Some solutions for n=6
..1....1....2....1....0....1....0....0....1....0....2....0....2....2....2....0
..3....0....2....4....1....4....0....0....0....1....0....2....2....2....1....0
..4....3....3....4....2....4....1....1....3....1....0....0....3....2....2....2
..3....1....0....1....2....3....3....2....2....2....2....4....1....0....2....1
..0....2....2....1....1....2....0....4....3....2....2....4....3....3....3....4
..4....0....2....4....1....2....0....2....2....4....4....1....4....4....0....0
..3....3....2....3....4....0....3....3....2....0....3....0....3....0....0....0
..3....1....4....3....3....1....0....0....4....4....0....3....1....4....3....0
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