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.util.*;

public class Hello {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		
		int n = scanner.nextInt();
		int[] fix = new int[101];
		int[] a = new int[101];
		int p1 = 0, p2 = 0;
		String ans = "";
		
		for (int i=1;i<=n;i++) {
			a[i] = scanner.nextInt();
			fix[a[i]]++;
		}
		
		for (int i=1;i<=n;i++) {
			if (fix[a[i]] == 1) {
				if (p1 == p2) {
					ans += 'A';
					p1++;
				} else {
					ans += 'B';
					p2++;
				}
				continue;
			} ans += 'A';
		}
		
		if (p1 == p2) {
			resolve(ans);
		}
		
		for (int i=1;i<=n;i++) {
			if (fix[a[i]] > 2 && ans.charAt(i-1) == 'A') {
				ans = ans.substring(0, i - 1) + 'B' + ans.substring(i);
				p2++;
				break;
			}
		}
		
		if (p1 == p2) {
			resolve(ans);
		}
		
		reject();
		
		scanner.close();
	}
	
	private static  void resolve(String ans) {
		System.out.println("YES");
		System.out.println(ans);
		
		System.exit(0);
	}
	
	private static void reject() {
		System.out.println("NO");
		
		System.exit(0);
	}
}