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;
using ll = long long;
using vi = vector<long long>;
using vl = vector<long long>;
using pii = pair<long long, long long>;
using pll = pair<long long, long long>;
const long long DX[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0},
                DY[9] = {-1, 0, 1, 0, -1, 1, 1, -1, 0};
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto i = begin(v); i != end(v); ++i)
    os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
template <class T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto i = begin(v); i != end(v); ++i) is >> *i;
  return is;
}
template <class T>
istream &operator>>(istream &is, pair<T, T> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
struct before_main_function {
  before_main_function() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
  }
} before_main_function;
bool ispal[5001][5001];
void palindromes(string s) {
  long long n = s.size();
  for (long long i = 0; i < n; i++) {
    long long l, u;
    auto append_pal = [&]() {
      while (0 <= l && u < n) {
        if (s[l] != s[u]) {
          break;
        }
        ispal[l][u] = true;
        l--;
        u++;
      }
    };
    l = u = i;
    append_pal();
    l = u = i;
    u++;
    append_pal();
  }
}
signed main() {
  string s;
  cin >> s;
  palindromes(s);
  long long n = ((long long)s.size());
  vector<long long> ans(n, 0);
  for (long long l = 0, llen = (long long)(n); l < llen; ++l) {
    for (long long r = l, rlen = (long long)(n); r < rlen; ++r) {
      if (!ispal[l][r]) continue;
      long long L = l, R = r;
      for (long long i = 0, ilen = (long long)(n); i < ilen; ++i) {
        if (!ispal[L][R]) break;
        ans[i]++;
        R = L + (R - L + 1) / 2 - 1;
      }
    }
  }
  cout << ans << endl;
  return 0;
}