A board of \(n cm \times n cm\) is divided in \(n^2\) little squares of \(1cm \times 1 cm\). If each square can be painted black or white. Find all ways to color the board such that each square of \(2 cm \times 2 cm\) formed by \(4\) little squares with a common vertex has \(2\) black squares and \(2\) whitesquares.

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