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.*;
import java.io.*;

public class Main
{
    static class Reader {
		BufferedReader br;
		StringTokenizer st;
 
		public Reader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
 
	}
	public static void main(String[] args) throws IOException 
	{
		Reader sc=new Reader();Main G=new Main();
		PrintWriter o = new PrintWriter(System.out);
		int n=sc.nextInt();int a[]=new int[n];int k1=0,k2=0;
		
		HashSet<Integer> h1=new HashSet<>();
		HashSet<Integer> h2=new HashSet<>();
		HashSet<Integer> h3=new HashSet<>();
		
		for (int i=0;i<n;i++)
		{
		    a[i]=sc.nextInt();
		    if (h1.contains(a[i]))
		    {
		        if (h2.contains(a[i]))
		        {
		            h3.add(a[i]);
		        }
		        else h2.add(a[i]);
		    }
		    else h1.add(a[i]);
		}
		
		if ((h1.size()-h2.size())%2==0)
		{
		    o.println("YES");
		    for (int i=0;i<n;i++)
		    {
		        if (h2.contains(a[i])) o.print("A");
		        else o.print(((k1++)%2==0)?"A":"B");
		    }
		}
		else if (h3.size()>0)
		{
		    o.println("YES");
		    for (int i=0;i<n;i++)
		    {
		        if (h3.contains(a[i])){o.print("B");h3.clear();}
		        else if (h2.contains(a[i])) o.print("A");
		        else o.print(((k1++)%2==0)?"A":"B");
		    }
		}
		else o.print("NO");
		
		
		//o.println(h1);
		//o.println(h2);
		//o.println(h3);
		
        o.flush();
        o.close();
	}
}