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