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EXAMPLE
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Corresponding "new" cubes are 0,0,1,8,0,1,8,0,1,8,0,1,8,125,0,1,8,64,0,1,8,0,1,8,0,1,8,125,0,1,8,0,1,8,27,64,0,1,8,0,1,8,125,0,1,8,0,1,8,0,1,8,64,0,1,8,125,0,1,8,0,1,8,0,1,8,0,1,8,27,64,125,0,1,8,0,1,8,0,1,8,0,1,8,125,0,1,8,64,216,512,0,1,8,0,1,8,0,1,8,125,0,1,8,0,1,8,27,64,0,1,8,0,1,8,125,0,1,8,0,1,8,0,1,8,64,0,1,8,125,0,1,8,0,1,8,0,1,8,0
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