Sereja and Two Lines

Sereja has a matrix A with N rows and M columns with positive integer elements. Consider the multiset Sij made from the elements in the ith row, along with those in the jth column of A (do not count the element Aij twice). Then, define a matrix F as Fij = maxx ∈ Sijcount(x, Sij), where count(x, S) gives the number of times a number x occurs in the multiset S. For example, for the matrix 1 2 1 2