Problem - Distinct Routes

You are given a directed graph with $n$ vertices and $m$ edges. Find the maximum number of edge-disjoint paths from vertex $1$ to vertex $n$. Output the number of paths and list each path. Paths are edge-disjoint if they do not share any edges (but can share vertices).

This is a max flow problem where each edge has capacity $1$. The flow value equals the number of disjoint paths. Then you need to extract the actual paths from the flow.