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