


"""simple docstring"""


from __future__ import annotations

import random


class  snake_case		:


   '''simple docstring'''

   A_						:     str									=			6


   def __init__(     self			:					List[str]  ):

     '''simple docstring'''
     __A						      =			list(range(1,	Dice.NUM_SIDES + 1  )  )






   def     _SCREAMING_SNAKE_CASE    (     self			:					Tuple  ):

     '''simple docstring'''
     return random.choice(self.sides  )





def  lowerCAmelCase    (   __UpperCamelCase		,	__UpperCamelCase = 2			):




  """simple docstring"""







  __A						      =			[Dice() for i in range(__UpperCamelCase			)]
  __A						      =			[0] * (len(__UpperCamelCase			) * Dice.NUM_SIDES + 1)
  for _ in range(__UpperCamelCase			):
    count_of_sum[sum(dice.roll() for dice in dices			)] += 1
  __A						      =			[round((count * 1_0_0) / num_throws		,	2			) for count in count_of_sum]
  return probability[num_dice:]  # remove probability of sums that never appear


if __name__ == "__main__":
       import doctest

       doctest.testmod()












"""simple docstring"""


from itertools import product



def  lowerCAmelCase    (   __UpperCamelCase = 1_5			):




  """simple docstring"""







  __A						      =			0.0
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42
  __A						      =			42

  for series in product(range(2			)		,	repeat=__UpperCamelCase			):
    __A						      =			series.count(1			)
    __A						      =			num_turns - num_blue
    if num_red >= num_blue:
      continue
    __A						      =			1.0
    for ind, col in enumerate(__UpperCamelCase		,	2			):
      if col == 0:
        prob *= (ind - 1) / ind
      else:
        prob *= 1 / ind

    total_prob += prob

  return int(1 / total_prob			)


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




