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