Problem: 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.

Examples

Input

abba


Output

6 1 0 0 


Input

abacaba


Output

12 4 1 0 0 0 0 

Note

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.

Solution (in JAVA):

Solution:

import java.util.*;

public class Work {
	static final int MAX = 5100;
	
	static int[][] dp = new int[MAX][MAX];
	static int[] ans = new int[MAX];
	
	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		String str = cin.next();
		
		for (int i = 1; i <= str.length(); i++) {
			dp[i][i] = 1;
			ans[1]++;
		}
		
		for (int len = 2; len <= str.length(); len++) {
			for (int i = 1; i + len - 1 <= str.length(); i++) {
				int j = i + len - 1;
				if (str.charAt(i - 1) != str.charAt(j - 1) || i + 1 <= j - 1 && dp[i + 1][j - 1] == 0) {
					dp[i][j] = 0;
				} else {
					dp[i][j] = dp[i][i + len / 2 - 1] + 1;
				}
				if (dp[i][j] != 0) ans[dp[i][j]]++;
			}
		}
		
		for (int i = str.length(); i >= 1; i--) ans[i] += ans[i + 1];
		for (int i = 1; i <= str.length(); i++) System.out.printf("%d ", ans[i]); 
	}
}