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.*;
public class algo513
{
    public static void main(String args[])
    {
        Scanner ex=new Scanner(System.in);
        int n=ex.nextInt();
        int arr[]=new int[101];
        int num[]=new int[n];
        for(int i=0;i<n;i++)
        {
            num[i]=ex.nextInt();
            arr[num[i]]++;
        }
        int count=0;
        for(int i=1;i<101;i++)
        {
            if(arr[i]==1)
            count++;
        }
        if(count==n&&n%2==1)
        System.out.println("NO");
        else
        {
            String ans="";
            int temp=count;
            int add=0,check=0;
            if(count%2==1)
            {
                for(int i=1;i<=100;i++)
                {
                    if(arr[i]>2)
                    {
                        add=i;
                        check=1;
                    }
                }
            }
            if(check==0&&count%2==1)
            {
                System.out.println("NO");
                return;
            }
            temp=temp/2;
            for(int i=0;i<n;i++)
            {
                if(count==0)
                {
                    ans=ans+'A';
                    continue;
                }
                if(arr[num[i]]==1)
                {
                    if(temp>0)
                    {
                        ans=ans+'A';
                        temp--;
                    }
                    else
                    ans=ans+'B';
                }
                else if(num[i]==add)
                {
                    if(check==1)
                    {
                        ans=ans+'A';
                        check=0;
                    }
                    else
                    ans=ans+'B';
                }
                else
                ans=ans+'B';
            }
            System.out.println("YES");
            System.out.println(ans);
        }
    }
}