An alphabet consists of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
letters. What is the maximal length of a word if we know that any two consecutive letters
![a,b](/media/m/7/d/8/7d8bdace47e602448e6040957d8cf923.png)
of the word are different and that the word cannot be reduced to a word of the kind
![abab](/media/m/8/3/e/83eb8df90a4875c229dde3c0b2393f7b.png)
with
![a\neq b](/media/m/e/9/8/e98c823356e8f13c26304aa34cdfff42.png)
by removing letters.
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An alphabet consists of $n$ letters. What is the maximal length of a word if we know that any two consecutive letters $a,b$ of the word are different and that the word cannot be reduced to a word of the kind $abab$ with $a\neq b$ by removing letters.