Directed Graphs and Network Flows · Hard problem

A flow network has source $s$, sink $t$, and vertices $a,b,c,d$ in between, with capacities $c(s,a)=8$, $c(s,b)=5$, $c(a,b)=3$, $c(a,c)=6$, $c(b,d)=5$, $c(c,d)=2$, $c(c,t)=5$, $c(d,t)=7$. Running Ford-Fulkerson from scratch, what is the maximum flow value from $s$ to $t$?