




import random
class 				__snake_case     :



				def __init__(					self					:						Any						,		_UpperCAmelCase					:						float						,		_UpperCAmelCase					:						float					)     ->			Optional[int]:





								'''simple docstring'''




								_lowerCAmelCase			:			Dict        =					x
								_lowerCAmelCase			:			int        =					y



				def 					SCREAMING_SNAKE_CASE				(					self					:						List[Any]					)     ->			int:





								'''simple docstring'''




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



				@classmethod
				def 					SCREAMING_SNAKE_CASE				(					cls					:						List[str]					)     ->			Tuple:





								'''simple docstring'''




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






def 							_UpperCAmelCase     (UpperCamelCase_       :       List[str]				):
				'''simple docstring'''


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

				_lowerCAmelCase			:			Optional[Any]        =					0
				for _ in range(lowercase_				):
								_lowerCAmelCase			:			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

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







def     __SCREAMING_SNAKE_CASE      (     lowercase_    ,   lowercase_					)				->		int:

    """simple docstring"""


    __UpperCamelCase     						=  1.0
    for i in range(1    ,   r + 1					):
        ret *= (n + 1 - i) / i
    return round(lowercase_					)




def     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		int:

    """simple docstring"""


    return choose(8 + n    ,   lowercase_					) + choose(9 + n    ,   lowercase_					) - 10




def     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		int:

    """simple docstring"""


    return sum(non_bouncy_exact(lowercase_					) for i in range(1    ,   n + 1					)					)




def     __SCREAMING_SNAKE_CASE      (     lowercase_ = 1_00					)				->		int:

    """simple docstring"""


    return non_bouncy_upto(lowercase_					)


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






