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;
string str;
int dp1[5007][5007];
int dp2[5007][5007];
int ff(int i, int j) {
  if (i > j) return 1;
  if (dp2[i][j] != -1) return dp2[i][j];
  if (str[i] != str[j]) return dp2[i][j] = 0;
  return dp2[i][j] = ff(i + 1, j - 1);
}
int f(int i, int j) {
  if (i == j) return 1;
  if (dp1[i][j] != -1) return dp1[i][j];
  int mid = (j - i + 1);
  mid /= 2;
  if (ff(i, j)) return dp1[i][j] = 1 + f(i, i + mid - 1);
  return dp1[i][j] = 0;
}
int main() {
  memset(dp1, -1, sizeof(dp1));
  memset(dp2, -1, sizeof(dp2));
  cin >> str;
  int i, j;
  vector<int> v(str.size() + 1, 0);
  for (i = 0; i < str.size(); i++)
    for (j = i; j < str.size(); j++) v[f(i, j)]++;
  for (i = str.size() - 1; i > 0; i--) v[i] += v[i + 1];
  for (i = 1; i <= str.size(); i++) printf("%d ", v[i]);
  return 0;
}