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.*;

public class First {
    private static final Scanner sc = new Scanner(System.in);
    private static final PrintWriter pw = new PrintWriter(System.out);
    private static StringBuffer ans = new StringBuffer();

    public static void main(String[] args) throws Exception {
        int n = sc.nextInt(), s = 0, t = 0, c = 0, d = 0;
        int[] a = new int[n];
        char[] b = new char[n];
        HashMap<Integer, Integer> cnt = new HashMap<>();
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            b[i] = 'A';
            if (!cnt.containsKey(a[i])) cnt.put(a[i], 1);
            else cnt.put(a[i], cnt.get(a[i]) + 1);
        }
        for (int x : cnt.values()) if (x == 1) s++;
        for (int x : cnt.keySet()) {
            if (t >= (s / 2)) break;
            if (cnt.get(x) == 1) {
                for (int i = 0; i < n; i++) {
                    if (a[i] == x) {
                        b[i] = 'B';
                        break;
                    }
                }
                t++;
            }
        }
        if (s % 2 == 1) {
            for (int x : cnt.keySet()) {
                if (cnt.get(x) > 2) {
                    for (int i = 0; i < n; i++) {
                        if (a[i] == x) {
                            b[i] = 'B';
                            break;
                        }
                    }
                    break;
                }
            }
        }
        for (char x : b) if (x == 'B') d++;
        for (int i = 0; i < n; i++) if (b[i] == 'A' && cnt.get(a[i]) == 1) c++;
        if (c == d) {
            ans.append("YES\n");
            for (char x : b) ans.append(x);
        } else ans.append("NO");
        pw.print(ans);
        sc.close();
        pw.close();
    }
}
class Scanner {
    private final BufferedReader br;
    private StringTokenizer st;
    public Scanner(InputStream in) {
        br = new BufferedReader(new InputStreamReader(in));
        st = new StringTokenizer("");
    }
    public String next() throws IOException {
        if (!st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    public void close() throws IOException {
        br.close();
    }
}
class PrintWriter {
    private final BufferedOutputStream pw;
    public PrintWriter(OutputStream out) {
        pw = new BufferedOutputStream(out);
    }
    public void print(Object o) throws IOException {
        pw.write(o.toString().trim().getBytes());
        pw.flush();
    }
    public void close() throws IOException {
        pw.close();
    }
}