





"""simple docstring"""






import random



class 						lowerCAmelCase       :






       def __init__( self     ,	a__     ,	a__  ):
              _UpperCAmelCase			     =  x
              _UpperCAmelCase			     =  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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							float:






       """simple docstring"""




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

       _UpperCAmelCase			     =  0
       for _ in range(SCREAMING_SNAKE_CASE				):
              _UpperCAmelCase			     =  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

    lowerCAmelCase_      =				'''Please enter the desired number of Monte Carlo simulations: '''
    lowerCAmelCase_      =				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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							bool:






       """simple docstring"""




       if not isinstance(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				):
              raise ValueError('Input series is not valid, valid series - [2, 4, 8]'				)
       if len(SCREAMING_SNAKE_CASE				) == 0:
              raise ValueError('Input list must be a non empty list'				)
       if len(SCREAMING_SNAKE_CASE				) == 1:
              return True
       try:
              _UpperCAmelCase			     =  series[1] / series[0]
              for index in range(len(SCREAMING_SNAKE_CASE				) - 1				):
                     if series[index + 1] / series[index] != common_ratio:
                            return False
       except ZeroDivisionError:
              return False
       return True

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							float:






       """simple docstring"""




       if not isinstance(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				):
              raise ValueError('Input series is not valid, valid series - [2, 4, 8]'				)
       if len(SCREAMING_SNAKE_CASE				) == 0:
              raise ValueError('Input list must be a non empty list'				)
       _UpperCAmelCase			     =  1
       for value in series:
              answer *= value
       return pow(SCREAMING_SNAKE_CASE,1 / len(SCREAMING_SNAKE_CASE				)				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()






