--description--

Let $S(A)$ represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:

1. $S(B) ≠ S(C)$; that is, sums of subsets cannot be equal.
2. If B contains more elements than C then $S(B) > S(C)$.

For this problem we shall assume that a given set contains n strictly increasing elements and it already satisfies the second rule.

Surprisingly, out of the 25 possible subset pairs that can be obtained from a set for which n = 4, only 1 of these pairs need to be tested for equality (first rule). Similarly, when n = 7, only 70 out of the 966 subset pairs need to be tested.

For n = 12, how many of the 261625 subset pairs that can be obtained need to be tested for equality?

Note: This problem is related to Problem 103 and Problem 105.

--hints--

subsetSumsMetaTesting() should return 21384.

assert.strictEqual(subsetSumsMetaTesting(), 21384);

--seed--

--seed-contents--

function subsetSumsMetaTesting() {

  return true;
}

subsetSumsMetaTesting();

--solutions--

// solution required