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  Vasya_and_Multisets
{
	public static void main(String[] args) throws IOException 
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw=new PrintWriter(System.out);

		int t=1;

		while(t-->0)
		{

			int n=Integer.parseInt(br.readLine());

			String str[]=br.readLine().trim().split(" ");
			int f[]=new int[101];
			
			HashMap<Integer,ArrayList<Integer>> mp=new HashMap<>();
			ArrayList<Integer> temp;

			for(int i=0;i<n;i++)
			{
				int x=Integer.parseInt(str[i]);
				f[x]++;

				if(mp.get(x)!=null)
				{
					temp=mp.get(x);
					temp.add(i);
					mp.put(x,temp);
				}
				else
				{
					temp=new ArrayList<>();
					temp.add(i);
					mp.put(x,temp);
				}
		
			}

			int o=0;
			int e=0;
			for(int i=1;i<101;i++)
			{
				if(f[i]==0)
					continue;

				if(f[i]==1)
				{
					o++;
				}
				else if(f[i]>2)
				{
					e++;
				}
			}

			if(o%2==1 && e==0)
			{
				pw.println("NO");
			}
			else
			{
				char ans[]=new char[n];
				Arrays.fill(ans,'#');
				int a=0;
				int b=0;

				for(int i=1;i<101;i++)
				{
					if(f[i]>2 || f[i]==0)
						continue;
					int y=0;
					if(a<b)
					{
						y=0;
					}
					else
					{
						y=1;
					}

					temp=mp.get(i);
					for(int x:temp)
					{
						if(y%2==0)
						{
							ans[x]='A';
							a++;
							y++;
						}
						else
						{
							ans[x]='B';
							y++;
							b++;
						}
					}
				}

				for(int i=1;i<101;i++)
				{
					if(f[i]<3 || f[i]==0)
						continue;
					int y=0;
					if(a<b)
					{
						a++;
						boolean v=false;
						temp=mp.get(i);
						for(int x:temp)
						{
							if(!v)
							{
								ans[x]='A';
								v=!v;	
							}
							else
							{
								ans[x]='B';
							}
							
						}
					}
					else if(a>b)
					{
						b++;
						boolean v=false;
						temp=mp.get(i);
						for(int x:temp)
						{
							if(!v)
							{
								ans[x]='B';
								v=!v;	
							}
							else
							{
								ans[x]='A';
							}
							
						}
					}
					else
					{
						temp=mp.get(i);
						for(int x:temp)
						{
							ans[x]='B';
						}
					}
					
				}





				
				pw.println("YES");
				pw.println(ans);
			}


			
			

		}
		pw.flush();
	}

	
}