



'''simple docstring'''




from __future__ import annotations


def 				lowerCAmelCase_   (	_lowerCamelCase:   list[int]       ,      _lowerCamelCase:   int					):
		__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		0
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		len(_lowerCamelCase					) - 1

		while i < j:
				if nums[i] + nums[j] == target:
						return [i, j]
				elif nums[i] + nums[j] < target:
						__SCREAMING_SNAKE_CASE       :		List[Any]           =		i + 1
				else:
						__SCREAMING_SNAKE_CASE       :		Dict           =		j - 1

		return []


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(f"{two_pointer([2, 7, 11, 15], 9) = }")




'''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() = }")