




from itertools import count
from math import asin, pi, sqrt
def  snake_case_					(		SCREAMING_SNAKE_CASE_    )      ->			float:
							return (
							    (1 - 2 * point) * sqrt(point - point**2    ) + 2 * point + asin(sqrt(1 - point    )    )
							) / 4
def  snake_case_					(		SCREAMING_SNAKE_CASE_    )      ->			float:
							lowercase__  :	str        =							(circles_number + 1 - sqrt(2 * circles_number    )) / (
							    2 * (circles_number**2 + 1)
							)
							lowercase__  :	int        =							circles_number * intersection_y

							lowercase__  :	Optional[int]        =							intersection_x * intersection_y / 2
							lowercase__  :	List[Any]        =							circle_bottom_arc_integral(
							    1 / 2    ) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE_    )

							return triangle_area + concave_region_area
def  snake_case_					(		SCREAMING_SNAKE_CASE_ = 1 / 10_00    )      ->			int:
							lowercase__  :	List[Any]        =							(1 - pi / 4) / 4

							for n in count(1    ):
														if concave_triangle_area(SCREAMING_SNAKE_CASE_    ) / l_section_area < fraction:
																					return n

							return -1


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





from __future__ import annotations

import math
import random
def  snake_case_					(		SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    ,SCREAMING_SNAKE_CASE_    )      ->			list[int]:
							lowercase__  :	List[Any]        =							d * e - 1
							lowercase__  :	Any        =							0
							lowercase__  :	Dict        =							0
							while p == 0:
														lowercase__  :	Dict        =							random.randint(2    ,n - 1    )
														lowercase__  :	int        =							k
														while True:
																					if t % 2 == 0:
																												lowercase__  :	str        =							t // 2
																												lowercase__  :	int        =							(g**t) % n
																												lowercase__  :	List[Any]        =							math.gcd(x - 1    ,SCREAMING_SNAKE_CASE_    )
																												if x > 1 and y > 1:
																																			lowercase__  :	Any        =							y
																																			lowercase__  :	Optional[int]        =							n // y
																																			break  # find the correct factors
																					else:
																												break  # t is not divisible by 2, break and choose another g
							return sorted([p, q]    )


if __name__ == "__main__":
						import doctest

						doctest.testmod()