Discrete Math, Pigeon Hole Principle/Sum of Elements of Subsets

Ok, so the question is to show for any set A of positive integers taken from {1,2,...,12}, A must contain two disjoint subsets whose elements when added up give the same sum.

Now, reading around on this site, what I have so far is that there are 2^6 possible subsets of a 6-element set, and the maximum possible sum is 57. I believe I'm supposed to then use the pigeon hole principle to show that it is true, but I'm not sure how to calculate the amount of disjoint subsets that have the same sum, which I'm thinking I have to find. Can someone help me out please?