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 vasyaandmultisets;

import java.util.*;
import java.io.*;

public class vasyaandmultisets {
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(fin.readLine());
		HashMap<Integer, Integer> sets = new HashMap<Integer, Integer>();
		StringTokenizer st = new StringTokenizer(fin.readLine());
		int[] nums = new int[n];
		for(int i = 0; i < n; i++) {
			nums[i] = Integer.parseInt(st.nextToken());
			sets.put(nums[i], sets.getOrDefault(nums[i], 0) + 1);
		}
		int numOnes = 0;
		boolean threeExists = false;
		for(int k : sets.keySet()) {
			if(sets.get(k) == 1) {
				numOnes ++;
			}
			else if(sets.get(k) >= 3) {
				threeExists = true;
			}
		}
		if(numOnes % 2 == 0 || (numOnes % 2 == 1 && threeExists)) {
			System.out.println("YES");
			StringBuilder fout = new StringBuilder();
			//put everything into A, except for the single digits into B
			int quota = numOnes / 2;
			boolean needExtra = (quota * 2 != numOnes);
			for(int i = 0; i < n; i++) {
				int next = sets.get(nums[i]);
				if(next >= 3 && needExtra) {
					needExtra = false;
					fout.append("B");
				}
				else if(next == 1 && quota != 0) {
					fout.append("B");
					quota --;
				}
				else {
					fout.append("A");
				}
			}
			System.out.println(fout);
		}
		else {
			System.out.println("NO");
		}
	}
}