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 CandidateCode {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int arr[] = new int[101];
        int n = sc.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            arr[a[i]]++;
        }
        int cnt = 0;
        for (int i = 0; i < n; i++) {
            if (arr[a[i]] == 1) {
                cnt++;
            }
        }
        if (cnt % 2 == 0) {
            System.out.println("YES");
            int x = 0;
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < n; i++) {
                if (arr[a[i]] == 1) {
                    if (x % 2 == 0) {
                        sb.append("A");
                    } else sb.append("B");
                    x++;
                } else sb.append("B");

            }
            System.out.println(sb);
        } else {
            boolean set1[] = new boolean[101];
            int x = 0;
            for (int i = 0; i < n; i++) {
                if (arr[a[i]] == 1) {
                    if (x % 2 == 1) {
                        set1[a[i]] = true;
                    }
                    x++;
                }
            }
            boolean isOdd=false;
            for (int i=0;i<n;i++){
                if (arr[a[i]]>2){
                    isOdd=true;
                    set1[a[i]]=true;
                    break;
                }
            }
            if (!isOdd) System.out.println("NO");
            else {
                System.out.println("YES");
                StringBuilder sb=new StringBuilder();
                for (int i=0;i<n;i++){
                    if (set1[a[i]]){
                        sb.append("A");
                        set1[a[i]]=false;
                    }
                    else sb.append("B");
                }
                System.out.println(sb);
            }
        }
    }
}