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:
//Code by Sounak, IIEST
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.Arrays;
public class Test1{
    public static void main(String args[])throws IOException{
        FastReader sc = new FastReader();
        StringBuilder sb = new StringBuilder();
        long mod=998244353l; 
        int n=sc.nextInt();
        int i,l=0;
        HashMap <Integer , Integer> arr = new HashMap();
        int a[]=new int[n];
        char res[]=new char[n];
        Arrays.fill(res,'A');
        int b[]=new int[n];
        int s2[]=new int[n];
        for(i=0;i<n;i++)
        {
            a[i]=sc.nextInt();
            if(arr.containsKey(a[i]))
            arr.put(a[i] , 1 + arr.get(a[i]));
            else
            {
                arr.put(a[i],1);
                b[l++]=a[i];
            }
        }
        int c1=0,c3=0;
        for(i=0;i<l;i++)
        {
            s2[i]=arr.get(b[i]);
            if(s2[i]==1)
            c1++;
            else if(s2[i]>=3 && c3==0)
            c3=b[i];
        }
        if(c1%2==1 && c3==0)
        System.out.println("NO");
        else
        {
            System.out.println("YES");
            int temp=0;
            if (c1%2==1)
            temp=1;
            c1/=2;
            for(i=0;i<n;i++)
            {
                if(arr.get(a[i])==1 && c1!=0)
                {
                    res[i]='B';
                    c1--;
                }
                if(temp==1 && arr.get(a[i])>=3)
                {
                    res[i]='B';
                    temp--;
                }
            }
            for(i=0;i<n;i++)
            System.out.print(res[i]);
            System.out.println();
        }
        //System.out.println(name);
    }
    static long gcd(long a, long b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
    
}


class FastReader {
    BufferedReader br;
    StringTokenizer st;
 
    public FastReader() { 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;
    }
}