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 n = s.length();
  vector<vector<int> > dp(n, vector<int>(n, 0));
  vector<vector<bool> > check(n, vector<bool>(n, false));
  for (int i = 0; i < n; i++) {
    dp[i][i] = 1;
    check[i][i] = true;
    if (i + 1 < n && s[i] == s[i + 1]) {
      dp[i][i + 1] = 2;
      check[i][i + 1] = true;
    }
  }
  for (int k = 3; k <= n; k++) {
    for (int i = 0; i + k <= n; i++) {
      int j = i + k - 1;
      if (s[i] == s[j] && check[i + 1][j - 1]) {
        check[i][j] = true;
        dp[i][j] = dp[i][i + k / 2 - 1] + 1;
      }
    }
  }
  vector<int> ans(n + 1);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (dp[i][j] != 0) {
        ans[dp[i][j]]++;
      }
    }
  }
  for (int i = n - 1; i >= 1; i--) ans[i] += ans[i + 1];
  for (int i = 1; i <= n; i++) cout << ans[i] << " ";
}