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.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public  final class VasyaAndMultiSetsCF {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int arr[]=new int[n];
        int count[]=new int[101];
        for(int i=0;i<n;i++){
            arr[i]=sc.nextInt();
            count[arr[i]]++;
        }
        ArrayList<Integer> single=new ArrayList<>();
        for(int i=1;i<=100;i++){
            if(count[i]==1){
                single.add(i);
            }
        }

        char ans[]=new char[n];
        Arrays.fill(ans,'A');
        if(single.size()%2==0){

            int size=single.size()/2;
            for(int i=0;i<n;i++){
                if(single.contains(arr[i]) && single.indexOf(arr[i])<size){
                    ans[i]='B';
                }
            }

            System.out.println("YES");
            for(char c:ans)
                System.out.print(c);
            System.out.println();
        }else{

            int val=-1;
            for(int i=1;i<=100;i++){
                if(count[i]>2){
                    val=i;
                    break;
                }
            }
            if(val!=-1){
                int size=single.size()/2;
                boolean isTrue=false;
                for(int i=0;i<n;i++){
                    if(single.contains(arr[i]) && single.indexOf(arr[i])<size){
                        ans[i]='B';
                    }   
                    if(!isTrue && arr[i]==val){
                        ans[i]='B';
                        isTrue=true;
                    }
                }

                System.out.println("YES");
                for(char c:ans)
                    System.out.print(c);
                System.out.println();
            }else
                System.out.println("NO");
        }
    }
}