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.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;


public class Main {

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] counter = new int[101];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            counter[a[i]]++;
        }
        int ones = 0;
        int odds = 0;
        for (int i = 1; i < 101; i++)
            if (counter[i] == 1) ones++;
            else if (counter[i] != 2 && counter[i] != 0) odds++;
//        System.err.println(ones + " " + odds);
        if (ones % 2 != 0 && odds == 0)
            out.println("NO");
        else {
            out.println("YES");
            ArrayList<Integer> one = new ArrayList<>();
            int odd = -1;
            for (int i = 0; i < n; i++) {
                if (counter[a[i]] == 1) {
                    one.add(i);
                    continue;
                }
                if (counter[a[i]] != 2) odd = i;

            }
            HashSet<Integer> B = new HashSet<>();
            for (int i = 1; i < one.size(); i += 2) {
                B.add(one.get(i));
            }
            if (one.size() % 2 != 0) B.add(odd);
            for (int i = 0; i < n; i++)
                if (B.contains(i)) out.print("B");
                else out.print("A");
        }
        out.flush();
        out.close();
    }

    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

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

}