Leetcode 3257. Maximum Value Sum by Placing Three Rooks II

Pick three cells on an m×n integer board so that no two share a row or column and the sum of their values is maximized — equivalently, find the maximum-weight partial matching of size 3 between rows and columns. With m,n up to 500, brute-force triples is infeasible, so the challenge is to derive an O(mn · polylog) / optimized precomputation or DP approach.