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 C1051{
	public static void main(String args[])throws IOException{
		Scanner sc=new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();
		int arr[]=new int[101];
		int store[]=new int[n];
		for(int i=0;i<n;i++){
			store[i]=sc.nextInt();
			arr[store[i]]++;
		}
		int nice=0,unnice=0;int rep=-1;
		for(int i=0;i<=100;i++){
			if(arr[i]==1)
				nice++;
			else if(arr[i]>1){
				if(arr[i]>2)
					rep=i;
				unnice++;
			}
		}
		if(nice%2==1&&rep==-1){
			pw.println("NO");
		}
		else if(nice%2==0){
			int p=0;
			pw.println("YES");
			for(int i=0;i<n;i++){
				if(arr[store[i]]>1){
					pw.print("A");
				}
				else{
					pw.print((char)(65+p));
					p^=1;
				}
			}
		}
		else {
			pw.println("YES");
			int p=0;
			for(int i=0;i<n;i++){
				if(arr[store[i]]>1){
					if(store[i]==rep){
						pw.print("B");
						rep=-1;
					}
					else
						pw.print("A");
				}
				else{
					pw.print((char)(65+p));
					p^=1;
				}
			}
		}
		pw.close();
	}
}