Palindromic characteristics of stringswith length $|s|$ is a sequence of $|s|$ integers, where $k$-th number is the total number of non-empty substrings of $s$ which are $k$-palindromes.

A string is $1$-palindrome if and only if it reads the same backward as forward.
A string is $k$-palindrome $(k>1)$ if and only if:

1. Its left half equals to its right half.
2. Its left and right halfs are non-empty $(k-1)$-palindromes.

The left half of string $t$ is its prefix of length $⌊|t|/2⌋$, and right half− the suffix of the same length. $⌊|t|/2⌋$ denotes the length of string $t$ divided by $2$, rounded down.
Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.