



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


def     UpperCamelCase(						__UpperCamelCase							:	float				):
		return (
		    (1 - 2 * point) * sqrt(point - point**2				) + 2 * point + asin(sqrt(1 - point				)				)
		) / 4


def     UpperCamelCase(						__UpperCamelCase							:	int				):
		lowerCAmelCase_    :  Optional[Any]             =				(circles_number + 1 - sqrt(2 * circles_number				)) / (
		    2 * (circles_number**2 + 1)
		)
		lowerCAmelCase_    :  Optional[int]             =				circles_number * intersection_y

		lowerCAmelCase_    :  Optional[int]             =				intersection_x * intersection_y / 2
		lowerCAmelCase_    :  str             =				circle_bottom_arc_integral(
		    1 / 2				) - circle_bottom_arc_integral(__UpperCamelCase				)

		return triangle_area + concave_region_area


def     UpperCamelCase(						__UpperCamelCase							:	float = 1 / 1000				):
		lowerCAmelCase_    :  List[str]             =				(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() = }''')










from __future__ import annotations

A__						:						Tuple          =      '''Alexander Joslin'''


def     UpperCamelCase(						__UpperCamelCase							:	int				):

		if number <= 0:
				lowerCAmelCase_    :  str             =				f"""n must be greater than 0. Got n = {number}"""
				raise ValueError(__UpperCamelCase				)

		lowerCAmelCase_    :  str             =				[number + 1] * (number + 1)

		# starting position
		lowerCAmelCase_    :  List[Any]             =				0
		for i in range(1  ,__UpperCamelCase				):
				lowerCAmelCase_    :  int             =				min(table[i + 1]  ,table[i] + 1				)
				# check if out of bounds
				if i * 2 <= number:
						lowerCAmelCase_    :  Union[str, Any]             =				min(table[i * 2]  ,table[i] + 1				)
				# check if out of bounds
				if i * 3 <= number:
						lowerCAmelCase_    :  Union[str, Any]             =				min(table[i * 3]  ,table[i] + 1				)
		return table[number]


if __name__ == "__main__":
						import doctest

						doctest.testmod()





