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