


from __future__ import annotations





def     _UpperCamelCase     (a__   :list[int]   ,			a__   :int       ):






							"""simple docstring"""





							UpperCamelCase__				     =			[]
							UpperCamelCase__				     =			[]
							UpperCamelCase__				     =			0
							UpperCamelCase__				     =			sum(a__       )
							create_state_space_tree(a__   ,			a__   ,			a__   ,			a__   ,			a__   ,			a__       )
							return result





def     _UpperCamelCase     (a__   :list[int]   ,			a__   :int   ,			a__   :int   ,			a__   :list[int]   ,			a__   :list[list[int]]   ,			a__   :int   ,			):






							"""simple docstring"""





							if sum(a__       ) > max_sum or (remaining_nums_sum + sum(a__       )) < max_sum:
														return
							if sum(a__       ) == max_sum:
														result.append(a__       )
														return
							for index in range(a__   ,			len(a__       )       ):
														create_state_space_tree(
														    a__   ,			a__   ,			index + 1   ,			[*path, nums[index]]   ,			a__   ,			remaining_nums_sum - nums[index]   ,			)
UpperCamelCase__											= [3, 34, 4, 12, 5, 2]
UpperCamelCase__											= 9
UpperCamelCase__											= generate_sum_of_subsets_soln(nums, max_sum)
print(*result)











from math import ceil, sqrt





def     _UpperCamelCase     (a__   :int = 100_0000       ):






							"""simple docstring"""





							UpperCamelCase__				     =			0

							for outer_width in range(3   ,			(limit // 4) + 2       ):
														if outer_width**2 > limit:
																					UpperCamelCase__				     =			max(ceil(sqrt(outer_width**2 - limit       )       )   ,			1       )
														else:
																					UpperCamelCase__				     =			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() = }""")




