Consider undirected graphs (with no weights). Often there are multiple shortest paths between two nodes of a graph. For example, in a graph with vertices {1, 2, 3, 4, 5} and edges {(1, 2), (1, 3), (2, 4), (3, 4), (4, 5)}, there are two shortest paths from 1 to 5: (1, 2, 4, 5), and (1, 3, 4, 5). Describe a linear-time algorithm such that, given an undirected, unweighted graph and two vertices u and v, the algorithm counts the number of distinct shortest paths from u to v. Justify its correctness and the running time.