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.Scanner;

public class P1051C
{
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] a = new int[101];
		int[] b = new int[101];
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
		{
			int p = scan.nextInt();
			arr[i] = p;
			a[p]++;
		}
		int t = 0;
		boolean gotoA = true;
		for (int i = 0; i < a.length; i++)
		{
			if (a[i] == 1)
			{
				if (!gotoA)
				{
					a[i]--;
					b[i]++;
				}
				t++;
				gotoA = !gotoA;
			}
		}
		if (!gotoA)
		{
			for (int i = 0; i < a.length; i++)
			{
				if (a[i] > 2)
				{
					a[i]--;
					b[i]++;
					gotoA = !gotoA;
					break;
				}
			}
		}
		if (!gotoA)
		{
			System.out.println("NO");
		}
		else
		{
			System.out.println("YES");
			StringBuilder sb = new StringBuilder();
			for (int i = 0; i < arr.length; i++)
			{
				if (a[arr[i]] > 0)
				{
					a[arr[i]]--;
					sb.append('A');
				}
				else
					sb.append('B');
			}
			System.out.println(sb);
		}
	}
}