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() {
  string s;
  cin >> s;
  int l = s.length();
  vector<vector<int>> dp(5000, vector<int>(5000, 0));
  vector<int> kk(s.size() + 1, 0);
  for (int length = 1; length <= l; length++) {
    for (int right = 0; right < s.size(); right++) {
      int r = right + length - 1;
      if (r >= s.size()) break;
      if (s[right] != s[r]) continue;
      if (right == r) {
        dp[r][r] = 1;
      } else if (length == 2) {
        dp[right][r] = 2;
      } else if (dp[right + 1][r - 1] > 0) {
        int haf = length / 2;
        int ml = right + haf - 1;
        int mr = r - haf + 1;
        dp[right][r] = 1 + min(dp[right][ml], dp[mr][r]);
      }
      kk[dp[right][r]]++;
    }
  }
  for (int i = l; i >= 1; i--) {
    kk[i - 1] = kk[i] + kk[i - 1];
  }
  for (int i = 1; i <= l; i++) {
    string pt = to_string(kk[i]) + " ";
    cout << pt;
  }
}