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 VasyaAndMultiSet {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        int s[]=new int[101];
        HashSet<Integer> hs=new HashSet<>();
        HashSet<Integer> ar=new HashSet<>();
        int x=0;
        int y=0;
        for(int i=0;i<n;i++)
        {
            a[i]=sc.nextInt();
            s[a[i]]++;
        }
        for(int i=1;i<101;i++)
        {
            if(s[i]==1)
            {
                hs.add(i);
                x++;
            }
            if(s[i]>=3)
            {
                y++;
                ar.add(i);
            }
            
        }
       if(x%2==1 && y==0)
       {
           System.out.println("NO");
           return;
       }
       else if(x%2==1 && y!=0)
       {
           System.out.println("YES");
           int c=0;
           int k=0;
           for(int i=0;i<n;i++)
           {
               if(c==0 && ar.contains(a[i]))
               {
                   System.out.print("A");
                    c=1;   
               }
               else if(k<x/2 && hs.contains(a[i]))
               {
                   System.out.print("A");
                   k++;   
               }    
               else
                   System.out.print("B");
           }
           
       }
       else
       {
           System.out.println("YES");
           int k=0;
           for(int i=0;i<n;i++)
           {
               if(k<x/2 && hs.contains(a[i]))
               {
                   System.out.print("A");
                   k++;
               }
               else
               {
                   System.out.print("B");
               }
           }
       }
       
    }
}