Restrict Palindromes

For a string $S$, we define $f(S)$ as the number of **distinct palindromic$^{\dagger}$ substrings$^{\ddagger}$** of $S$. For example, $f(abaa) = 4$ because we can find the palindrome substrings $a, b, aa$ and $aba$. Call a string $S$ good if $f(S) \le 5$, i.e. it has at most $5$ distinct palindrome substrings. You are given an integer $N$. Construct any good string of length $N$ using only lo