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 multiset {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		HashMap<Integer,Integer> h= new HashMap<Integer,Integer>();
		int[] a = new int[n];
		int max=0;
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
			if(!h.containsKey(a[i])){
				h.put(a[i], 1);
			}
			else{
				h.put(a[i],h.get(a[i])+1);
			}
			max=Math.max(max, h.get(a[i]));
		}
		int count=0;
		for(Map.Entry<Integer,Integer> e : h.entrySet()){
			if(e.getValue()==1){
				count++;
			}
		}
		if(count%2==0){
			System.out.println("YES");
			boolean f=true;
			for(int i=0;i<n;i++){
				if(h.get(a[i])==1){
					if(f){
						System.out.print("A");
						f=false;
					}
					else{
						System.out.print("B");
						f=true;
					}
				}
				else{
					System.out.print("A");
				}
			}
		}
		else{
			if(max<3){
				System.out.println("NO");
			}
			else{
				boolean f=true;
				boolean g=true;
				System.out.println("YES");
				for(int i=0;i<n;i++){
					if(h.get(a[i])==1){
						if(f){
							System.out.print("A");
							f=false;
						}
						else{
							f=true;
							System.out.print("B");
						}
						
					}
					else if(g==true&&h.get(a[i])>=3){
						System.out.print("B");
						g=false;
					}
					else{
						System.out.print("A");
					}
				}
			}
		}

	}

}