Directed Graphs and Network Flows · Challenge problem

A network of one-way cables joins $s,a,b,c,m,x,d,e,f,t$: $s\to a$, $s\to b$, $s\to c$; $a\to m$, $b\to m$, $c\to m$; $m\to x$; $x\to d$, $x\to e$, $x\to f$; $d\to t$, $e\to t$, $f\to t$ (every cable is usable only in the stated direction, and no cable has a stated capacity beyond $1$). What is the minimum number of cables that must be cut to disconnect $s$ from $t$?