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.stream.IntStream;
import java.util.Arrays;
import java.util.Iterator;
import java.util.Set;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class CVasyaIMultimnozhestva {
        public void solve(int testNumber, InputReader in, PrintWriter out) {

            int n = in.nextInt();
            int[] s = in.nextArr(n);

            Map<Integer, Integer> ms = GeekInteger.multiSet(s);
            Set<Integer> ones = new HashSet<>();
            Set<Integer> doubles = new HashSet<>();
            Set<Integer> many = new HashSet<>();
            for (int key : ms.keySet()) {
                if (ms.get(key) == 1) {
                    ones.add(key);
                }
                if (ms.get(key) == 2) {
                    doubles.add(key);
                }
                if (ms.get(key) > 2) {
                    many.add(key);
                }

            }
            if (ones.size() % 2 != 0 && many.isEmpty()) {
                out.println("NO");
                return;
            }

            int k = Integer.MAX_VALUE;
            if (ones.size() % 2 != 0) {
                k = many.iterator().next();
//            ones.add(many.iterator().next());
            }

            int onesHalf = ones.size() / 2;
            int tho = doubles.size();
            out.println("YES");

//        int kos =
            for (int i = 0; i < n; i++) {

                if (ones.contains(s[i])) {
                    if (onesHalf > 0) {
                        out.print("B");
                        onesHalf--;
//                    if ()
//                        ones.remove(s[i]);
                    } else {
                        out.print("A");
                    }
                    continue;
                }

                if (k == (s[i])) {
//                if (onesHalf > 0) {
                    out.print("B");
                    k = Integer.MAX_VALUE;
//                    onesHalf--;
//                    if ()
//                        ones.remove(s[i]);
//                } else {
//                    out.print("A");
//                }
                    continue;
                }

                if (doubles.contains(s[i])) {
                    if (tho > 0) {
                        out.print("B");
                        tho--;
                    } else {
                        out.print("A");
                    }
                    continue;
                }
                out.print("A");


            }


        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

        public int[] nextArr(int size) {
            return Arrays.stream(new int[size]).map(c -> nextInt()).toArray();
        }

    }

    static class GeekInteger {
        public static Map<Integer, Integer> multiSet(int[] arr) {
            Map<Integer, Integer> co = new HashMap<>();
            for (int i : arr) co.merge(i, 1, Integer::sum);
            return co;
        }

    }
}