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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class DiverseSubstrings {
    public static void main(String[] args) {
        InputReader r = new InputReader(System.in);
        char[] arr = r.next().toCharArray();
        boolean[] set = new boolean[26];
        for (char c : arr)
            set[c - 'a'] = true;
        int size = 0;
        for (boolean b : set)
            if (b)
                size++;
        System.out.println(size);
        long[] res = new long[28];
        int[][] next = new int[arr.length][26];
        Arrays.fill(next[arr.length - 1], -1);
        next[arr.length - 1][arr[arr.length - 1] - 'a'] = arr.length - 1;
        for (int i = arr.length - 2; i >= 0; i--) {
            for (int j = 0; j < 26; j++)
                next[i][j] = next[i + 1][j];
            next[i][arr[i] - 'a'] = i;
        }
        boolean[] vis = new boolean[26];
        for (int i = 0; i < arr.length; i++) {
            Arrays.fill(vis, false);
            int index = i;
            int itr = 0;
            while (true) {
                int nextOcc = 1 << 28, nextChar = -1;
                for (int j = 0; j < 26; j++) {
                    if (vis[j])
                        continue;
                    int first = next[index][j];
                    if (first == -1)
                        continue;
                    if (nextOcc > first) {
                        nextOcc = first;
                        nextChar = j;
                    }
                }
                if (nextChar == -1) {
                    res[itr] += arr.length - index;
                    break;
                }
                vis[nextChar] = true;
                res[itr] += (nextOcc - index);
                index = nextOcc;
                itr++;
            }
        }
        for (int i = 1; i <= size; i++)
            System.out.println(res[i]);
    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public InputReader(FileReader stream) {
            reader = new BufferedReader(stream);
            tokenizer = null;
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
                return null;
            }
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}