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;
const int MX = 5003;
int pal[MX][MX];
int m[MX];
int main() {
  string s;
  cin >> s;
  int ln = s.size();
  for (int i = 0; i < ln; i++) {
    pal[i][i] = 1;
    m[1]++;
  }
  for (int i = 0; i < ln - 1; i++) {
    if (s[i] == s[i + 1]) {
      pal[i][i + 1] = 2;
      m[2]++;
    }
  }
  for (int len = 3; len <= ln; len++) {
    for (int i = 0; i < ln - len + 1; i++) {
      int j = i + len - 1;
      if (s[i] != s[j]) continue;
      if (pal[i][i + len / 2 - 1] == pal[i + len / 2 + len % 2][j]) {
        if (pal[i + 1][j - 1] != 0) {
          pal[i][j] = pal[i][i + len / 2 - 1] + 1;
          m[pal[i][j]]++;
        }
      } else {
        if (pal[i + 1][j - 1] != 0) {
          pal[i][j] = 1;
          m[1]++;
        }
      }
    }
  }
  int sum = 0;
  for (int i = ln; i >= 1; i--) m[i] = m[i] + m[i + 1];
  for (int i = 1; i <= ln; i++) cout << m[i] << " ";
  cout << endl;
  return 0;
}