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.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class DPalindromicCharacteristics {
        long p = 31;
        long[] pow;
        long[] hash;
        long[] hashinv;
        int[] ans;
        int n;

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int t = 1;
            // t= sc.nextInt();
            while (t-- > 0) {
                char[] arr = sc.nextLine().toCharArray();
                n = arr.length;
                pow = new long[n];
                hash = new long[n];
                hashinv = new long[n];
                long po = 1;
                for (int i = 0; i < n; i++) {
                    pow[i] = po;
                    po *= p;
                }
                long now = 0;
                for (int i = 0; i < n; i++) {
                    now *= p;
                    now += (arr[i] - 'a' + 1);
                    hash[i] = now;
                }
                now = 0;
                for (int i = n - 1; i >= 0; i--) {
                    now *= p;
                    now += (arr[i] - 'a' + 1);
                    hashinv[i] = now;
                }
                ans = new int[n];
                for (int k = 1; k <= n; k++)
                    for (int i = 0; i + k <= n; i++) {
                        solve(i, k, 0);
                    }

                for (int x : ans) pw.print(x + " ");
            }
        }

        void solve(int i, int len, int lvl) {
            long hash1 = hash[i + len - 1];
            if (i > 0) hash1 = hash1 - (hash[i - 1] * pow[len]);
            long hash2 = hashinv[i];
            if (i + len - 1 < n - 1) hash2 = hash2 - (hashinv[i + len] * pow[len]);
            if (hash1 == hash2) {
                ans[lvl]++;
                if (i + 2 * len <= n) solve(i, 2 * len, lvl + 1);
                if (i + 2 * len < n) solve(i, 2 * len + 1, lvl + 1);
            }

        }

    }

    static class Scanner {
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

    }
}