

import random

class  a     :


						def __init__(				self  ,    A_  ,    A_		):







										'''simple docstring'''


										_UpperCAmelCase				:						List[str]       						=			x
										_UpperCAmelCase				:						Dict       						=			y


						def 				_UpperCAmelCase (				self		):







										'''simple docstring'''


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





						@classmethod
						def 				_UpperCAmelCase (				cls		):







										'''simple docstring'''


										return cls(x=random.random()  ,    y=random.random()		)







def 							__SCREAMING_SNAKE_CASE							( lowerCAmelCase:     int       )      ->				float:
				if number_of_simulations < 1:
								raise ValueError("At least one simulation is necessary to estimate PI."       )

				_UpperCAmelCase				:						Any       						=			0
				for _ in range(lowerCAmelCase       ):
								_UpperCAmelCase				:						Tuple       						=			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

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





from __future__ import annotations

SCREAMING_SNAKE_CASE_						=					'Alexander Joslin'

def 							__SCREAMING_SNAKE_CASE							( lowerCAmelCase:     int       )      ->				int:

				if number <= 0:
								_UpperCAmelCase				:						Optional[Any]       						=			F'n must be greater than 0. Got n = {number}'
								raise ValueError(lowerCAmelCase       )

				_UpperCAmelCase				:						Dict       						=			[number + 1] * (number + 1)

				# starting position
				_UpperCAmelCase				:						Dict       						=			0
				for i in range(1     ,					lowerCAmelCase       ):
								_UpperCAmelCase				:						int       						=			min(table[i + 1]     ,					table[i] + 1       )
								# check if out of bounds
								if i * 2 <= number:
												_UpperCAmelCase				:						int       						=			min(table[i * 2]     ,					table[i] + 1       )
								# check if out of bounds
								if i * 3 <= number:
												_UpperCAmelCase				:						int       						=			min(table[i * 3]     ,					table[i] + 1       )
				return table[number]


if __name__ == "__main__":
					import doctest

					doctest.testmod()


