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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> A(n), Ch(100);
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    Ch[A[i] - 1]++;
  }
  int c = 0, d = 0;
  for (int i = 0; i < 100; i++) {
    if (Ch[i] == 1)
      c++;
    else if (Ch[i] > 2)
      d++;
  }
  if (c % 2 == 1 && d == 0)
    cout << "NO" << endl;
  else {
    cout << "YES" << endl;
    int y = c % 2;
    for (int i = 0; i < n; i++) {
      if (Ch[A[i] - 1] == 1) {
        cout << char('A' + c % 2);
        c--;
      } else if (y == 1 && Ch[A[i] - 1] > 2) {
        cout << "A";
        y--;
      } else {
        cout << "B";
      }
    }
  }
}