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 JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;


public class Main {
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    static int[][] a;
    static int n;
    
    static void solve() throws Exception {
        char[] s = ("#" + next()).toCharArray();
        n = s.length-1;
        boolean[] used = new boolean[26];
        for (int i = 1; i <= n; i++) {
            used[s[i]-'a'] = true;
        }
        int maxD = 0;
        for (int i = 0; i < 26; i++) {
            if (used[i]) {
                maxD++;
            }
        }
        out.println(maxD);
        long[] res = new long[maxD+1];
        for (int i = 1; i <= maxD; i++) {
            int[] cnt = new int[26];
            int r = 0;
            int d = 0;
            for (int l = 1; l <= n; l++) {
                if (r < l) {
                    r = l;
                    cnt = new int[26];
                    cnt[s[l]-'a']++;
                    d = 1;
                }
                while (r+1 <= n) {
                    if (d == i && cnt[s[r+1]-'a'] == 0) {
                        break;
                    }
                    cnt[s[r+1]-'a']++;
                    if (cnt[s[r+1]-'a'] == 1) {
                        d++;
                    }
                    r++;
                }
                res[i] += r-l+1;
                cnt[s[l]-'a']--;
                if (cnt[s[l]-'a'] == 0) {
                    d--;
                }
            }
            out.println(res[i]-res[i-1]);
        }
    }

    static int sqr(int x) {
        return x*x;
    }
    
    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }
    
    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }
    
    static String nextLine() throws IOException {
        tok = new StringTokenizer("");
        return in.readLine();
    }

    static boolean hasNext() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return false;
            }
            tok = new StringTokenizer(s);
        }
        return true;
    }

    public static void main(String args[]) {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            //in = new BufferedReader(new FileReader("input.in"));
            //out = new PrintWriter(new FileWriter("output.out"));
            solve();
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            java.lang.System.exit(1);
        }
    }
}