# Problem 105: Special subset sums: testing
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: S(B) ≠ S(C); that is, sums of subsets
cannot be equal. If B contains more elements than C then S(B) > S(C).
For example, {81, 88, 75, 42, 87, 84, 86, 65} is not a special sum set
because 65 + 87 + 88 = 75 + 81 + 84, whereas {157, 150, 164, 119, 79,
159, 161, 139, 158} satisfies both rules for all possible subset pair
combinations and S(A) = 1286. Using sets.txt (right click and "Save
Link/Target As..."), a 4K text file with one-hundred sets containing
seven to twelve elements (the two examples given above are the first two
sets in the file), identify all the special sum sets, A1, A2, ..., Ak,
and find the value of S(A1) + S(A2) + ... + S(Ak). NOTE: This problem is
related to Problem 103 and Problem 106.