Time Limit: 3 seconds
Memory Limit: 256 megabytes
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:
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.
In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.