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:
//package com.company;
import java.math.BigInteger;
import java.util.*;
import java.io.*;

public class Main  {

    public static void main(String[] args) {
        Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        int A[]=new int[n];
        for(int i=0;i<n;i++)
        {
            A[i]=in.nextInt();
        }
        Hashtable<Integer,Integer>map=new Hashtable<>();

        for(int i=0;i<n;i++)
        {
            if(!map.containsKey(A[i]))
            {
                map.put(A[i],1);
            }
            else
            {
                map.put(A[i],map.get(A[i])+1);
            }
        }
        Set<Integer>unique=new HashSet<>();
        int morethree=0;
        int which=0;
        for(Map.Entry<Integer,Integer>entry: map.entrySet())
        {
            if(entry.getValue()==1)
            {
                unique.add(entry.getKey());
            }
            if(entry.getValue()>2)
            {
                morethree=1;
                which=entry.getKey();
            }
        }
        if(unique.size()%2==0)
        {
            String ans="";
            int cnt=0;
            int i=0;
            while(cnt<unique.size()/2&&i<n)
            {
                if(map.get(A[i])==1)
                {
                    cnt++;
                }
                ans=ans+"A";
                i++;
            }
            while(i<n)
            {
                if(map.get(A[i])==1)
                {
                    ans=ans+"B";
                }
                else
                {
                    ans=ans+"A";
                }
                i++;
            }
            System.out.println("YES");
            System.out.println(ans);
        }
        else if(morethree==1)
        {
            String ans="";
            int flg=0;
            int cnt=0;
            int i=0;
            while(cnt<=(unique.size()/2)&&i<n)
            {
                if(map.get(A[i])==1)
                {
                    cnt++;
                    ans=ans+"A";
                }
                else if(A[i]==which&&flg==0)
                {
                    ans=ans+"B";
                    flg++;

                }
                else
                {
                    ans=ans+"A";
                }

                i++;
            }
            while(i<n)
            {
                if(map.get(A[i])==1)
                {
                    ans=ans+"B";
                }
                else if(A[i]==which&&flg==0)
                {
                    ans=ans+"B";
                    flg++;
                }
                else
                {
                    ans=ans+"A";
                }
                i++;
            }
            System.out.println("YES");
            System.out.println(ans);


        }
        else
        {
            System.out.println("NO");
        }
    }

}