Compensated words

Consider a word $s$ of length $n$ , with only letters ‘a’ and ‘b’. For any prefix $p$ of $s$ , let $a(p)$ be the number of ‘a’ within $p$ , and let $b(p)$ be the number of ‘b’ within $p$ . In this problem, we say that $s$ is compensated if and only if for every of the $n + 1$ prefixes $p$ of $s$ we have $\vert a(p) - b(p) \vert \le 2$ .

For instance, “abbaaabb” is compensated, but “abbaaaab” is not, because “abbaaaa” is a prefix with five ‘a’ and two ‘b’. As other examples, neither “bbb” nor “bbbbbb” are compensated.

Given an $n$ , print all compensated words of this length.

Input

Input consists of an $n$ between 1 and 18.

Output

Print in alphabetical order all compensated words with $n$ characters chosen between ‘a’ and ‘b’.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T21:33:02.364Z