Dummy Palindromic Strings

A *dummy palindromic string* (DPS) is a string which can be converted into a palindrome by performing each of the following operations exactly once: - Permute the characters of the string in an arbitrary way. - Choose a valid index $i$ and change the $i$-th character of the resulting string to a **different** character (not necessarily present in the original string). You are given a string $S$.