Directed Graphs and Network Flows · Challenge problem

A flow network has source $s$, sink $t$, and two parallel routes: $s\to a \to t$ with $c(s,a)=3$, $c(a,t)=2$, and $s \to b \to t$ with $c(s,b)=2$, $c(b,t)=2$ (current maximum flow $4$). What is the smallest increase to $c(a,t)$ alone that raises the maximum flow to $5$?