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 com.sun.org.apache.xalan.internal.xsltc.compiler.util.Type;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
public class h{
    public static void main(String[]args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = null;
        int n = Integer.parseInt(br.readLine());
        st = new StringTokenizer(br.readLine());
        int[]num=new int[n];
        int[]count=new int[101];
        int all=0;
        for(int i =0;i<n;i++){
            int temp =Integer.parseInt(st.nextToken());
            num[i]=temp;
            count[temp]++;
            all++;
        }
        int c =0;
        for(int i:count){
           if(i==1)
               c++;
        }
        if(c%2!=0&&all==c){
            System.out.println("NO");
        }
        else{
            char []ans= new char[n];
            if(c%2==0){
                int x= c/2;
                int i=0;
                for ( i=0 ;i<n&&x>0;i++){
                    if (count[num[i]]==1){
                        ans[i]='A';
                        x--;
                    }

                }
                c/=2;
                for (i =i;i<n&&c>0;i++){
                    if (count[num[i]]==1){
                        ans[i]='B';
                        c--;
                    }

                }
                for ( i =0;i<n;i++){
                   if (count[num[i]]!=1)
                    ans[i]='B';
                }
                System.out.println("YES");
                for(i=0;i<n;i++){
                    System.out.print(ans[i]);
                }
            }
            else{
                int f=-1;
                for(int i =0;i<101;i++) {
                    if (count[i] > 2) {
                        f = i;
                        break;
                    }
                }
                if (f==-1)
                    System.out.println("NO");
                else{
                    int x = c/2;
                    int i=0;
                    for ( i=0 ;i<n&&x>0;i++){
                        if (count[num[i]]==1) {
                            ans[i] = 'A';
                            x--;
                        }

                    }
                    for ( i =0;i<n;i++){
                        if(num[i]==f){
                            ans[i]='A';
                            break;
                        }
                    }
                    for (i=0;i<n;i++){
                        if(ans[i]!='A')
                            ans[i]='B';
                    }
                    System.out.println("YES");
                    for(i =0;i<n;i++){
                        System.out.print(ans[i]);
                    }

                }

            }

        }




    }

}