# Palindromic characteristics

Time Limit: 3 seconds

Memory Limit: 256 megabytes

## Description

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.

## Input

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

## Output

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

## Sample Input

InputabbaOutput6 1 0 0 InputabacabaOutput12 4 1 0 0 0 0

## Sample Output

None

## Hint

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.

None