Equal Summed Subsets
시간 제한1초메모리 제한1024 MB
집합 {1, 2, ..., N}을 같은 합을 갖는 두 부분집합으로 나누는 경우의 수를 순서쌍을 구분하지 않고 센다. N은 36 이하이다.
문제
Given the set of integers {1, 2, 3, ..., N}, determine the total number of ways you can divide the set into two equal-summed subsets A and B of that set. The union of A and B is the set of integers {1,2,...n} and A and B have no integers in common. Do not count answers that are just mirror images of each other, e.g.:
{1, 4} and {2, 3}
vs.
{2, 3} and {1, 4}
counts as a single solution, not two solutions just because the two sets can be ordered the other way.
입력
A single line with an integer 1 ≤ N ≤ 36 that denotes the size of the set.
출력
A single line with an integer that tells how many pairs of equal summed subsets can be created.