PROBLEM 3 (25 POINTS) Let G(V, E) be an undirected and unweighted graph with n nodes. Let T1, T2, ...,Tk be k= n - 1 distinct spanning trees of G. Devise a polynomial-time algorithm that finds a spanning tree T = (V, ET) in G that contains at least one edge from each Ti. (Prove correctness and polynomial runtime.) Definition: two trees (or for that matter any graphs) on a set of nodes are distinct, if they differ in at least one edge