Let G = (V, E) be a directed graph. Define a graph G² = (V', E' ) as follows: V' = V: E' if there is a a path of length 2 between u and v in G.

Suppose that a directed graph G is given as adjacency list. Give a O(mn)-time algorithm to compute G² . Derive the time bound. Here m is number of edges in G and n is number of vertices in G