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.*;

public class VasyaMultisets {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        Map<Integer, Integer> freqs = new HashMap<>();
        int[] nums = new int[n];
        for (int i = 0; i < n; i++) {
            int curr = in.nextInt();
            nums[i] = curr;
            freqs.put(curr, freqs.getOrDefault(curr, 0) + 1);
        }

        int numUniques = 0;
        boolean above3Exists = false;
        for (int i : freqs.keySet()) {
            if (freqs.get(i) == 1) {
                numUniques++;
            } else if (freqs.get(i) >= 3) {
                above3Exists = true;
            }
        }

        if (numUniques % 2 == 1 && !above3Exists) {
            System.out.println("NO");
        } else {
            StringBuilder ans = new StringBuilder();
            boolean putInA = true;
            boolean firstAbove3 = true;
            for (int i : nums) {
                if (freqs.get(i) == 1) {
                    if (putInA) {
                        ans.append("A");
                    } else {
                        ans.append("B");
                    }
                    putInA = !putInA;
                } else if (freqs.get(i) == 2) {
                    ans.append("A");
                } else {
                    if (firstAbove3 && numUniques % 2 == 1) {
                        ans.append("B");
                    } else {
                        ans.append("A");
                    }
                    firstAbove3 = false;
                }
            }

            System.out.println("YES");
            System.out.println(ans);
        }

    }
}