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A tromino (more accurately, a right tromino) is an L-shaped tile formed by three $1 \times 1$ squares. The problem is to cover any $2^n$-by-$2^n$ chessboard with one missing square (anywhere on the board) with trominoes. Trominoes should cover all the squares of the board except the missing one with no overlaps. Design a divide-and-conquer algorithm for this problem.

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