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