




'''simple docstring'''





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





def UpperCAmelCase						(					UpperCAmelCase_	):
				return (
				    (1 - 2 * point) * sqrt(point - point**2	) + 2 * point + asin(sqrt(1 - point	)	)
				) / 4





def UpperCAmelCase						(					UpperCAmelCase_	):
				_a							:       str       					=			(circles_number + 1 - sqrt(2 * circles_number	)) / (
				    2 * (circles_number**2 + 1)
				)
				_a							:       int       					=			circles_number * intersection_y

				_a							:       Union[str, Any]       					=			intersection_x * intersection_y / 2
				_a							:       Optional[Any]       					=			circle_bottom_arc_integral(
				    1 / 2	) - circle_bottom_arc_integral(UpperCAmelCase_	)

				return triangle_area + concave_region_area





def UpperCAmelCase						(					UpperCAmelCase_ = 1 / 1_000	):
				_a							:       Optional[int]       					=			(1 - pi / 4) / 4

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

				return -1


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








'''simple docstring'''





def UpperCAmelCase						(					UpperCAmelCase_	):
    _a							:       List[Any]       					=			len(UpperCAmelCase_	)
    for cycle_start in range(0      ,  array_len - 1	):
        _a							:       int       					=			array[cycle_start]

        _a							:       int       					=			cycle_start
        for i in range(cycle_start + 1      ,  UpperCAmelCase_	):
            if array[i] < item:
                pos += 1

        if pos == cycle_start:
            continue

        while item == array[pos]:
            pos += 1

        _a					,   _a							:       List[str]       					=			item, array[pos]
        while pos != cycle_start:
            _a							:       Any       					=			cycle_start
            for i in range(cycle_start + 1      ,  UpperCAmelCase_	):
                if array[i] < item:
                    pos += 1

            while item == array[pos]:
                pos += 1

            _a					,   _a							:       List[Any]       					=			item, array[pos]

    return array


if __name__ == "__main__":
  assert cycle_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
  assert cycle_sort([0, 1, -1_0, 1_5, 2, -2]) == [-1_0, -2, 0, 1, 2, 1_5]


