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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  string s;
  cin >> s;
  int n = s.length();
  vector<int> res(n + 1, 0);
  vector<vector<int>> dp(n + 1, vector<int>(n + 1, 0));
  for (int k = 1; k <= n; k++) {
    for (int l = 0; l < n - k + 1; l++) {
      int r = l + k;
      if (k == 1) {
        dp[l][r] = 1;
        continue;
      }
      if (k == 2) {
        dp[l][r] = ((s[l] == s[r - 1]) ? 2 : 0);
        continue;
      }
      if (s[l] != s[r - 1] or !dp[l + 1][r - 1]) {
        continue;
      }
      dp[l][r] = 1;
      int m = (l + r) / 2;
      if (k & 1) {
        if (dp[l][m] and dp[m + 1][r]) {
          dp[l][r] = dp[l][m] + 1;
        }
      } else {
        if (dp[l][m] and dp[m][r]) {
          dp[l][r] = dp[l][m] + 1;
        }
      }
    }
  }
  for (int k = 1; k <= n; k++) {
    for (int l = 0; l < n - k + 1; l++) {
      res[dp[l][l + k]]++;
    }
  }
  for (int i = n - 1; i > 0; i--) {
    res[i] += res[i + 1];
  }
  for (int i = 1; i <= n; i++) {
    cout << res[i] << ' ';
  }
  cout << '\n';
  return 0;
}