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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.util.Set;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CVasyaAndMultisets solver = new CVasyaAndMultisets();
        solver.solve(1, in, out);
        out.close();
    }

    static class CVasyaAndMultisets {
        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            int n = sc.nextInt();
            int[] tab = new int[n];
            for (int i = 0; i < n; i++) {
                tab[i] = sc.nextInt();
            }
            HashMap<Integer, Integer> occ = new HashMap<>();
            for (int i = 0; i < n; i++) {
                if (occ.get(tab[i]) == null) {
                    occ.put(tab[i], 1);
                } else {
                    occ.put(tab[i], occ.get(tab[i]) + 1);
                }
            }
            int nb1 = 0;
            int nb2 = 0;
            Iterator<Map.Entry<Integer, Integer>> it = occ.entrySet().iterator();
            Map.Entry<Integer, Integer> a;
            while (it.hasNext()) {
                a = it.next();
                if (a.getValue() == 1) {
                    nb1++;
                } else if (a.getValue() > 2) {
                    nb2++;
                }
            }
            char[] ans = new char[n];
            for (int i = 0; i < n; i++) {
                ans[i] = 'A';
            }
            if (nb1 % 2 == 0) {
                out.println("YES");
                int nb = nb1 / 2;
                for (int i = 0; i < n; i++) {
                    if (occ.get(tab[i]) == 1 && nb > 0) {
                        ans[i] = 'B';
                        nb--;
                    } else if (occ.get(tab[i]) == 1) {
                        ans[i] = 'A';
                    }
                }
                for (int i = 0; i < n; i++) {
                    out.print(ans[i]);
                }
            } else {
                int nb = nb1 / 2;
                if (nb2 == 0) {
                    out.println("NO");
                    return;
                }
                out.println("YES");
                for (int i = 0; i < n; i++) {
                    if (occ.get(tab[i]) == 1 && nb > 0) {
                        ans[i] = 'B';
                        nb--;
                    }
                    if (nb == 0) {
                        break;
                    }
                }
                for (int i = 0; i < n; i++) {
                    if (occ.get(tab[i]) > 2) {
                        ans[i] = 'B';
                        break;
                    }
                }
                for (int i = 0; i < n; i++) {
                    out.print(ans[i]);
                }
            }

        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

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

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

    }
}