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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Map.Entry;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class dk {
	public static void main(String[] args) throws NumberFormatException, IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] A = new int[n];
		int nice = 0;
		TreeMap<Integer, Integer> tm = new TreeMap<>();
		for (int i = 0; i < n; i++) {
			A[i] = sc.nextInt();
			if (!tm.containsKey(A[i]))
				tm.put(A[i], 0);
			tm.put(A[i], tm.get(A[i]) + 1);
		}
		for (Entry<Integer, Integer> e : tm.entrySet()) {
			if (e.getValue() == 1)
				nice++;
		}
		int who = 0;
		char[] res = new char[n];
		for (int i = 0; i < n; i++) {
			if (tm.get(A[i]) == 1) {
				res[i] = (char) (who + 'A');
				who ^= 1;
			} else
				res[i] = 'A';

		}
		if (nice % 2 == 1) {
			for (int i = 0; i < n; i++) {
				if (tm.get(A[i]) > 2) {
					res[i] = 'B';
					nice--;
					break;
				}

			}
		}
		if (nice % 2 == 0) {
			System.out.println("YES");
			System.out.println(String.valueOf(res));
		} else
			System.out.println("NO");
		out.close();
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

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

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

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