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.util.Arrays;
import java.util.Scanner;


public class Bog {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		String s = sc.nextLine();
		int[] last = new int[26];
		int[] sort = new int[26];
		long[] count = new long[26];
		int prev = -1;
		Arrays.fill(last, -1);
		char c;
		for(int i = 0; i < s.length(); i++){
			prev = -1;
			c = s.charAt(i);
			last[c-'a'] = i;
			sort = last.clone();
			Arrays.sort(sort);
			for(int j = 0; j < 26; j++){
				count[25-j] += sort[j] - prev;
				prev = sort[j];
			}
		}
		int most = -1;
		for(int i = 0; i < 26; i++){
			if(count[i] > 0){
				most = i;
			}
		}
		System.out.println(most+1);
		for(int i = 0; i < most+1; i++){
			System.out.println(count[i]);
		}
		
	}

}