Given is an \(n\times n\) board, with an integer written in each grid. For each move, I can choose any grid, and add \(1\) to all \(2n-1\) numbers in its row and column. Find the largest \(N(n)\), such that for any initial choice of integers, I can make a finite number of moves so that there are at least \(N(n)\) even numbers on the board.