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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Arrays;


public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    
    static class Task {
    	 public void solve(InputReader in, PrintWriter out) {
    		 int n = in.nextInt();
    		 int[] s = new int[n];
    		 int[] ab = new int[n];
    		 int[] cnt = new int[101];
    		 int aCnt = 0;
    		 int bCnt = 0;
    		 for (int i = 0; i < n; i++) {
    			 s[i] = in.nextInt();
    			 cnt[s[i]]++;
    		 }
    		 for (int i = 1; i < 101; i++) {
    			 if (cnt[i] == 1) {
    				 if (aCnt < bCnt) {
    					 aCnt++;
    					 ab[I(s, i)] = 1;
    				 }
    				 else {
    					 bCnt++;
    					 ab[I(s, i)] = 2;
    				 }
    			 }
    		 }

    		 if (bCnt > aCnt) {
    			 boolean b = false;
    			 for (int i = 0; i < 101; i++) {
    				 if (cnt[i] > 2) {
    					 ab[I(s, i)] = 1;
    					 b = true;
    					 break;
    				 }
    			 }
    			 if (!b) {
    				 out.println("NO");
    				 return;
    			 }
    		 }
    		 
    		 out.println("YES");
    		 for (int i = 0; i < n; i++) {
    			 if (ab[i] == 1)
    				 out.print("A");
    			 else 
    				 out.print("B");
    		 }
     	 }	   
    } 
    
    static int I(int[] s, int n) {
    	for (int i = 0; i < s.length; i++) {
    		if (s[i] == n)
    			return i;
    	}
    	return -1;
    }
    
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        
        public long nextLong() {
        	return Long.parseLong(next());
        }

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