Consider the matrix P\in{\mathbb R}^{6\times 225}\,\, whose elements P_{ij} are \,\,+1\, when \,(i,j) = (1,24), (1,206), (2,39), (2,207),\, etc. \,\,-1\, when \,(i,j) = (1,11), (2,27), (3,43),\, ...

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