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 com.pb.codeforces.practice;

import java.util.Scanner;

public class CF1051C {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] arr = new int[n];
		int[] cnt = new int[101];
		int maxCnt = 0;
		int maxVal = 0;
		for(int i=0; i<n; i++) {
			arr[i] = in.nextInt();
			cnt[arr[i]]++;
		}
		int nCnt = 0;
		for(int i=0; i<cnt.length; i++) {
			nCnt = cnt[i] == 1 ? nCnt + 1 : nCnt;
			if(maxCnt < cnt[i]) {
				maxCnt = cnt[i];
				maxVal = i;
			}
		}
		if(nCnt%2 != 0) {
			if(maxCnt <= 2) {
				System.out.println("NO");
			}else {
				System.out.println("YES");
				String ans = "";
				char ff = 'A';
				boolean set = true;
				for(int i=0; i<arr.length; i++) {
					if(cnt[arr[i]] != 1) {
						if(arr[i] == maxVal) {
							if(set) { ans+='B'; set = false; }else { ans+='A'; }
						}else {
							ans+='A';
						}
					}else {
						ans+=ff;
						ff = ff == 'A' ? 'B' : 'A';
					}
				}
				System.out.println(ans);
			}
		}else {
			System.out.println("YES");
			String ans = "";
			char ff = 'A';
			for(int i=0; i<arr.length; i++) {
				if(cnt[arr[i]] != 1) {
					ans+='A';
				}else {
					ans+=ff;
					ff = ff == 'A' ? 'B' : 'A';
				}
			}
			System.out.println(ans);
		}
	}
}