Suppose you are given a directed graph $G=(V,E)$ where each vertex, uinV, is labeled

with a unique value $L(u)$ from the set $\{1,$dots,$|V|\}.$ For each vertex $u,$ let $R(u)$ denote the

set of vertices reachable from $u$ in $G.$ Define max$(u)$ to be the vertex $v_u^{**}$ in $R(u)$ with the

maximum label, i$.$e$.L(v_u^{**})L(v)$ for all vinR$(u).$

Give an $O(|V|+|E|)$ time algorithm to compute max$(u)$ for all vertices in uinV. Briefly

justify correctness and runtime of your algorithm.