Directed Graphs and Network Flows · Challenge problem

A flow network has source $s$, sink $t$, and vertices $a,b,c$ with capacities $c(s,a)=6$, $c(s,b)=5$, $c(a,c)=4$, $c(a,t)=2$, $c(b,c)=3$, $c(b,t)=4$, $c(c,t)=6$. A flow currently sends $f(s,a)=3$, $f(a,c)=3$, $f(c,t)=3$, $f(s,b)=4$, $f(b,t)=4$ (every other arc carries $0$) – a valid flow of value $7$. By how much can the total flow still be increased by rerouting along augmenting paths?