Directed Graphs and Network Flows · Superchallenge problem

A flow network has source $s$, sink $t$, and vertices $a,b,c,d,e$ with capacities $c(s,a)=9$, $c(s,b)=7$, $c(a,c)=4$, $c(a,d)=3$, $c(b,d)=4$, $c(b,e)=6$, $c(c,d)=2$, $c(d,e)=3$, $c(c,t)=6$, $c(d,t)=2$, $c(e,t)=7$ (maximum flow $13$, achieved exactly by the cut $\{s,a,b,d,e\}$, whose three crossing arcs are $a\to c$, $d\to t$, $e\to t$). If you could raise the capacity of exactly ONE of these three arcs without limit, which choice allows the largest possible new maximum flow, and what is that new maximum flow?