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