Some solutions for n=4
......1..........1..........1..........1..........1..........1..........1....
.....1.1........2.2........1.1........3.3........1.1........3.3........3.1...
....2.1.3......2.3.2......2.2.1......3.2.3......1.2.2......2.2.3......2.3.1..
...2.1.1.3....2.3.3.3....2.2.1.3....2.2.3.3....2.2.3.3....2.3.3.3....2.3.3.3.
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......1..........1..........1..........1..........1..........1..........1....
.....1.1........3.1........2.1........2.3........2.1........1.1........1.2...
....1.1.3......3.3.1......2.2.2......2.2.3......2.2.3......1.2.1......1.2.3..
...2.2.2.3....2.2.3.3....2.2.3.3....2.3.3.3....2.3.3.3....2.2.2.3....2.2.3.3.
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