
"""simple docstring"""

import random






class 			_lowercase  :




	def __init__(					self						,					UpperCAmelCase_						,					UpperCAmelCase_   )						->				None:
			lowerCamelCase	:     int            =       x
			lowerCamelCase	:     Optional[Any]            =       y




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




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


def 						UpperCAmelCase   (						a_     ):





		'''simple docstring'''


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

		lowerCamelCase	:     Any            =       0
		for _ in range(__lowerCamelCase     ):
				lowerCamelCase	:     str            =       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				=					'Please enter the desired number of Monte Carlo simulations: '
					_A				=					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"""

from __future__ import annotations

lowercase           =							{1: 1}






def _lowerCAmelCase						(	__lowerCamelCase:int ):

						'''simple docstring'''






						if n in COLLATZ_SEQUENCE_LENGTHS:
												return COLLATZ_SEQUENCE_LENGTHS[n]
						__magic_name__      =  n // 2 if n % 2 == 0 else 3 * n + 1
						__magic_name__      =  collatz_sequence_length(__lowerCamelCase ) + 1
						__magic_name__      =  sequence_length
						return sequence_length






def _lowerCAmelCase						(	__lowerCamelCase:int = 1_0_0_0_0_0_0 ):

						'''simple docstring'''






						__magic_name__      =  max((collatz_sequence_length(__lowerCamelCase ), i) for i in range(1			,    __lowerCamelCase ) )
						return result[1]


if __name__ == "__main__":
			print(solution(int(input().strip())))



