





'''simple docstring'''







from itertools import product





def 							lowerCamelCase_   (	SCREAMING_SNAKE_CASE__   :      int = 15 )			->						int:
						UpperCAmelCase_      :   float      =	0.0
						UpperCAmelCase_      :   float
						UpperCAmelCase_      :   int
						UpperCAmelCase_      :   int
						UpperCAmelCase_      :   int
						UpperCAmelCase_      :   int
						UpperCAmelCase_      :   tuple[int, ...]

						for series in product(range(2 ),      repeat=SCREAMING_SNAKE_CASE__ ):
												UpperCAmelCase_      :   str      =	series.count(1 )
												UpperCAmelCase_      :   Dict      =	num_turns - num_blue
												if num_red >= num_blue:
																		continue
												UpperCAmelCase_      :   int      =	1.0
												for ind, col in enumerate(SCREAMING_SNAKE_CASE__,      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() = }''')








"""simple docstring"""





def     _A    (    UpperCamelCase_	:			int,     UpperCamelCase_	:			int = 1000)      ->		str:
   '''simple docstring'''


   if (not isinstance(UpperCamelCase_,     UpperCamelCase_)) or (digit_position <= 0):
      raise ValueError("Digit position must be a positive integer")
   elif (not isinstance(UpperCamelCase_,     UpperCamelCase_)) or (precision < 0):
      raise ValueError("Precision must be a nonnegative integer")

   # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
   # accurate
   __lowercase								=		(
       4 * _subsum(UpperCamelCase_,     1,     UpperCamelCase_)
       - 2 * _subsum(UpperCamelCase_,     4,     UpperCamelCase_)
       - _subsum(UpperCamelCase_,     5,     UpperCamelCase_)
       - _subsum(UpperCamelCase_,     6,     UpperCamelCase_)
   )

   # return the first hex digit of the fractional part of the result
   return hex(int((sum_result % 1) * 16))[2:]




def     _A    (    UpperCamelCase_	:			int,     UpperCamelCase_	:			int,     UpperCamelCase_	:			int)      ->		float:
   '''simple docstring'''


   __lowercase								=		0.0
   for sum_index in range(digit_pos_to_extract + precision):
      __lowercase								=		8 * sum_index + denominator_addend
      if sum_index < digit_pos_to_extract:
         # if the exponential term is an integer and we mod it by the denominator
         # before dividing, only the integer part of the sum will change;
         # the fractional part will not
         __lowercase								=		pow(
             16,     digit_pos_to_extract - 1 - sum_index,     UpperCamelCase_)
      else:
         __lowercase								=		pow(16,     digit_pos_to_extract - 1 - sum_index)
      total += exponential_term / denominator
   return total


if __name__ == "__main__":
   import doctest

   doctest.testmod()




