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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class VaysaAndMultisets {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));		
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n= Integer.parseInt(st.nextToken());
		int[] a=new int[n];
		int[] f=new int[101];
		
		StringTokenizer st1 = new StringTokenizer(br.readLine());
		for(int i=0;i<n;i++) {
			a[i]=Integer.parseInt(st1.nextToken());
			f[a[i]]++;
		}
		int swag=0,getHim=0;
		int swagNum=-1;
		for(int i=0;i<f.length;i++) {
			if(f[i]==1) getHim++;
			if(f[i]>2) {
				swag++;
				swagNum=i;
			}
		}
		if(getHim%2==1&&swag==0) {
			System.out.println("NO");
			return;
		}
		System.out.println("YES");
		boolean placeHere=false;
		if(getHim%2==0) swagNum=Integer.MIN_VALUE;
		
		boolean b=true;
		for(int i=0; i<n; i++) {
			if(a[i]==swagNum) {
				if(placeHere) {
					System.out.print("B");
				}
				else {
					System.out.print("A");
					placeHere=true;
				}
			}
			else if(f[a[i]]==1) {
				System.out.print(b?"B":"A");
				b=!b;
			}
			else System.out.print("B");
		}

	}

}