



from __future__ import annotations


def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				create_state_space_tree(lowerCamelCase__					,			[]					,			0					,			[0 for i in range(len(lowerCamelCase__						)						)]						)


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__					,			):

				"""simple docstring"""


				if index == len(lowerCamelCase__						):
								print(lowerCamelCase__						)
								return

				for i in range(len(lowerCamelCase__						)						):
								if not index_used[i]:
												current_sequence.append(sequence[i]						)
												lowercase__					:   Dict													=					True
												create_state_space_tree(lowerCamelCase__					,			lowerCamelCase__					,			index + 1					,			lowerCamelCase__						)
												current_sequence.pop()
												lowercase__					:   Dict													=					False
lowerCAmelCase__					  =  [3, 1, 2, 4]
generate_all_permutations(sequence)

lowerCAmelCase__					  =  ["A", "B", "C"]
generate_all_permutations(sequence_a)









from math import ceil, sqrt


def  __lowerCamelCase (       lowerCamelCase__ = 1_000_000						):

				"""simple docstring"""


				lowercase__					:   int													=					0

				for outer_width in range(3					,			(limit // 4) + 2						):
								if outer_width**2 > limit:
												lowercase__					:   List[str]													=					max(ceil(sqrt(outer_width**2 - limit						)						)					,			1						)
								else:
												lowercase__					:   List[str]													=					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() = }''')




