"""simple docstring"""
from itertools import product







def 		__a  (      _SCREAMING_SNAKE_CASE = 15  )      ->int:
  a__:	float     				=      0.0
  a__:	float
  a__:	int
  a__:	int
  a__:	int
  a__:	int
  a__:	tuple[int, ...]

  for series in product(range(2  )						,	repeat=_SCREAMING_SNAKE_CASE  ):
    a__:	Optional[Any]     				=      series.count(1  )
    a__:	Optional[int]     				=      num_turns - num_blue
    if num_red >= num_blue:
      continue
    a__:	Tuple     				=      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() = }")










import random




class 							__A	:





				"""simple docstring"""







				def __init__(					self				,    lowerCamelCase__				,    lowerCamelCase__       ):




									"""simple docstring"""

									__UpperCamelCase :   Optional[Any]									=x
									__UpperCamelCase :   int									=y


				def  __lowercase				(					self       ):




									"""simple docstring"""

									return (self.x**2 + self.y**2) <= 1







				@classmethod
				def  __lowercase				(					cls       ):




									"""simple docstring"""

									return cls(x=random.random()				,    y=random.random()       )






def 				A	(			a_   )	->		float:
					if number_of_simulations < 1:
										raise ValueError('At least one simulation is necessary to estimate PI.'   )

					__UpperCamelCase :   List[str]									=0
					for _ in range(a_   ):
										__UpperCamelCase :   Optional[int]									=Point.random_unit_square()

										if random_point.is_in_unit_circle():
															number_in_unit_circle += 1

					return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
							# import doctest

							# doctest.testmod()
							from math import pi

							A_			:Optional[int]	    =		'''Please enter the desired number of Monte Carlo simulations: '''
							A_			:int	    =		estimate_pi(int(input(prompt).strip()))
							print(f"An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}")

