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