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;

public class C {
	public static void main(String[] args) throws IOException {
		BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(input.readLine());
		
		String[] tokens = input.readLine().split(" ");
		int[] multiset = new int[n];
		int[] counts = new int[101];
		int[] plan = new int[101];
		
		for (int i = 0; i < plan.length; i++) {
			plan[i] = -1;
		}
		
		for (int i = 0; i < n; i++) {
			int next = Integer.parseInt(tokens[i]);
			multiset[i] = next;
			counts[next]++;
		}
		
		int single = 0;
		int multiple = 0;
		
		for (int i = 0; i < 101; i++) {
			if (counts[i] == 1) {
				single++;
			} else if (counts[i] > 2) {
				multiple++;
			}
		}
		
		if (!(single % 2 == 0 || multiple > 0)) {
			System.out.println("NO");
		} else {
			System.out.println("YES");
			int score = 0;
			
			String[] planner = new String[n];
			
			for (int i = 0; i < n; i++) {
				int next = multiset[i];
				if (plan[next] == 0) {
					planner[i] = "A";
				} else if (plan[next] == 1) {
					planner[i] = "B";
				} else if (counts[next] == 2) {
					planner[i] = "A";
					plan[next] = 1;
				} else if (counts[next] == 1) {
					if (score == 0) {
						planner[i] = "A";
						plan[next] = 1;
						score++;
					} else if (score > 0) {
						planner[i] = "B";
						plan[next] = 0;
						score--;
					}
				}
			}
			
			for (int i = 0; i < n; i++) {
				int next = multiset[i];
				if (counts[next] > 2) {
					if (plan[next] == 0) {
						planner[i] = "A";
					} else if (plan[next] == 1) {
						planner[i] = "B";
					} else {
						if (score == 0) {
							planner[i] = "A";
							plan[next] = 0;
						} else if (score > 0) {
							planner[i] = "B";
							plan[next] = 0;
							score--;
						}
					}
				}
			}
			
			for (int i = 0; i < n; i++) {
				System.out.print(planner[i]);
			}
		}
	}
}