Problem: Vasya has a multiset s consisting of n integer numbers. Vasya calls some number x nice if it appears in the multiset exactly once. For example, multiset \{1, 1, 2, 3, 3, 3, 4\} contains nice numbers 2 and 4.

Vasya wants to split multiset s into two multisets a and b (one of which may be empty) in such a way that the quantity of nice numbers in multiset a would be the same as the quantity of nice numbers in multiset b (the quantity of numbers to appear exactly once in multiset a and the quantity of numbers to appear exactly once in multiset b).

Input

The first line contains a single integer n~(2 ≤ n ≤ 100).

The second line contains n integers s_1, s_2, ... s_n~(1 ≤ s_i ≤ 100) — the multiset s.

Output

If there exists no split of s to satisfy the given requirements, then print "NO" in the first line.

Otherwise print "YES" in the first line.

The second line should contain a string, consisting of n characters. i-th character should be equal to 'A' if the i-th element of multiset s goes to multiset a and 'B' if if the i-th element of multiset s goes to multiset b. Elements are numbered from 1 to n in the order they are given in the input.

If there exist multiple solutions, then print any of them.

Examples

Input

4
3 5 7 1


Output

YES
BABA


Input

3
3 5 1


Output

NO

Solution (in JAVA):

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



public class Main {

    public static void main(String[] args) {
        FastReader fr =new FastReader();
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        int n = fr.nextInt();
        int[] s = new int[n] , k = new int[103];

        for (int i = 0; i < n; i ++){
            s[i] = fr.nextInt();
            k[s[i]] ++;
        }

        int counter1 = 0, counter3 = 0;

        for (int i = 0; i < 103; i ++) {
            if (k[i] == 1) counter1++;
            else if (k[i] >= 3) counter3++;
        }

        if ((counter1 % 2 == 1)&&(counter3 == 0)) {
            out.print("NO");
            out.close();
            return;
        }
        out.println("YES");

        char[] chars = new char[n];
        boolean bol = true;

        for (int i = 0; i < n; i ++){
            if (k[s[i]] == 1){
                if (bol) chars[i] = 'A';
                else chars[i] = 'B';
                bol = !bol;
            }
        }

        for (int i = 0; i < n; i ++){
            if ((!bol)&&(k[s[i]] > 2)) {
                chars[i] = 'B';
                bol = !bol;
            } else if (k[s[i]] > 1){
                chars[i] = 'A';
            }
        }
        String ss = String.valueOf(chars);
        out.print(ss);
        out.close();
    }





    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}