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 Main2 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int[] cntArray = new int[101];
        
        int N = in.nextInt();
        int[] arr = new int[N];
        
        for(int i = 0; i < N; i++) {
            arr[i] = in.nextInt();
            cntArray[arr[i]]++;
            
        }
        
        int niceNumbers = 0;
        for(int i = 0; i < 101; i++) {
            if(cntArray[i] == 1) {
                niceNumbers++;
                //System.out.print(i + " ");
            }
        }
        
        int index = -1;
        if(niceNumbers % 2 == 1) {
            for(int i = 0; i < N; i++) {
                //System.out.print(cntArray[arr[i]] + " ");
                if(cntArray[arr[i]] > 2) {
                    index = i;
                    break;
                }
            }
            
            if(index == -1) {
                System.out.println("NO");
                return;
            }
        }

        System.out.println("YES");
        
        StringBuilder sb = new StringBuilder();
        HashSet<Integer> A = new HashSet<Integer>();
        
        for(int i = 0; A.size() < (niceNumbers / 2); i++) 
            if(cntArray[i] == 1) A.add(i);
        
        for(int i = 0; i < N; i++) {
            if(A.contains(arr[i]) || i == index) sb.append("A");
            else sb.append("B");
        }
          
        System.out.println(sb);
    }
}