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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		int n, val;
		Scanner sc= new Scanner(System.in);
		n=sc.nextInt();
		int[] arr= new int[n];
		int i, count=0, pos=-1;
		Map<Integer, Integer> mp = new HashMap<Integer, Integer>();
		for(i=0;i<n;i++){
		    arr[i]=sc.nextInt();
		    
		}
		for(i=0;i<100;i++)
		{
		    mp.put(i+1, 0);
		}
		for(i=0;i<n;i++){
		    val=mp.get(arr[i]);
		    mp.put(arr[i], val+1);
		}
		char[] col= new char[n];
		char t='A';
		for(i=0;i<n;i++){
		    if(mp.get(arr[i])==1){
		    col[i]=t;
		    count++;
		    if(t=='A')
		    t='B';
		    else
		    t='A';
		    }
		    
		    if(mp.get(arr[i])>2)
		    pos=i;
		}
		if(count%2!=0){
		    if(pos==-1){
		        System.out.println("NO");
		        return;
		    }
		    else
		    col[pos]='B';
		}
		System.out.println("YES");
		for(i=0;i<n;i++){
		    if(col[i]!='B')
		    col[i]='A';
		}
		for(i=0;i<n;i++)
		System.out.print(col[i]);
	}
}