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 R835D {

    public static void main(String[] args) {
        String s=new Scanner(System.in).next();
        int l=s.length(), m;
        int[][]dp=new int[l][l];
        int[]a=new int[l+1];
        for(int i=0; i<l; i++) dp[i][i]=1;
        for(int i=0; i<l-1; i++) dp[i][i+1]=(s.charAt(i)==s.charAt(i+1))?2:0;
        for(int k=2; k<l; k++)
            for(int i=0; i<l-k; i++)
                if (s.charAt(i)!=s.charAt(i+k) || dp[i+1][i+k-1]==0)
                    dp[i][i+k]=0;
                else
                    dp[i][i+k]=dp[i][i+(k+1)/2-1]+1;
        for(int i=0; i<l; i++)
            for(int j=i; j<l; j++)
                a[dp[i][j]]++;
        for(int i=l-1; i>0; i--)
            a[i]+=a[i+1];
        for(int i=1; i<=l; i++) System.out.print(a[i]+" ");
    }
}