






"""simple docstring"""





import random







class 						_a  :





   '''simple docstring'''






   def __init__(       self					, UpperCAmelCase_					, UpperCAmelCase_)			->   Optional[int]:




          '''simple docstring'''




          lowercase__:							int         =     x
          lowercase__:							List[Any]         =     y





   def __lowercase							(       self)			->   List[str]:




          '''simple docstring'''




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





   @classmethod
   def __lowercase							(       cls)			->   Tuple:




          '''simple docstring'''




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







def 							A(    snake_case_						):
       """simple docstring"""





       if number_of_simulations < 1:
              raise ValueError("At least one simulation is necessary to estimate PI."						)

       lowercase__:							Any         =     0
       for _ in range(snake_case_						):
              lowercase__:							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

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








'''simple docstring'''







def 				_snake_case (		lowercase = 1_0_0_0						)       ->       int:
				__a       :     Any								=	[]
				__a       :     List[Any]								=	[]
				__a       :     Any								=	3
				__a       :     Optional[Any]								=	5
				__a       :     Optional[Any]								=	1
				while True:
								__a       :     List[str]								=	z * temp
								if result < n:
												zmulti.append(lowercase						)
												temp += 1
								else:
												__a       :     Any								=	1
												break
				while True:
								__a       :     Optional[int]								=	x * temp
								if result < n:
												xmulti.append(lowercase						)
												temp += 1
								else:
												break
				__a       :     Any								=	list(set(xmulti + zmulti						)						)
				return sum(lowercase						)


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