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We have a chessboard of size $\left(k^2-k+1\right) \times\left(k^2-k+1\right)$, where $k-1=p$ is a prime number. For each prime $p$, give a method of distribution of the numbers 0 and 1 , one number in each square of the chessboard, in such a manner that in each row or column there are exactly $k$ zeros, and no rectangle with sides parallel to the sides of the chessboard has zeros on the vertices.
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