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