Find a network flow solution for the following:

You want to place knights on an n n chessboard. The chessboard has n2 positions from (0; 0) to

(n 1;n 1). A knight at position (x;y) is able to attack up to eight different positions: (x + 2;y + 1),

(x + 2;y 1), (x + 1;y + 2), (x + 1;y 2), (x 1;y + 2), (x 1;y 2), (x 2;y + 1), and (x 2;y 1)for

each position that lies on the board, of course. Moreover, some positions are blocked so that you

cannot place knights on them. Given n and a list of all blocked positions, find a way to place as

many knights as possible on the chessboard so that the placed knights cannot attack each other.