# Palindromic characteristics

## 题目描述

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&gt;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.

## 输入输出格式

### 输入格式

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

### 输出格式

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

## 输入输出样例

### 输入样例 #1

``````abba
``````

### 输出样例 #1

``````6 1 0 0
``````

### 输入样例 #2

``````abacaba
``````

### 输出样例 #2

``````12 4 1 0 0 0 0
``````

## 说明

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.