from itertools import count
from math import asin, pi, sqrt






def    __lowerCamelCase	(		lowerCAmelCase__			):
       return (
           (1 - 2 * point) * sqrt(point - point**2			) + 2 * point + asin(sqrt(1 - point			)			)
       ) / 4






def    __lowerCamelCase	(		lowerCAmelCase__			):
       lowerCAmelCase__  			=      (circles_number + 1 - sqrt(2 * circles_number			)) / (
           2 * (circles_number**2 + 1)
       )
       lowerCAmelCase__  			=      circles_number * intersection_y

       lowerCAmelCase__  			=      intersection_x * intersection_y / 2
       lowerCAmelCase__  			=      circle_bottom_arc_integral(
           1 / 2			) - circle_bottom_arc_integral(lowerCAmelCase__			)

       return triangle_area + concave_region_area






def    __lowerCamelCase	(		lowerCAmelCase__ = 1 / 1_0_0_0			):
       lowerCAmelCase__  			=      (1 - pi / 4) / 4

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

       return -1


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

def    __lowerCamelCase	(		lowerCAmelCase__			):
       return " ".join([word[::-1] for word in input_str.split()]			)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
