$[7$ marks$]$ Consider the following flow network $N.$ Run the Ford$-$Fulkerson algorithm to find a maximum st$-$flow $f$ in $N,$ and also find a minimum cut of $N.$ When choosing augmenting paths, use BFS starting from vertex $s$ to find the shortest path from $s$ to $t$ in the residual network. When running BFS$,$ visit adjacent vertices in ascending order.

For each iteration of Ford$-$Fulkerson, draw the st$-$flow $f$ in $N,$ the corresponding residual network $N_f,$ and indicate the augmenting path.