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