import torch
from torch import autograd



class        lowercase_  (  autograd.Function						):



	"""simple docstring"""





	@staticmethod
	def       SCREAMING_SNAKE_CASE_    (							__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->List[Any]:
								lowerCAmelCase     		=		inputs.numel()
								lowerCAmelCase     		=		int(0.0_0_5 * nb_elems    ) + 1
								if sigmoid:
															lowerCAmelCase     		=		(torch.sigmoid(lowerCAmelCase__    ) > threshold).type(inputs.type()    )
								else:
															lowerCAmelCase     		=		(inputs > threshold).type(inputs.type()    )
								if mask.sum() < nb_min:
															# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
															lowerCAmelCase     		=		inputs.flatten().kthvalue(max(nb_elems - nb_min		,      1    )    ).values
															lowerCAmelCase     		=		(inputs > k_threshold).type(inputs.type()    )
								return mask




	@staticmethod
	def       SCREAMING_SNAKE_CASE_    (							__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->Optional[int]:
								return gradOutput, None, None



class        lowercase_  (  autograd.Function						):



	"""simple docstring"""





	@staticmethod
	def       SCREAMING_SNAKE_CASE_    (							__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->str:
								lowerCAmelCase     		=		inputs.clone()
								lowerCAmelCase		,				lowerCAmelCase     		=		inputs.flatten().sort(descending=lowerCAmelCase__    )
								lowerCAmelCase     		=		int(threshold * inputs.numel()    )

								# flat_out and mask access the same memory.
								lowerCAmelCase     		=		mask.flatten()
								lowerCAmelCase     		=		0
								lowerCAmelCase     		=		1
								return mask




	@staticmethod
	def       SCREAMING_SNAKE_CASE_    (							__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->str:
								return gradOutput, None



class        lowercase_  (  _UpperCAmelCase						):



	"""simple docstring"""





	@staticmethod
	def       SCREAMING_SNAKE_CASE_    (							__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->List[str]:
								lowerCAmelCase     		=		inputs.clone()
								lowerCAmelCase		,				lowerCAmelCase     		=		inputs.abs().flatten().sort(descending=lowerCAmelCase__    )
								lowerCAmelCase     		=		int(threshold * inputs.numel()    )

								# flat_out and mask access the same memory.
								lowerCAmelCase     		=		mask.flatten()
								lowerCAmelCase     		=		0
								lowerCAmelCase     		=		1
								return mask




import random




class        lowercase_  :



	"""simple docstring"""





	def __init__(							self		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->None:
								lowerCAmelCase     		=		x
								lowerCAmelCase     		=		y


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




	@classmethod
	def       SCREAMING_SNAKE_CASE_    (							cls    )						->Tuple:
								return cls(x=random.random()		,      y=random.random()    )

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

							lowerCAmelCase     		=		0
							for _ in range(snake_case__							):
														lowerCAmelCase     		=		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

	lowercase__      :    int          =     '''Please enter the desired number of Monte Carlo simulations: '''
	lowercase__      :    Dict          =     estimate_pi(int(input(prompt).strip()))
	print(f'An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}')



