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 MyClass {
    public static void main(String args[])
    {
        MyScanner sc=new MyScanner();
        int n=sc.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        a[i]=sc.nextInt();
        
        int c[]=new int [101];
        for(int i=0;i<n;i++)
        c[a[i]]++;
        
        int nn=0;
        int oc=0;
        for(int i=1;i<=100;i++)
        {
            if(c[i]==1)
            nn++;
            else if(c[i]%2==1)
            oc++;
            else if(c[i]%2==0&&c[i]>2)
            oc++;
        }
        if(nn%2==1&&oc==0)
        System.out.println("NO");
        else if(nn%2==1&&oc>0)
        {
             System.out.println("YES");
             int flag=0;
            
            int m=1;
            for(int i=0;i<n;i++)
            {
                if(c[a[i]]==1)
                {
                    if(m==1)
                    {
                    System.out.print('A');
                    m=-1;
                    }
                    else if(m==-1)
                    {
                         System.out.print('B');
                    m=1;
                    }
                }
                else if(c[a[i]]%2==1&&c[a[i]]>1&&flag==0)
                {
                    flag=1;
                    System.out.print('B');
                }
                else if(c[a[i]]%2==0&&c[a[i]]>2&&flag==0)
                {
                    flag=1;
                    System.out.print('B');
                }
                else
                System.out.print('A');
            }
        }
        else
        {
            System.out.println("YES");
            
            int m=1;
            for(int i=0;i<n;i++)
            {
                if(c[a[i]]==1)
                {
                    if(m==1)
                    {
                    System.out.print('A');
                    m=-1;
                    }
                    else if(m==-1)
                    {
                         System.out.print('B');
                    m=1;
                    }
                }
                else
                System.out.print('A');
            }
        }
          
       
    }
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            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;
        }
    }
}