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