We call a string $$$s$$$ of length $$$n$$$ good, if and only if $$$n \bmod 2 = 0$$$ and $$$s[1,\dfrac{n}{2}] = s[\dfrac{n}{2}+1,n]$$$ (i.e. there exists a string $$$t$$$ that $$$s = t + t$$$.)
You are given a string $$$s$$$. For each $$$r \in [1,n]$$$:
- Find all good substrings ending at position $$$r$$$.
- The guess is: Their length can be divided into $$$\mathcal O(\log n)$$$ consecutive intervals.
Is the guess correct?