
'''simple docstring'''

import random


class   a_  :




       def __init__(     self   ,   snake_case_   ,   snake_case_  ):
         _lowerCAmelCase       :  List[str]   				=					x
         _lowerCAmelCase       :  List[str]   				=					y




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







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



def 	_UpperCAmelCase				(  _lowerCamelCase						:       int		)    ->						float:
  if number_of_simulations < 1:
    raise ValueError("""At least one simulation is necessary to estimate PI."""		)

  _lowerCAmelCase       :  Tuple   				=					0
  for _ in range(_lowerCamelCase		):
    _lowerCAmelCase       :  Union[str, Any]   				=					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 	_UpperCAmelCase				(  _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int  ,      _lowerCamelCase						:       int		)    ->						float:
  if common_ratio == 1:
    # Formula for sum if common ratio is 1
    return num_of_terms * first_term

  # Formula for finding sum of n terms of a GeometricProgression
  return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)


