Directed Graphs and Network Flows · Superchallenge problem

A flow network has source $s$, sink $t$, and vertices $a,b,c$ with capacities $c(s,a)=5$, $c(s,b)=3$, $c(a,c)=2$, $c(b,c)=2$, $c(c,t)=4$ (current maximum flow $4$). What is the smallest TOTAL increase, split between $c(a,c)$ and $c(c,t)$ in whatever way works best, needed to raise the maximum flow to $6$?