Directed Graphs and Network Flows · Hard problem

In a flow network with source $s$, sink $t$, and vertices $a,b,c$ in between, the capacities are $c(s,a)=8$, $c(s,b)=8$, $c(a,b)=2$, $c(a,c)=3$, $c(a,t)=1$, $c(b,c)=1$, $c(b,t)=2$, $c(c,t)=10$. Among the four cuts $S_1=\{s\}$, $S_2=\{s,a\}$, $S_3=\{s,a,b\}$, $S_4=\{s,b\}$ (with $T$ everything else), what is the smallest of the four capacities?