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