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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Stack;
import java.util.StringTokenizer;

public class C {

	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static PrintWriter out;

	public static String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}

	public static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	public static float nextFloat() throws IOException {
		return Float.parseFloat(next());
	}

	public static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public static void main(String[] args) throws IOException {

		long res = 0;

		int n = nextInt();

		int[] arr = new int[n];
		HashMap<Integer, Integer> map = new HashMap<>();

		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
			if (map.get(arr[i]) == null) {
				map.put(arr[i], 1);
			} else {
				map.put(arr[i], map.get(arr[i]) + 1);
			}
		}

		int nice = 0;
		int could_be_nice = 0;

		for (Entry<Integer, Integer> entry : map.entrySet()) {
			int key = entry.getKey();
			int value = entry.getValue();
			if (value == 1) {
				nice++;
			}
			if (value > 2) {
				could_be_nice++;
			}
		}

		StringBuilder str = new StringBuilder();

		if (nice % 2 != 0) {
			if (could_be_nice == 0) {
				System.out.println("NO");
			} else {
				boolean hook = false;
				char a = 'A';
				System.out.println("YES");
				int r = nice;
				for (int i = 0; i < n; i++) {
					int key = arr[i];
					int value = map.get(key);
					if (value == 1 && r != 0 && r > nice / 2) {
						r--;
						str.append("A");
					} else if (value == 1 && r != 0 && r <= nice / 2) {
						r--;
						str.append("B");
					} else {
						if (!hook && value > 2) {
							str.append('B');
							hook = true;
						} else {
							str.append(a);
						}
					}
				}
			}
		} else {
			char a = 'A';
			System.out.println("YES");
			int r = nice;
			for (int i = 0; i < n; i++) {
				int key = arr[i];
				int value = map.get(key);
				if (value == 1 && r != 0 && r > nice / 2) {
					r--;
					str.append("A");
				} else if (value == 1 && r != 0 && r <= nice / 2) {
					r--;
					str.append("B");
				} else {
					str.append(a);
				}
			}
		}
		System.out.println(str);
	}
}