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 maxn = 5005;
const int inf = 0x3f3f3f3f;
char s[maxn];
int dp[maxn][maxn];
int ans[maxn];
int main() {
  cin >> s;
  int n = strlen(s);
  for (int i = (0); i < (n); i++) dp[i][1] = 1, ans[1]++;
  for (int j = (2); j < (n + 1); j++) {
    for (int i = (0); i < (n); i++) {
      if (i + j - 1 >= n) break;
      if (s[i] != s[i + j - 1] || (j > 2 && dp[i + 1][j - 2] == 0))
        dp[i][j] = 0;
      else
        dp[i][j] = dp[i][j / 2] + 1;
      ans[dp[i][j]]++;
    }
  }
  for (int i = (n + 1) - 1; i >= 1; i--) ans[i] += ans[i + 1];
  for (int i = (1); i < (n + 1); i++) cout << ans[i] << ' ';
  return 0;
}