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.*;
import java.io.*;
import java.math.*;
public class hi{
   
   
   
    public static void main(String[] args)  {
        
        Scanner sc = new Scanner(System.in);
        int n= sc.nextInt();
        int[] nb = new int[n];
        int[] a = new int[101];
        for(int i=0;i<n;i++){
            nb[i] = sc.nextInt();
            a[nb[i]]++;
        }
        int nice = 0;
        for(int i=0;i<=100;i++) if(a[i]==1) nice++;
        if(nice%2==1){
            int k=-1;
            for(int i=0;i<101;i++){
                if(a[i]>2){
                    k = i;
                    break;
                }
            }
            if(k==-1) System.out.println("NO");
            else{
                System.out.println("YES");
                nice /=2;
                nice++;
                StringBuilder sb = new StringBuilder("");
                int l=0;
                for(int i=0;i<n;i++){
                    if(a[nb[i]]!=1){
                        sb.append("A");
                    }else{
                        if(l<nice){
                            sb.append("A");
                            l++;
                        }else{
                            sb.append("B");
                        }
                    }
                }
                for(int i=0;i<n;i++){
                    if(nb[i]==k){
                        sb.setCharAt(i,'B');
                        break;
                    }
                }
                System.out.println(sb.toString());
            }
        }else{
            System.out.println("YES");
            nice /=2;
            StringBuilder sb = new StringBuilder("");
            int l=0;
            for(int i=0;i<n;i++){
                if(a[nb[i]]!=1){
                    sb.append("A");
                }else{
                    if(l<nice){
                        sb.append("A");
                        l++;
                    }else{
                        sb.append("B");
                    }
                }
            }
            System.out.println(sb.toString());
        }
    }
    
}