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.Scanner;

public class Main3 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        int[] arr = new int[n];
        int[] cnt = new int[101];
        int ones = 0;
        boolean extras = false;
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
            cnt[arr[i]]++;
            if (cnt[arr[i]] == 1) ones++;
            else if (cnt[arr[i]] == 2) ones--;
            else if (cnt[arr[i]] > 2) extras = true;
        }

        if (ones % 2 == 1 && !extras) System.out.println("NO");
        else {
            System.out.println("YES");
            boolean useExtra = ones % 2 == 1;
            int onesused = 0;
            for (int i = 0; i < n; i++) {
                if (cnt[arr[i]] > 2 && useExtra) { System.out.print("A"); useExtra = false; }
                else if (cnt[arr[i]] > 1) System.out.print("B");
                else {
                    onesused++;
                    if (onesused <= ones / 2) System.out.print("A");
                    else System.out.print("B");
                }
            }
            System.out.println();
            System.out.flush();
        }
    }
}