





'''simple docstring'''



import random






class 							__lowercase				:







	'''simple docstring'''

	def __init__(self   ,_lowerCamelCase   ,_lowerCamelCase       )							->							None:







				'''simple docstring'''





				__lowercase   =							x
				__lowercase   =							y


	def   _UpperCAmelCase   (self       )							->							bool:







				'''simple docstring'''





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


	@classmethod
	def   _UpperCAmelCase   (cls       )							->							List[Any]:







				'''simple docstring'''





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





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

			__lowercase   =							0
			for _ in range(lowerCamelCase_ ):
						__lowercase   =							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)}''')












'''simple docstring'''



import math




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5						,				int(math.sqrt(lowerCamelCase_ ) + 1 )						,				6 ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True




def       _lowerCAmelCase  ( lowerCamelCase_	:     int = 6_0_0_8_5_1_4_7_5_1_4_3 ):

			try:
						__lowercase   =							int(lowerCamelCase_ )
			except (TypeError, ValueError):
						raise TypeError('''Parameter n must be int or castable to int.''' )
			if n <= 0:
						raise ValueError('''Parameter n must be greater than or equal to one.''' )
			__lowercase   =							0
			if is_prime(lowerCamelCase_ ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase_ ):
						return n
			for i in range(3						,				int(math.sqrt(lowerCamelCase_ ) ) + 1						,				2 ):
						if n % i == 0:
									if is_prime(n // i ):
												__lowercase   =							n // i
												break
									elif is_prime(lowerCamelCase_ ):
												__lowercase   =							i
			return max_number


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





