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 whatever; // 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 Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
	 Scanner sc=new Scanner(System.in);
	 int n=sc.nextInt();
	 
	 String res="";
	 HashMap<Integer,Integer> map=new HashMap<>();
	 char[] ans=new char[n];
	 Arrays.fill(ans,'A');
	 
	 int nice=0;
	 int[] a=new int[n];
	 
	 for(int i=0;i<n;i++){
	  a[i]=sc.nextInt();
	  if(map.containsKey(a[i])){
	   map.put(a[i],map.get(a[i])+1);
	  }
	  else map.put(a[i],1);
	 }
	 for(int i=0;i<n;i++)if(map.get(a[i])==1)nice++;
	 
	 boolean flag=false;
	 
	 if(nice%2==0){
	  flag=true;	
	  int temp=0;	
	  for(int i=0;i<n;i++){
	   if(temp<nice && temp%2==0 && map.get(a[i])==1){ans[i]='A';temp++;}
	   else if(temp<nice && temp%2==1 && map.get(a[i])==1) {ans[i]='B';temp++;}
	   if(temp>=nice) break;
	  }	
	 }
	 else{
	   int temp=-1;	
	   for(int i=0;i<n;i++){
	   if(map.get(a[i])>2){flag=true;temp=i;break;}	
	  }
	  if(flag && temp!=-1) {
	  	ans[temp]='B';map.put(a[temp],map.get(a[temp])-1);
	  	temp=0;	
	  for(int i=0;i<n;i++){
	   if(temp<nice-1 && temp%2==0 && map.get(a[i])==1){ans[i]='A';temp++;}
	   else if(temp<nice-1 && temp%2==1 && map.get(a[i])==1) {ans[i]='B';temp++;}
	   if(temp>=nice-1) break;
	  }
	 }
	}
	if(flag){
	System.out.println("YES");	
	for(int i=0;i<ans.length;i++) res+=ans[i];
	System.out.println(res);
	}
	else System.out.println("NO");
}
}