



'''simple docstring'''





import math






class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     List[Any]      ,     _a				:     Tuple      ,     _a				:     Any      ,     _a				:     Dict       ) -> Union[str, Any]:
    __lowerCamelCase	:	List[Any]   	=			x
    __lowerCamelCase	:	int   	=			y
    __lowerCamelCase	:	Dict   	=			z




  def __repr__(			self				:     List[str]       ) -> str:
    return f'Point({self.x}, {self.y}, {self.z})'




def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase	)				->				float:
  return math.sqrt(abs((b.x - a.x) ** 2 + (b.y - a.y) ** 2 + (b.z - a.z) ** 2	)	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()











'''simple docstring'''





import random






class  lowerCamelCase_   :
  """simple docstring"""




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




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




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




def 	a_					(							_lowerCAmelCase	)				->				float:
  if number_of_simulations < 1:
    raise ValueError('At least one simulation is necessary to estimate PI.'	)

  __lowerCamelCase	:	Optional[int]   	=			0
  for _ in range(_lowerCAmelCase	):
    __lowerCamelCase	:	Dict   	=			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)}''')






