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