There is a chessboard of n^2 squares. A pawn is standing on the lower left corner of the chessboard, i.e. on O (0,0), and its primary goal is to reach the upper right corner of the chessboard, i.e. N (n, n). The only moves allowed are diagonal shortcuts through squares. Once a square is crossed it is destroyed so that it is impossible to cross again. The secondary goal of the pawn on its way to N is to destroy as many squares as possible. What is the maximum possible number of destroyed squares f(n), provided the primary goal has been reached?
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