Trace the Edmonds$-$Karp algorithm on the following flow network. To save space, it suffices to specify the selected augmenting path used at each iteration of the algorithm and the amount of flow passed through that path. Also show the final residual network. Describe each path as a sequence of vertices on the path $($e$.$g$.,\backslash ($ s B G t $\backslash )).$ Describe each path as a sequence of vertices on the path and the amount of flow along that path. In the case of multiple shortest paths between $\backslash ($ s $\backslash )$ and $\backslash ($ t $\backslash ),$ pick the lexicographically smallest path.