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