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 Codeforces {
    private static void sport(int[] a) {
        int n = a.length;
        Map<Integer,Integer> map = new HashMap<>();
        for (int i : a) {
            map.put(i,map.getOrDefault(i,0)+1);
        }
        Set<Integer> good = new HashSet<>();
        Set<Integer> agood = new HashSet<>();
        for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
            if (entry.getValue()==1){
                good.add(entry.getKey());
            }
        }
        boolean flag=false;
        if (good.size()%2==1){
            flag=true;
        }
        int lim= good.size()/2;
        Iterator<Integer> iterator = good.iterator();
        while (lim>0){
            Integer next = iterator.next();
            agood.add(next);
            lim--;
        }
        StringBuilder builder = new StringBuilder();
        for (int i : a) {
            if (agood.contains(i)){
                builder.append("A");
            }else{
                if (map.get(i)>2&&flag){
                    flag=false;
                    builder.append("A");
                }else {
                    builder.append("B");
                }
            }
        }
        if (flag){
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        System.out.println(builder.toString());
    }


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i]=sc.nextInt();
        }
        sport(a);
    }
}