

import random


class      lowerCamelCase_ :




 def __init__(			self  ,  _UpperCAmelCase  ,  _UpperCAmelCase							):
   __UpperCAmelCase	:  Optional[Any]		=     x
   __UpperCAmelCase	:  int		=     y




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




 @classmethod
 def     a       (			cls							):
   return cls(x=random.random()  ,  y=random.random()							)





def  _snake_case		(snake_case_					:     Union[str, Any]  )							->		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

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













from __future__ import annotations






def 				A	(			a_				,a_   )	->		list[int]:
					__UpperCamelCase :   dict[int, int]									={}
					for index, val in enumerate(a_   ):
										__UpperCamelCase :   Union[str, Any]									=target - val
										if compl in chk_map:
															return [chk_map[compl], index]
										__UpperCamelCase :   List[Any]									=index
					return []


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(f"{two_sum([2, 7, 11, 15], 9) = }")

