Palindromic Equivalence

For two strings $A$ and $B$ with the same length $N$, we will say that they are *equivalent* if the following rule holds: For each pair of integers $l$ and $r$ ($1 \le l \le r \le N$), the substring of $A$ between the $l$-th and $r$-th character (inclusive) is a palindrome if and only if the substring of $B$ between the $l$-th and $r$-th character (inclusive) is a palindrome. You are given a st