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 codeforces.div2;


import java.util.*;

public class VasyaAndMultisets {

    static public void print(int arr[]) {


        int even = 0;
        HashSet<Integer> set = new HashSet<>();
        HashMap<Integer, Integer> map = new HashMap<>();
        for(int i = 0; i < arr.length; i++) {
            map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
        }

        boolean flag = false;
        int check = 0;
        for(Map.Entry<Integer, Integer> entry : map.entrySet()) {
            if(entry.getValue() == 1) {
                set.add(entry.getKey());
            }
            if(entry.getValue() > 2) {
                flag = true;
                check = entry.getKey();
            }
        }

        if(set.size()%2 == 0) {
            System.out.println("YES");
            StringBuilder sb = new StringBuilder();
            int count = 0;
            for(int i = 0; i < arr.length; i++) {
                if(set.contains(arr[i]) && count%2!=0) {
                    sb.append('A');
                    count++;
                } else {
                    if(set.contains(arr[i]) && count%2 ==0 ){
                        sb.append('B');
                        count++;
                    } else {
                        sb.append('A'
                        );
                    }
                }
            }
            System.out.println(sb.toString());
        } else {
            if(set.size()%2!=0 && flag == false) {
                System.out.println("NO");
            } else {
                int count = 0;

                System.out.println("YES");
                StringBuilder sb = new
                        StringBuilder();
                for(int i = 0; i < arr.length; i++) {
                    if(set.contains(arr[i]) && count%2 == 0) {
                        sb.append('A');
                        count++;
                    } else {
                        if(set.contains(arr[i]) && count%2!=0) {
                            sb.append('B');
                            count++;
                        } else {
                            if(arr[i] == check) {
                                sb.append('B');
                                check = Integer.MAX_VALUE;
                            } else {
                                sb.append('A');
                            }
                        }
                    }
                }
                System.out.println(sb.toString());
            }
        }
    }


    public static void main(String []args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int i = 0;
        int arr[] = new int[n];
        while ( i < n) {
            arr[i++] = sc.nextInt();
        }
        print(arr);
    }
}