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.BufferedInputStream;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner s = new Scanner(new BufferedInputStream(System.in));
		int n = s.nextInt();
		int[] arr = new int[n];
		int[] map = new int[105];
		int count = 0;
	    boolean extra = false;
		for (int i = 0; i < n; i++) {
			arr[i] = s.nextInt();
			map[arr[i]]++;
			if (map[arr[i]] == 1) {
				count++;
			} else if (map[arr[i]] == 2) {
				count--;
			} else {
				extra = true;
			}
		}
		if (count % 2 == 1 && !extra) {
			System.out.println("NO");
		} else {
			int half = count / 2;
			if(count % 2 == 0) {
				extra = false;
			}
			System.out.println("YES");
			StringBuilder build = new StringBuilder();
			for (int i = 0; i < n; i++) {
				if (map[arr[i]] == 1) {
					if (half > 0) {
						half--;
						build.append('A');
					} else {
						build.append('B');
					}
				} else if (extra && map[arr[i]] > 2) {
					extra = false;
					build.append('A');
				} else {
					build.append('B');
				}
			}
			System.out.println(build);
		}
		System.out.flush();
	}
}