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 albert.codeforces.vasyaandmultisets1051c;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Solution {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        Map<Integer, Integer> map = new HashMap<>();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            int num = scanner.nextInt();
            map.put(num, map.getOrDefault(num, 0) + 1);
            arr[i] = num;
        }

        int single = 0;
        int maxCountMult = 0;
        for (int val : map.values()) {
            if (val == 1) {
                single++;
            } else {
                maxCountMult = Math.max(maxCountMult, val);
            }
        }

        List<String> ans = new ArrayList<>(n);
        if (single % 2 == 0) {
            System.out.println("YES");
            int last = 0;
            for (int value : arr) {
                if (map.get(value) == 1) {
                    ans.add(last == 0 ? "A" : "B");
                    last = (last + 1) % 2;
                } else {
                    ans.add("A");
                }
            }
            System.out.println(String.join("", ans));
        } else if (maxCountMult > 2) {
            System.out.println("YES");
            int a = 0;
            int b = 0;
            boolean balanced = false;
            int last = 0;
            boolean set = false;
            for (int i : arr) {
                if (map.get(i) == 1) {
                    ans.add(last == 0 ? "A" : "B");
                    last = (last + 1) % 2;
                } else if (map.get(i) > 2 && !set) {
                    ans.add("B");
                    set = true;
                } else {
                    ans.add("A");
                }
            }
            System.out.println(String.join("", ans));
        } else {
            System.out.println("NO");
        }
    }
}