Core Idea - Max Flow with Unit Capacities

Treat each road as an edge with capacity $1$. The maximum flow from $1$ to $n$ equals the maximum number of edge-disjoint paths from source to destination. By max-flow min-cut theorem, the minimum cut capacity equals the max flow.

Since capacities are $1$, the min cut is the minimum number of edges to remove. Compute max flow using Dinic or Ford-Fulkerson. The flow value is the answer to the question: how many roads must be blocked?