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?