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.*;
import java.util.*;
public class cd {

	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter out =new PrintWriter (System.out);
		int n=sc.nextInt(); 
        int [] arr=new int[n];
        char [] ab=new char[n]; Arrays.fill(ab, 'B');
         boolean f=true;
        HashMap<Integer,Integer> o=new HashMap(); HashSet<Integer> g=new HashSet(); 
        for(int i=0;i<n;i++) {
        	arr[i]=sc.nextInt(); g.add(arr[i]);
        	if(o.containsKey(arr[i])) {
        		o.put(arr[i],o.get(arr[i])+1);
        	}
        	else
        		o.put(arr[i],1);
        	
        } int c=0; int v=0; 
        for(int j:g) {
        	if(o.get(j)==1) {
        		c++;
        	}
        	else if(o.get(j)>2) {
        		v++;
        	}	
        } 
        if(c%2!=0 && v==0) {
        	f=false;
        }
        if(f) {
        	out.println("YES");
        	if(c%2==0) {
        		c=c/2; int j=0;
        		while(c>0) {
        			if(o.get(arr[j])==1) {
        				ab[j]='A';
        				c--;}
                      j++;
        		}
        	}
        	else {
        		c=c/2; int j=0;
        		while(c>0) {
        			if(o.get(arr[j])==1) {
        				ab[j]='A'; c--;}
        			 j++;
        		}
        		for(int i=0;i<n;i++) {
        			if(o.get(arr[i])>2) {
        				ab[i]='A';
        				break;
        			}
        		}
        	}
        
        	for(int r=0;r<n;r++)
        		out.print(ab[r]);
        }
        else {
        	out.println("NO");
        }
        out.flush();
	}
	static	class Scanner{
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
        public Scanner(String file) throws Exception {br = new BufferedReader(new FileReader(file));}
        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public String nextLine()throws IOException{return br.readLine();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public double nextDouble() throws IOException {return Double.parseDouble(next());}
        public char nextChar()throws IOException{return next().charAt(0);}
        public Long nextLong()throws IOException{return Long.parseLong(next());}
        public boolean ready() throws IOException{return br.ready();}
        public void waitForInput() throws InterruptedException {Thread.sleep(3000);}
    }
}