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>
int N, S, c[27];
long long f[27];
char s[300005];
struct st {
  int a[27], k, p;
  st() { k = 0, memset(s, 0, sizeof(s)); }
  void ins() {
    if (++p <= N) k += !a[s[p]]++;
  }
  void del(int p) {
    if (p) k -= !--a[s[p]];
  }
} a[27];
int main() {
  scanf("%s", s + 1), N = strlen(s + 1);
  for (int i = 1; i <= N; i++) c[s[i] -= 97] = 1;
  for (int i = 0; i < 26; i++) S += c[i];
  printf("%d\n", S);
  for (int i = 0; i <= N; i++) {
    a[0].p = i + 1;
    for (int j = 1; j <= S; j++) {
      a[j].del(i);
      for (; a[j].p <= N && a[j].k <= j; a[j].ins())
        ;
      f[j] += a[j].p - a[j - 1].p;
    }
  }
  for (int i = 1; i <= S; i++) printf("%I64d\n", f[i]);
}