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.Scanner;
public class Function {
	public static void main(String[] args) {
    Scanner input =new Scanner(System.in);
  
    int n =input.nextInt();
    int u = 0;
    char[]t = new char[n];
    int [] x =new  int [n];
    int [] seq=new int [101];
    boolean [] w = new boolean[101];
    int count =0;
    int p = Integer.MIN_VALUE;
    for(int i=0;i<n;i++)
    {
    	x[i] = input.nextInt();
        seq[x[i]]++;
        if(seq[x[i]]>p)
        	{
        	p= seq[x[i]];
        	u = x[i];
        	}
    }
    for(int i=0;i<101;i++)
    {
    	if(seq[i]==1)
    		{
    		count++;
    		w[i]=true;
    		}
    	//if(seq[i]>p)
    	//{
    	//	p = i;
    	//	System.out.println(p);
    	//}
    }
  if(count == 0)
    {
    	int y = 0;
    	System.out.println("YES");
    	while(y<n)
    	{
    		y++;
    		System.out.print("A");
    	}
    }
    else if(count%2==1&&p<3)
    {
    	System.out.println("NO");
    }
    else if(count%2==1)
    {
    	int l = 0;
    	System.out.println("YES");
    	for(int j=0;j<n;j++)
    	{
    		if(l<count/2)
    		{
    			if(w[x[j]]==true&&l<count/2)
    			{
    				t[j]  = 'A';l++;
    			}
    			else t[j]='B';
    			
    		}
    		else t[j] = 'B';
    	}
	for(int i=0;i<n;i++)
	{
		if(x[i]==u)
		{
			 t[i] = 'A';
			String ff = new String(t);
			System.out.println(ff);
			break;
		}
		
	}
     
    }
    else
    {
    	int l = 0;
    	System.out.println("YES");
    	for(int j=0;j<n;j++)
    	{
    		if(l<count/2)
    		{
    			if(w[x[j]]==true&&l<count/2)
    			{
    				t[j]  = 'A';l++;
    			}
    			else t[j]='B';
    			
    		}
    		else t[j] = 'B';
        }
    String h = new String(t);System.out.println(h);
    }    	
   
    	
  
    
	}

}