Directed Graphs and Network Flows · Challenge problem

A network has $s,a,b,c,d,t$ with two-way links $sa,sb,ac,bc,ad,bd,ct,dt,ab$, and each of $a,b,c,d$ may be used by at most ONE path from $s$ to $t$ (unlimited use at $s,t$ themselves). What is the maximum number of internally vertex-disjoint paths from $s$ to $t$?