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;
char str[300010];
int n, ans = 0, s[300010][30];
long long f[300010][30], t[30];
int main() {
  scanf("%s", str);
  n = strlen(str);
  for (int i = 0; i < n; i++) {
    f[i][1] = 1;
    s[i][1] = 1 << (str[i] - 'a');
  }
  for (int i = 0; i < n - 1; i++)
    for (int j = 1; j <= 26; j++)
      if (f[i][j])
        if (((1 << (str[i + 1] - 'a')) | s[i][j]) != s[i][j]) {
          s[i + 1][j + 1] = (1 << (str[i + 1] - 'a')) | s[i][j];
          f[i + 1][j + 1] += f[i][j];
        } else {
          f[i + 1][j] += f[i][j];
          s[i + 1][j] = s[i][j];
        }
  for (int i = 0; i < n; i++)
    for (int j = 1; j <= 26; j++)
      t[j] += f[i][j], ans = max(ans, j * (f[i][j] > 0));
  printf("%d\n", ans);
  for (int i = 1; i <= ans; i++) printf("%I64d\n", t[i]);
  return 0;
}