Directed Graphs and Network Flows · Hard problem

A network has $s,a,b,t$ with capacities $c(s,a)=3$, $c(s,b)=1$, $c(a,b)=3$, $c(a,t)=1$, $c(b,t)=3$. Pushing the single path $s\to a\to b\to t$ first (to its own bottleneck) saturates every arc on it, after which NO path using only forward arcs remains from $s$ to $t$. What is this network's actual maximum flow value?