Walks, Paths and Connectivity · Hard problem

A network has a source $s$ and a sink $t$. From $s$ there are links to three relay points $a,b,c$. Relays $a$ and $b$ both link onward to relay $d$; relay $c$ links onward to relay $e$. Finally $d$ and $e$ each link to $t$. What is the maximum number of edge-disjoint paths from $s$ to $t$?