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