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