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