Walks, Paths and Connectivity · Superchallenge problem

A network has source $0$ splitting into $4$ links to $1,2,3,4$; then $1,2$ both link to a relay $5$, and $3,4$ both link to a relay $6$; then $5$ links to $7,8$ and $6$ links to $9,10$; finally $7,8,9,10$ all link to the sink $11$. Find the maximum number of pairwise EDGE-disjoint paths from $0$ to $11$, minus the maximum number of pairwise internally VERTEX-disjoint paths from $0$ to $11$.