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:

/*
 * Created by cravuri on 9/20/18
 */

import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class VasyaAndMultisets {

   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      int[] set = new int[n];
      int[] num = new int[101];
      for (int i = 0; i < n; i++) {
         set[i] = sc.nextInt();
         num[set[i]]++;
      }
      Set<Integer> num1 = new HashSet<>();
      Set<Integer> numG = new HashSet<>();
      for (int i = 1; i <= 100; i++) {
         if (num[i] == 1) {
            num1.add(i);
         } else if (num[i] > 2) {
            numG.add(i);
         }
      }
      if (numG.size() > 0) {
         if (num1.size() % 2 == 0) {
            System.out.println("YES");
            boolean a = true;
            for (int i = 0; i < n; i++) {
               if (num1.contains(set[i])) {
                  if (a) {
                     System.out.print("A");
                  } else {
                     System.out.print("B");
                  }
                  a = !a;
               } else {
                  System.out.print("A");
               }
            }
            System.out.println();
         } else {
            System.out.println("YES");
            boolean a = true;
            boolean found = false;
            for (int i = 0; i < n; i++) {
               if (num1.contains(set[i])) {
                  if (a) {
                     System.out.print("A");
                  } else {
                     System.out.print("B");
                  }
                  a = !a;
               } else if (numG.contains(set[i])) {
                  if (!found) {
                     System.out.print("B");
                     found = true;
                  } else {
                     System.out.print("A");
                  }
               } else {
                  System.out.print("A");
               }
            }
            System.out.println();
         }
      } else {
         if (num1.size() % 2 == 0) {
            System.out.println("YES");
            boolean a = true;
            for (int i = 0; i < n; i++) {
               if (num1.contains(set[i])) {
                  if (a) {
                     System.out.print("A");
                  } else {
                     System.out.print("B");
                  }
                  a = !a;
               } else {
                  System.out.print("A");
               }
            }
            System.out.println();
         } else {
            System.out.println("NO");
         }
      }
//      if (a == 0) {
//         0
//      }
//      if (a == 1) {
//         +1 or -1
//      }
//      if (a == 2) {
//         0
//      }
//      if (a > 2) {
//         0 or +1 or -1
//      }
   }

}