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;
const int MAXN = 3 * 100000 + 10;
int n, p[26], b[26];
long long Tohka[26];
char str[MAXN];
int main() {
  scanf("%s", str + 1);
  n = strlen(str + 1);
  for (int i = 0; i < 26; ++i) p[i] = n + 1;
  for (int i = n; i >= 1; --i) {
    p[str[i] - 'a'] = i;
    memcpy(b, p, sizeof(b));
    sort(b, b + 26);
    for (int i = 1; i < 26; ++i)
      if (b[i - 1] != n + 1)
        Tohka[i - 1] += b[i] - b[i - 1];
      else
        break;
    Tohka[25] += n + 1 - b[25];
  }
  int Mashiro = 0;
  for (; Tohka[Mashiro]; ++Mashiro)
    ;
  cout << Mashiro << endl;
  for (int i = 0; i < 26; ++i)
    if (Tohka[i])
      cout << Tohka[i] << endl;
    else
      break;
  fclose(stdin);
  fclose(stdout);
  return 0;
}