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 f() {}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  vector<int> a(n);
  {
    for (auto& i : a) cin >> i;
  };
  map<int, int> cnt, cia;
  vector<int> ones;
  for (int i : a) ++cnt[i];
  for (auto& p : cnt) {
    if (p.second == 1) ones.push_back(p.first);
  }
  for (int i = 0; i < ones.size(); i++) {
    if (i % 2) ++cia[ones[i]];
  }
  if (ones.size() % 2 == 1) {
    bool ret = false;
    for (auto& p : cnt) {
      if (p.second > 2) {
        ret = true;
        ++cia[p.first];
        break;
      }
    }
    if (!ret) {
      cout << "NO";
      return 0;
    }
  }
  string ret(n, 'B');
  for (int i = 0; i < n; i++) {
    if (cia[a[i]] > 0) ret[i] = 'A';
    --cia[a[i]];
  }
  cout << "YES\n" << ret;
  return 0;
}