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 dp[5500][5500], ans[5500];
int main() {
  char s[5500];
  while (~scanf("%s", s + 1)) {
    memset(ans, 0, sizeof(ans));
    int slen = strlen(s + 1);
    if (slen == 1) {
      printf("1\n");
      continue;
    }
    for (int k = 1; k <= slen; k++) {
      dp[k][k] = 1;
      ans[1]++;
    }
    for (int len = 2; len <= slen; len++)
      for (int l = 1; l <= slen; l++) {
        int r = l + len - 1;
        if (r > slen) break;
        if (s[l] != s[r] || (l + 1 <= r - 1 && dp[l + 1][r - 1] == 0))
          dp[l][r] = 0;
        else
          dp[l][r] = dp[l][l + len / 2 - 1] + 1;
        if (dp[l][r]) ans[dp[l][r]]++;
      }
    for (int i = slen; i >= 1; i--) ans[i] += ans[i + 1];
    printf("%d", ans[1]);
    for (int k = 2; k <= slen; k++) printf(" %d", ans[k]);
    printf("\n");
  }
  return 0;
}