How many ordered pairs of sets (A, B) are there such that the union of A and B is the set {1,2,3,4,5,6,7}? One example of such a pair is (A, B) = ({1,3,4,5,7}, {1,2,5,6}) [which is considered different than ({1,2,5,6}, {1,3,4,5,7})].