After you reduce it to maximum bipartite matching you just use whatever stock algorithm for bipartite matching you want. Another comment links to the official

After you reduce it to maximum bipartite matching you just use whatever stock algorithm for bipartite matching you want. Another comment links to the official writeup. The official writeup says that you can think about it as the "rook subproblem" and the "bishop subproblem" separately. This is the easiest way to think about it imo.