Give a linear-time algorithm that takes as input a dag G = (V, E) and two vertices s and t, and returns the number of simple paths from s to t in G. For example, the dag as given in Q4 contains exactly four simple paths from vertex r to vertex s, ryqs, ryqws, ruyqs, and ruyqws. (Your algorithm needs only to count the simple paths, not list them.) Explain why your algorithm runs in O(n) time.