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.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {

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

		FastScanner scan = new FastScanner();
		PrintWriter pw = new PrintWriter(System.out);

		int n = scan.nextInt(), mx = 100;
		int[] a = new int[n];
		cnt = new int[mx + 1];
		for (int i = 0; i < n; i++)
			cnt[a[i] = scan.nextInt()]++;
		dp = new int[mx + 1][n + 1][n + 1];
		ans = new int[mx + 1];
		if (solve(0, 0, 0)) {
			pw.println("YES");
			for (int i = 0; i < n; i++) {
				if (ans[a[i]]-- > 0)
					pw.print('A');
				else
					pw.print('B');
			}
		} else
			pw.println("NO");

		pw.flush();
	}

	static int cnt[], dp[][][], ans[];

	static boolean solve(int val, int a, int b) {
		if (val > 100)
			return a == b;
		if (dp[val][a][b] != 0)
			return dp[val][a][b] == 1;
		if (cnt[val] == 0)
			return (dp[val][a][b] = solve(val + 1, a, b) ? 1 : -1) == 1;
		if (cnt[val] == 1) {
			if (solve(val + 1, a + 1, b)) {
				ans[val] = 1;
				return (dp[val][a][b] = 1) == 1;
			}
			if (solve(val + 1, a, b + 1)) {
				ans[val] = 0;
				return (dp[val][a][b] = 1) == 1;
			}
		}
		if (cnt[val] == 2) {
			if (solve(val + 1, a, b)) {
				ans[val] = 2;
				return (dp[val][a][b] = 1) == 1;
			}
		}
		if (cnt[val] >= 3) {
			if (solve(val + 1, a + 1, b)) {
				ans[val] = 1;
				return (dp[val][a][b] = 1) == 1;
			}
			if (solve(val + 1, a, b + 1)) {
				ans[val] = cnt[val] - 1;
				return (dp[val][a][b] = 1) == 1;
			}
			if (solve(val + 1, a, b)) {
				ans[val] = 0;
				return (dp[val][a][b] = 1) == 1;
			}
		}
		return (dp[val][a][b] = -1) == 1;
	}

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() throws Exception {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = new StringTokenizer("");
		}

		public FastScanner(String filename) throws Exception {
			br = new BufferedReader(new FileReader(filename));
			st = new StringTokenizer("");
		}

		public String nextLine() throws Exception {
			return br.readLine();
		}

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

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

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

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