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 CodeForces;

import java.util.HashMap;
import java.util.Scanner;

public class VasyaAndMultisets {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int arr[]=new int[n];
		for(int i=0;i<n;i++)
		{
			arr[i]=s.nextInt();
		}
		HashMap<Integer,Integer> map=new HashMap<>();
		int count=0;int num=0;
		for(int i=0;i<n;i++)
		{
			if(!map.containsKey(arr[i]))
			{
				map.put(arr[i],1);
			}
			else
			{
				map.put(arr[i],map.get(arr[i])+1);
			}
		}
		for(int x:map.keySet())
		{
			if(map.get(x)==1)
			{
				count++;
			}
			if(num==0&&map.get(x)>2)
			{
				num=x;
			}
		}
		char ch[]=new char[arr.length];
		StringBuilder ans=new StringBuilder();
		//System.out.println(count);
		if(count==0)
		{
			System.out.println("YES");
			for(int i=0;i<n;i++)
			{
				ans.append('A');
			}
			System.out.println(ans);
		}
		else if(count%2==0)
		{
			System.out.println("YES");
			int temp=0;
			for(int i=0;i<arr.length;i++)
			{
				if(map.get(arr[i])==1)
				{
					if(temp<count/2)
					{
						ch[i]='A';
					}
					else
					{
						ch[i]='B';
					}
					temp++;
				}
				else
				{
					ch[i]='A';
				}	
			}
			System.out.println(String.valueOf(ch));
		}
		else
		{
			if(num==0)
			{
				System.out.println("NO");
			}
			else
			{
				int temp=0;
				for(int i=0;i<arr.length;i++)
				{
					if(map.get(arr[i])==1)
					{
						if(temp<count/2)
						{
							ch[i]='A';
						}
						else
						{
							ch[i]='B';
						}
						temp++;
					}
					else if(arr[i]==num)
					{
						ch[i]='A';
						num=0;
					}
					else
					{
						ch[i]='B';
					}
				}
				System.out.println("YES");
				System.out.println(String.valueOf(ch));
			}
		}
		
		

	}

}