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