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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
         public static void main(String[] args){
            FastReader s = new FastReader();
            int n=s.nextInt();
            int arr[] = new int[n];
            int freq[] = new int[101];
            for(int i=0;i<n;i++){
                int num =s.nextInt();
                arr[i]=num;
                freq[num]++;
            }

            int unique =0,ct=0,in=9999;
            for(int i=0;i<101;i++){
                if(freq[i]==1){
                    unique++;
                }
                if(freq[i]>=3){
                    ct++;
                    in=i;
                }
            }
            if(unique%2==0){
                System.out.println("YES");
                String str = "";
                boolean flag=true;
                for(int j=0;j<n;j++){
                    if(freq[arr[j]]!=1){
                        str+="B";
                    }
                    else {
                        if (flag) {
                            str += "B";
                        }else {
                            str += "A";
                        }
                        flag=!flag;
                    }
                }
                System.out.println(str);
                return;
            }

            if(ct>0){
                System.out.println("YES");
                String str = "";
                boolean flag=true;
                for(int j=0;j<n;j++){

                    if(arr[j]==in){
                        str+="A";
                        in=99999;
                        continue;
                    }

                    if(freq[arr[j]]!=1){
                        str+="B";
                    }
                    else {
                        if (flag) {
                            str += "B";
                        }else {
                            str += "A";
                        }
                        flag=!flag;
                    }
                }
                System.out.println(str);
                return;
            }

            System.out.println("NO");
      }

}