

'''simple docstring'''

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





def 				A_					(	snake_case	):
  return (
      (1 - 2 * point) * sqrt(point - point**2	) + 2 * point + asin(sqrt(1 - point	)	)
  ) / 4





def 				A_					(	snake_case	):
  SCREAMING_SNAKE_CASE:str   =   (circles_number + 1 - sqrt(2 * circles_number	)) / (
      2 * (circles_number**2 + 1)
  )
  SCREAMING_SNAKE_CASE:int   =   circles_number * intersection_y

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

  return triangle_area + concave_region_area





def 				A_					(	snake_case = 1 / 1000	):
  SCREAMING_SNAKE_CASE: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() = }''')









'''simple docstring'''

from collections import Counter





def 				A_					(	snake_case	):
  return sum(socks_by_color // 2 for socks_by_color in Counter(snake_case	).values()	)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    A_      =							[int(x) for x in input("Enter socks by color :").rstrip().split()]
    print(f'''sock_merchant({colors}) = {sock_merchant(colors)}''')






