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 Top[30], hs[30], g[30], n, ls;
long long Ans[30];
char A[300000 + 3];
int main() {
  scanf("%s", A + 1);
  n = strlen(A + 1);
  for (int i = n; i >= 1; i--) {
    int x = A[i] - 'a';
    if (Top[x]) {
      for (int j = hs[x]; j < ls; j++) g[j] = g[j + 1], hs[g[j]] = j;
      ls--;
    }
    Top[x] = i;
    g[++ls] = x;
    hs[x] = ls;
    for (int j = ls; j > 1; j--) Ans[ls - j + 1] += Top[g[j - 1]] - Top[g[j]];
    Ans[ls] += n - Top[g[1]] + 1;
  }
  printf("%d\n", ls);
  for (int i = 1; Ans[i]; i++) printf("%I64d\n", Ans[i]);
}