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.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {
	
	// value -> index list
	private static Map<Integer , List<Integer>> map = new HashMap<>();
	private static char[] output = new char[1000];
	
	public static void main(String[] args) {		
		
		Scanner scan = new Scanner(System.in);
	
		int i , n = scan.nextInt();
		for (i = 0;i < n;i ++) {
			int value = scan.nextInt();
			if (!map.containsKey(value)) {
				map.put(value , new ArrayList<>());				
			}
			map.get(value).add(i);
		}
		int cnt = 0;
		boolean containsMoreThan2 = false;
		for (List<Integer> list : map.values()) {
			if (list.size() == 1) {
				cnt ++;			
			}
			if (list.size() > 2) {
				containsMoreThan2 = true;
			}
		}
		if (cnt % 2 == 1) {
			if (containsMoreThan2) {
				int useValue = 0;
				for (Map.Entry<Integer , List<Integer>> entry : map.entrySet()) {
					if (entry.getValue().size() > 2) {
						useValue = entry.getKey();
						break;
					}
				}
				// use Value
				output[map.get(useValue).get(0)] = 'B';
				for (i = 1;i < map.get(useValue).size();i ++) {
					output[map.get(useValue).get(i)] = 'A';
				}
				boolean flag = true;
				for (Map.Entry<Integer , List<Integer>> entry : map.entrySet()) {
					if (entry.getKey() != useValue) {
						// single element, in turn
						if (entry.getValue().size() == 1) {
							if (flag) {
								output[entry.getValue().get(0)] = 'A';
								flag = false;
							} else {
								output[entry.getValue().get(0)] = 'B';
								flag = true;
							}
						} else {
							for (i = 0;i < entry.getValue().size();i ++) {
								output[entry.getValue().get(i)] = 'A';
							}
						}
					}
				}
				System.out.println("YES");
				for (i = 0;i < n;i ++) {
					System.out.print(output[i]);
				}
				System.out.println();
			} else {
				System.out.println("NO");
			}
		} else {
			boolean flag = true;
			for (Map.Entry<Integer , List<Integer>> entry : map.entrySet()) {
				// single element, in turn
				if (entry.getValue().size() == 1) {
					if (flag) {
						output[entry.getValue().get(0)] = 'A';
						flag = false;
					} else {
						output[entry.getValue().get(0)] = 'B';
						flag = true;
					}
				} else {
					for (i = 0;i < entry.getValue().size();i ++) {
						output[entry.getValue().get(i)] = 'A';
					}
				}
			}		
			System.out.println("YES");
			for (i = 0;i < n;i ++) {
				System.out.print(output[i]);
			}
			System.out.println();
		}
		
	}
	
	
}