



'''simple docstring'''




import math
from collections.abc import Callable


def 				lowerCAmelCase_   (	_lowerCamelCase:   Callable[[float], float]       ,      _lowerCamelCase:   float       ,      _lowerCamelCase:   float					):
		__SCREAMING_SNAKE_CASE       :		float           =		xa
		__SCREAMING_SNAKE_CASE       :		float           =		xa
		while True:
				if x_n == x_na or function(_lowerCamelCase					) == function(_lowerCamelCase					):
						raise ZeroDivisionError("""float division by zero, could not find root"""					)
				__SCREAMING_SNAKE_CASE       :		float           =		x_na - (
				    function(_lowerCamelCase					) / ((function(_lowerCamelCase					) - function(_lowerCamelCase					)) / (x_na - x_n))
				)
				if abs(x_na - x_na					) < 10**-5:
						return x_na
				__SCREAMING_SNAKE_CASE       :		Any           =		x_na
				__SCREAMING_SNAKE_CASE       :		Tuple           =		x_na


def 				lowerCAmelCase_   (	_lowerCamelCase:   float					):
		return math.pow(_lowerCamelCase       ,      3					) - (2 * x) - 5


if __name__ == "__main__":
						print(intersection(f, 3, 3.5))




'''simple docstring'''




from math import ceil, sqrt


def 				lowerCAmelCase_   (	_lowerCamelCase:   int = 1_00_00_00					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0

		for outer_width in range(3       ,      (limit // 4) + 2					):
				if outer_width**2 > limit:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		max(ceil(sqrt(outer_width**2 - limit					)					)       ,      1					)
				else:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		1
				if (outer_width - hole_width_lower_bound) % 2:
						hole_width_lower_bound += 1

				answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

		return answer


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