$(21$ points$)3.$ Execute the Ford$-$Fulkerson algorithm on the following graph. When there are

multiple augmenting paths available, pick the shortest one $($that is the one with the fewest edges$).$

If multiple shortest paths are available, choose the one that increases the flow the most.

Hint: reference to Section $24\mathrm{.}2$ in the textbook

$(15$ points$)3\mathrm{.}1$ The maximum flow $($i$.$e$.,$ the amount of flow on each edge$)$ and its value.

$(6$ points$)3\mathrm{.}2$ The minimum cut $($which should be formatted as two sets of vertices$)$ and its

capacity.