






'''simple docstring'''


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






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






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 __a    :	Any									=						(circles_number + 1 - sqrt(2 * circles_number		)) / (
     2 * (circles_number**2 + 1)
 )
 __a    :	Optional[Any]									=						circles_number * intersection_y

 __a    :	Union[str, Any]									=						intersection_x * intersection_y / 2
 __a    :	Dict									=						circle_bottom_arc_integral(
     1 / 2		) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE__		)

 return triangle_area + concave_region_area






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__ = 1 / 1000		):
 __a    :	Union[str, 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() = }")












'''simple docstring'''


def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__ = 30		):
 __a    :	Tuple									=						exponent + 2
 __a    :	str									=						(1 + 5**0.5) / 2
 __a    :	Any									=						(phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

 return int(SCREAMING_SNAKE_CASE__		)


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




