Walks, Paths and Connectivity · Challenge problem

Vertices $s=0$ and $t=1$ are joined only by four internally-disjoint paths: two of length $2$ (through $2$ and through $3$), one of length $3$ (through $4,5$), and one of length $5$ (through $6,7,8,9$). What is the maximum number of pairwise edge-disjoint paths from $0$ to $1$?