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.math.BigDecimal;
import java.math.MathContext;
import java.util.*;
import java.io.*;
public class Main {
    public static void main(String[] args) throws IOException {
        //Code starts
        FastReader ip = new FastReader();
        OutputStream output = System.out;
        PrintWriter out = new PrintWriter(output);
        int n=ip.nextInt();
        int[] arr =new int[n];
        HashMap<Integer,ArrayList<Integer>> hm=new HashMap<>();
        char[] ans=new char[n];
        for(int i=0;i<n;i++){
            arr[i]=ip.nextInt();
            if(hm.containsKey(arr[i])){
                ArrayList<Integer> al=hm.get(arr[i]);
                al.add(i);
                hm.put(arr[i],al);
            }else{
                ArrayList<Integer> al=new ArrayList<>();
                al.add(i);
                hm.put(arr[i],al);
            }
        }

        int ac=0;
        int bc=0;

        for(Integer x:hm.keySet()){
             if(hm.get(x).size()==1){
                 if(ac==bc){
                     ac++;
                     ans[hm.get(x).get(0)]='A';
                 }else {
                     bc++;
                     ans[hm.get(x).get(0)]='B';
                 }
             }
        }

        for(Integer x:hm.keySet()){
            if(hm.get(x).size()==2){
                ac++;
                bc++;
                ans[hm.get(x).get(0)]='A';
                ans[hm.get(x).get(1)]='B';
            }else if(hm.get(x).size()==3){
                if(ac>bc){
                    ans[hm.get(x).get(0)]='B';
                    bc++;
                    for(int j=1;j<hm.get(x).size();j++){
                        ans[hm.get(x).get(j)]='A';
                    }
                }else{
                    for(int j=0;j<hm.get(x).size();j++){
                        ans[hm.get(x).get(j)]='B';
                    }
                }
            }else if(hm.get(x).size()!=1){
                if(ac>bc){
                    ans[hm.get(x).get(0)]='B';
                    bc++;
                    for(int j=1;j<hm.get(x).size();j++){
                        ans[hm.get(x).get(j)]='A';
                    }
                }else{
                    for(int j=0;j<hm.get(x).size();j++){
                        ans[hm.get(x).get(j)]='B';
                    }
                }
            }
        }

        if(ac!=bc){
            out.print("NO");
        }else{
            out.println("YES");
            String res=new String(ans);
            out.println(res);
        }


        out.close();
        //Code ends
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        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;
        }
    }

}