$(20$ points$)$ Determine the maximum flow from node $1$ to node $5$ in the network below, as well as the optimum flow in each arc. Write down each of the breakthrough paths in the order in which you find them, as well as the resulting amount of flow on each breakthrough path. Use these flow values to compute the maximal flow in the network. Write out the resulting residual capacities on each arc after each breakthrough path is found, and use the final residual capacities on each arc to determine the optimum flow in each arc.