Some solutions for n=3
...3.3.3.3...3.1.2.2...2.1.3.3...2.2.2.2...3.2.2.2...3.3.3.2...2.2.2.2
...3.3.3.3...3.3.2.2...2.3.3.3...1.2.2.3...3.2.1.2...3.1.3.3...2.2.3.1
...1.2.2.3...3.3.3.2...3.3.3.3...1.1.1.1...2.2.1.1...1.1.3.3...2.2.3.1
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...3.3.2.2...1.1.2.2...3.2.2.1...1.1.3.3...2.3.3.3...1.1.3.3...1.1.2.2
...3.3.1.2...1.2.2.2...3.1.1.1...1.3.3.3...2.3.3.1...1.3.3.3...1.2.2.2
...3.3.3.3...2.2.3.2...3.1.1.1...1.1.2.3...2.2.3.3...3.3.2.2...1.1.2.3
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