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.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class C_407 {
	

	public static void main(String[] args) throws IOException {
		BufferedReader input = new BufferedReader (new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out, true);
		int n = Integer.parseInt(input.readLine());
		int[] nums = new int[n];
		char[] ans = new char[n];
		Arrays.fill(ans, 'B');
		int a = 0;
		int b = 0;
		Map<Integer, Integer> numCount = new HashMap();
		
		String[] line = input.readLine().split(" ");
		for (int i = 0; i < n; i++) {
			nums[i] = Integer.parseInt(line[i]);
			numCount.put(nums[i], numCount.getOrDefault(nums[i], 0) + 1);
		}
		
		for (int i = 0; i < n; i++) {
			if (numCount.get(nums[i]) == 1) {
				if (a > b) {
					b++;
				} else {
					a++;
					ans[i] = 'A';
				}
			}
		}
		
		if (a != b) {
			for (int i = 0; i < n; i++) {
				if (numCount.get(nums[i]) > 2) {
					if (a > b) {
						b++;
						for (int j = 0; j < n; j++) {
							if (nums[i] == nums[j]) {
								ans[j] = 'A';
							}
						}
						ans[i] = 'B';
					} else {
						a++;
						ans[i] = 'A';
					}
					break;
				}
			}
		}
		
		if (a == b) {
			pw.println("YES");
			pw.println(new String(ans));
		} else {
			pw.println("NO");
		}
		
		
		input.close();
		pw.close();
	}
}