






import random
class   UpperCamelCase			:







		"""simple docstring"""



		def __init__(	self		:							List[str]    ,_SCREAMING_SNAKE_CASE		:							Optional[int]    ,_SCREAMING_SNAKE_CASE		:							str		)     -> List[str]:


						'''simple docstring'''
						A									=   x
						A									=   y
		def    A(	self		:							Dict		)     -> Any:


						'''simple docstring'''
						return (self.x**2 + self.y**2) <= 1







		@classmethod
		def    A(	cls		:							str		)     -> Union[str, Any]:


						'''simple docstring'''
						return cls(x=random.random()    ,y=random.random()		)







def   snake_case		(				UpperCAmelCase						:							List[Any] ):




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

				A									=   0
				for _ in range(UpperCAmelCase ):
								A									=   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()






