

from itertools import product






def 					__lowercase      (     _A						,    _A			)     ->						Any:
      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   sides_number
      SCREAMING_SNAKE_CASE :      int       =   max_face_number * dice_number
      SCREAMING_SNAKE_CASE :      str       =   [0] * (max_total + 1)

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

      return totals_frequencies






def 					__lowercase      (     )     ->						Any:
      SCREAMING_SNAKE_CASE :      Tuple       =   total_frequency_distribution(
          sides_number=4						,    dice_number=9			)
      SCREAMING_SNAKE_CASE :      Tuple       =   total_frequency_distribution(
          sides_number=6						,    dice_number=6			)

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

      SCREAMING_SNAKE_CASE :      Tuple       =   (4**9) * (6**6)
      SCREAMING_SNAKE_CASE :      List[Any]       =   peter_wins_count / total_games_number

      SCREAMING_SNAKE_CASE :      str       =   round(_A						,    ndigits=7			)

      return rounded_peter_win_probability


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







from math import ceil






def 					__lowercase      (     _A = 1001			)     ->						int:
      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   1

      for i in range(1						,    int(ceil(n / 2.0			)			)			):
            SCREAMING_SNAKE_CASE :      Dict       =   2 * i + 1
            SCREAMING_SNAKE_CASE :      Optional[int]       =   2 * i
            SCREAMING_SNAKE_CASE :      str       =   total + 4 * odd**2 - 6 * even

      return total


if __name__ == "__main__":
  import sys

  if len(sys.argv) == 1:
    print(solution())
  else:
    try:
      UpperCAmelCase__ :     str				    =    int(sys.argv[1])
      print(solution(n))
    except ValueError:
      print("""Invalid entry - please enter a number""")




