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.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.StringTokenizer;

public class EducationalRound51C {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		out=new PrintWriter (new BufferedOutputStream(System.out));
		FastReader s=new FastReader();
		int n=s.nextInt();
		int[] arr=new int[n];
		HashMap<Integer,Integer> storer=new HashMap<>();
		for(int i=0;i<n;i++) {
			arr[i]=s.nextInt();
			if(storer.containsKey(arr[i])) {
				storer.put(arr[i], storer.get(arr[i])+1);
			}else {
				storer.put(arr[i],1);
			}
		}
		int nice=0;
		int twos=0;
		int rest=0;
		for(Integer x:storer.values()) {
			if(x==1) {
				nice++;
			}else if(x==2) {
				twos++;
			}else {
				rest++;
			}
		}
		if(nice%2==1 && rest==0) {
			out.println("NO");
			out.close();
			return;
		}
		StringBuilder ans=new StringBuilder();
		if(nice%2==0) {
			int count=nice/2;
			for(int i=0;i<n;i++) {
				int current=storer.get(arr[i]);
				if(current==1) {
					if(count!=0) {
						ans.append('A');
						count--;
					}else {
						ans.append('B');
					}
				}else {
					ans.append('A');
				}
			}
		}else {
			int count = (nice/2)+1;
			boolean flag=true;
			for(int i=0;i<n;i++) {
				int current=storer.get(arr[i]);
				if(current==1) {
					if(count!=0) {
						count--;
						ans.append('A');
					}else {
						ans.append('B');
					}
				}else if(current>2 && flag){
					ans.append('B');
					flag=false;
				}else {
					ans.append('A');
				}
			}
		}
		out.println("YES");
		out.println(ans);
		out.close();
	}

	public static PrintWriter out;
	
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			return str;
		}
	}
	
}