Let S be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of S so that the union of the two subsets is S? The order of selection does not matter; for example, the pair of subsets \{a, c\},\{b, c, d, e, f\} represents the same selection as the pair \{b, c, d, e, f\},\{a, c\}.