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