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.*;
import java.io.*;

/*

*/

public class Main{

    public static void main(String[] args) throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        StringTokenizer st=new StringTokenizer(br.readLine());
        int n=Integer.parseUnsignedInt(st.nextToken());
        HashMap<Integer,Integer> map=new HashMap<>();
        int[] arr=new int[n];
        st=new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++){
            arr[i]=Integer.parseInt(st.nextToken());
            if(map.containsKey(arr[i])){
                map.replace(arr[i],map.get(arr[i])+1);
            }else {
                map.put(arr[i],1);
            }
        }
        int sum1=0;
        int sum2=0;
        StringBuilder str=new StringBuilder("");
        for(int i=0;i<n;i++){
            if(map.get(arr[i])==1){
                if(sum1<=sum2){
                    str.append('A');
                    sum1++;
                }else {
                    str.append('B');
                    sum2++;
                }
            }else {
                str.append('A');
            }
        }
        if(sum1==sum2){
            pw.println("YES");
            pw.println(str);
        }else {
            StringBuilder ansStr=new StringBuilder("");
            int flag=0;
            for(int i=0;i<n;i++){
                if(map.get(arr[i])>=3){
                    ansStr.append('B');
                    for(int j=i+1;j<n;j++){
                        ansStr.append(str.charAt(j));
                    }
                    flag=1;
                    break;
                }else {
                    ansStr.append(str.charAt(i));
                }
            }
            if(flag==1){
                pw.println("YES");
                pw.println(ansStr);
            }else {
                pw.println("NO");
            }
        }


        pw.close();
    }
}