Problem: String diversity is the number of symbols that occur in the string at least once. Diversity of s will be denoted by d(s). For example , d("aaa")=1, d("abacaba")=3.

Given a string s, consisting of lowercase Latin letters. Consider all its substrings. Obviously, any substring diversity is a number from 1 to d(s). Find statistics about substrings diversity: for each k from 1 to d(s), find how many substrings of s has a diversity of exactly k.

Input

The input consists of a single line containing s. It contains only lowercase Latin letters, the length of s is from 1 to 3·105.

Output

Print to the first line the value d(s). Print sequence t1, t2, ..., td(s) to the following lines, where ti is the number of substrings of s having diversity of exactly i.

Examples

Input

abca


Output

3
4
3
3


Input

aabacaabbad


Output

4
14
19
28
5

Note

Consider the first example.

We denote by s(i, j) a substring of "abca" with the indices in the segment [i, j].

  * s(1, 1) =  "a", d("a") = 1
  * s(2, 2) =  "b", d("b") = 1
  * s(3, 3) =  "c", d("c") = 1
  * s(4, 4) =  "a", d("a") = 1
  * s(1, 2) =  "ab", d("ab") = 2
  * s(2, 3) =  "bc", d("bc") = 2
  * s(3, 4) =  "ca", d("ca") = 2
  * s(1, 3) =  "abc", d("abc") = 3
  * s(2, 4) =  "bca", d("bca") = 3
  * s(1, 4) =  "abca", d("abca") = 3



Total number of substring with diversity 1 is 4, with diversity 2 equals 3, 3 diversity is 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  map<char, int> m;
  long long ar[26] = {0};
  string s;
  cin >> s;
  for (int i = (int)s.length() - 1; i >= 0; i--) {
    m[s[i]] = i;
    vector<int> v;
    for (map<char, int>::iterator it = m.begin(); it != m.end(); it++) {
      v.push_back(it->second);
    }
    sort(v.begin(), v.end());
    for (int i = 0; i < (int)v.size(); i++) {
      int t = i < (int)v.size() - 1 ? v[i + 1] : (int)s.length();
      ar[i] += t - v[i];
    }
  }
  vector<long long> a;
  for (int i = 0; i < 26; i++) {
    if (ar[i]) {
      a.push_back(ar[i]);
    }
  }
  cout << a.size() << endl;
  for (int i = 0; i < a.size(); i++) {
    cout << a[i] << endl;
  }
  return 0;
}