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.Scanner;

public class PalindromeCharacteristics {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		String s = scanner.next();
		int l = s.length();

		int[][] dp = new int[l + 1][l + 1];
		int[] count = new int[l + 1];
		int l2, k;

		for (int i = 1; i <= l; i++) {
			l2 = l - i + 1;
			for (int j = 0; j < l2; j++) {
				k = j + i - 1;
				
				if (j == k)
					dp[j][k] = 1;
				else if (s.charAt(j) == s.charAt(k) && (j + 2 > k || dp[j + 1][k - 1] > 0))
					dp[j][k] = Math.min(dp[j][j - 1 + i / 2], dp[k + 1 - i / 2][k]) + 1;

				count[dp[j][k]]++;
			}
		}

		StringBuilder sb = new StringBuilder();

		for (int i = l - 1; i >= 1; i--)
			count[i] += count[i + 1];
		for (int i = 1; i <= l; i++)
			sb.append(count[i] + " ");

		System.out.println(sb.toString());
	}
}