Given a digraph G $=($V$,$ E$),$ its transitive closure G$$ is a digraph defined as follows: It

has the same vertex set V as G and contains an edge from a vertex a to another vertex b if and only if there is a directed path from a to b in G$.$ Suppose we want to design a DP algorithm that outputs G$$ on input G$.$ Design the subinstances and the Bellman Equation. $($Note that though this is not an optimization problem, DP is still helpful.$)$