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>
int main() {
  size_t n;
  std::cin >> n;
  std::vector<int> s(n);
  std::map<int, int> count;
  for (size_t i = 0; i != n; ++i) {
    std::cin >> s[i];
    ++count[s[i]];
  }
  int ones = 0, mtones = 0;
  for (auto kv : count) {
    switch (kv.second) {
      case 1:
        ++ones;
        break;
      case 2:
        break;
      default:
        ++mtones;
        break;
    }
  }
  if (ones % 2 == 1 && mtones == 0) {
    std::cout << "NO" << std::endl;
  } else {
    std::cout << "YES" << std::endl;
    bool print_b = ones % 2 == 1;
    bool a = true;
    for (int i : s) {
      if (count[i] == 1) {
        std::cout << (a ? 'A' : 'B');
        a = !a;
      } else if (print_b && count[i] > 2) {
        std::cout << 'B';
        print_b = false;
      } else
        std::cout << 'A';
    }
  }
}