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