Rooks Attack

\(3\) rooks are arranged on a \(27 \times 27\) chess board so that no rook is attacking another. How many places can a \(4\)th rook be placed so that it is attacking exactly one other rook on the board?

Details and assumptions

The rook (also called castle) is a chess piece that attacks horizontally and vertically (in the same row and column).

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