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