":
 print(solution())



