A11152 | Palindromic characteristics

Palindromic characteristics of string $s$ with 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.

The first line contains the string $s$ ( $1<=|s|<=5000$ ) consisting of lowercase English letters.

Print $|s|$ integers — palindromic characteristics of string $s$ .