Let U = {1, 2, 3}. Let 2^U denote the powerset of U. Consider an undirected graph G whose vertex set is 2^U. For any A, B ∈ 2^U, (A, B) is an edge in G if and only if (i) A ≠ B, and (ii) either A ⊂ B or B ⊂ A. For any vertex A in G, the set of all possible orderings in which the vertices of G can be visited in a Breadth First Search (BFS) starting from A is denoted by B(A).
If ∅ denotes the empty set, then the cardinality of B(∅) is _______.