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