import random




class 				__lowerCAmelCase					:



 '''simple docstring'''

 def __init__(     self    :						Optional[Any]    ,     lowerCamelCase    :						float    ,     lowerCamelCase    :						float					)	->							None:
        _UpperCamelCase       :    Union[str, Any]					  =					x
        _UpperCamelCase       :    Optional[int]					  =					y

 def    __snake_case   (     self    :						Tuple					)	->							bool:
        return (self.x**2 + self.y**2) <= 1

 @classmethod
 def    __snake_case   (     cls    :						Dict					)	->							Optional[Any]:
        return cls(x=random.random()    ,     y=random.random()					)







def SCREAMING_SNAKE_CASE			(       lowercase_:		int			):
       if number_of_simulations < 1:
              raise ValueError('At least one simulation is necessary to estimate PI.'			)

       _UpperCamelCase       :    Dict					  =					0
       for _ in range(lowercase_			):
              _UpperCamelCase       :    Optional[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)}''')




def SCREAMING_SNAKE_CASE			(       lowercase_:		list[int]			):

       # validate:
       if not isinstance(lowercase_						,  lowercase_			) or not all(
           isinstance(lowercase_						,  lowercase_			) and item >= 0 for item in citations			):
              raise ValueError('The citations should be a list of non negative integers.'			)

       citations.sort()
       _UpperCamelCase       :    List[str]					  =					len(lowercase_			)

       for i in range(lowercase_			):
              if citations[len_citations - 1 - i] <= i:
                     return i

       return len_citations


if __name__ == "__main__":
 import doctest

 doctest.testmod()



