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 data[(int)2e5];
int dp[5001][5001];
int used[5001][5001];
string s;
int magic(int l, int r) {
  if (l > r) return 1;
  if (used[l][r] != -1) return used[l][r];
  if (l == r) {
    data[1]++;
    return used[l][r] = 1;
  }
  int lk, rk, k, flag = 1, middle = (l + r) / 2;
  lk = magic(l, (r - l) % 2 == 0 ? (middle - 1) : middle);
  rk = magic(middle + 1, r);
  k = min(lk, rk) + 1;
  if (s[l] == s[r] and magic(l + 1, r - 1)) {
    for (int i = 1; i <= k; i++) data[i]++;
    return used[l][r] = k;
  }
  return used[l][r] = 0;
}
int main() {
  memset(used, -1, sizeof(used));
  cin >> s;
  int n = s.size() - 1;
  for (int i = 0; i <= n; i++) {
    for (int j = i; j <= n; j++) magic(i, j);
  }
  for (int i = 1; i <= s.size(); i++) cout << data[i] << " ";
  return 0;
}