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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DPalindromicCharacteristics solver = new DPalindromicCharacteristics();
        solver.solve(1, in, out);
        out.close();
    }

    static class DPalindromicCharacteristics {
        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            String s = sc.nextLine();
            int n = s.length();
            boolean[][] dp = new boolean[n][n];
            for (int i = 0; i < n; i++) {
                dp[i][i] = true;
                if (i < n - 1 && s.charAt(i) == s.charAt(i + 1)) {
                    dp[i][i + 1] = true;
                }
            }
            for (int i = 3; i <= n; i++) {
                for (int j = 0; j + i - 1 < n; j++) {
                    if (dp[j + 1][j + i - 2] && s.charAt(j) == s.charAt(j + i - 1)) {
                        dp[j][j + i - 1] = true;
                    }
                }
            }

            long[] ans = new long[n];
            for (int i = 0; i < n; i++) {
                for (int j = i; j < n; j++) {
                    if (i == j) {
                        ans[0]++;
                        continue;
                    }
                    if (dp[i][j]) {
                        ans[0]++;
                        int end = j;
                        int act = 0;
                        while (true) {
                            act++;
                            end = i + (end - i + 1) / 2 - 1;
                            if (dp[i][end]) {
                                ans[act]++;
                            } else {
                                break;
                            }
                            if (i == end) {
                                break;
                            }
                        }
                    }
                }
            }
            for (long i : ans) {
                out.print(i + " ");
            }

        }

    }

    static class inputClass {
        BufferedReader br;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}