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