And with 7 substrings of length 3, it's provably minimal, since making every 3-substring a permutation of 123 forces every element after the first 2. Assuming without loss of generality that it starts with 1 2, it is forced to start with
1 2 3 1 2 3
but there already repeats the same permutation. So one substring must be wasted (in the article this is phrased as having to traverse one higher cost edge in the corresponding graph).
