Directed Graphs and Network Flows · Hard problem

A flow network has source $s$, sink $t$, and vertices $a,b,c$, with capacities $c(s,a)=7$, $c(s,b)=2$, $c(a,b)=3$, $c(a,c)=4$, $c(b,c)=2$, $c(b,t)=3$, $c(c,t)=6$. A flow sends $f(s,a)=7$, $f(s,b)=2$, $f(a,b)=3$, $f(b,c)=2$, $f(b,t)=3$, with $f(a,c)$ fixed by conservation at $a$ and $f(c,t)$ fixed by conservation at $c$. Is this flow already maximum, and if so, what is the maximum flow value?