



'''simple docstring'''
from __future__ import annotations


def 	lowercase_						( lowerCAmelCase__						:	List[str]			):

			"""simple docstring"""





			__UpperCAmelCase :   Optional[int]    					=  [0] * max_one

			for i in range(0      ,				a_			):
						__UpperCAmelCase :   Optional[int]    					=  i

			for i in range(2      ,				a_			):
						if totients[i] == i:
									for j in range(a_      ,				a_      ,				a_			):
												totients[j] -= totients[j] // i

			return totients


def 	lowercase_						( lowerCAmelCase__						:	int      ,				lowerCAmelCase__						:	List[str]			):

			"""simple docstring"""





			return sorted(str(a_			)			) == sorted(str(a_			)			)


def 	lowercase_						( lowerCAmelCase__						:	Tuple = 10000000			):

			"""simple docstring"""





			__UpperCAmelCase :   List[str]    					=  1  # i
			__UpperCAmelCase :   int    					=  0  # φ(i)
			__UpperCAmelCase :   List[str]    					=  get_totients(max_n + 1			)

			for i in range(2      ,				max_n + 1			):
						__UpperCAmelCase :   Optional[Any]    					=  totients[i]

						if i * min_denominator < min_numerator * t and has_same_digits(a_      ,				a_			):
									__UpperCAmelCase :   List[Any]    					=  i
									__UpperCAmelCase :   int    					=  t

			return min_numerator


if __name__ == "__main__":
					print(F'{solution() = }')












import random




class 							__A	:





				"""simple docstring"""







				def __init__(					self				,    lowerCamelCase__				,    lowerCamelCase__       ):




									"""simple docstring"""

									__UpperCamelCase :   Optional[Any]									=x
									__UpperCamelCase :   int									=y


				def  __lowercase				(					self       ):




									"""simple docstring"""

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







				@classmethod
				def  __lowercase				(					cls       ):




									"""simple docstring"""

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






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

					__UpperCamelCase :   List[str]									=0
					for _ in range(a_   ):
										__UpperCamelCase :   Optional[int]									=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

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

