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;
using ii = pair<int, int>;
using vi = vector<int>;
using vii = vector<ii>;
using vvi = vector<vi>;
using iii = pair<int, ii>;
using viii = vector<iii>;
using ll = long long int;
using vc = vector<char>;
using vb = vector<bool>;
using ib = pair<int, bool>;
using vib = vector<ib>;
struct obj {
  int a, b, c;
};
struct cmp1 {
  bool operator()(obj const& o1, obj const& o2) { return o1.a < o2.a; }
} c1;
struct cmp2 {
  bool operator()(obj const& o1, obj const& o2) { return o1.b < o2.b; }
} c2;
bool resuelveCaso() {
  int n;
  cin >> n;
  if (!cin) return false;
  map<int, int> m;
  vi v;
  for (int i = 0; i < n; ++i) {
    int aux;
    cin >> aux;
    if (m.find(aux) == m.end()) {
      m.insert(make_pair(aux, 0));
    }
    v.push_back(aux);
    ++m[aux];
  }
  int unicos = 0, tresomas = 0;
  for (auto it = m.begin(); it != m.end(); ++it) {
    if (it->second == 1)
      ++unicos;
    else if (it->second >= 3)
      ++tresomas;
  }
  if (unicos % 2 == 1 && tresomas == 0)
    cout << "NO\n";
  else {
    cout << "YES\n";
    if (unicos % 2 == 0) {
      bool cont = true;
      for (int i = 0; i < v.size(); ++i) {
        if (m[v[i]] == 1) {
          if (cont) {
            cout << 'A';
            cont = false;
          } else {
            cout << 'B';
            cont = true;
          }
        } else {
          cout << 'A';
        }
      }
    } else {
      bool cont = true;
      bool tresomasusado = false;
      for (int i = 0; i < v.size(); ++i) {
        if (m[v[i]] == 1) {
          if (cont) {
            cout << 'A';
            cont = false;
          } else {
            cout << 'B';
            cont = true;
          }
        } else if (m[v[i]] >= 3 && !tresomasusado) {
          cout << "B";
          tresomasusado = true;
        } else {
          cout << 'A';
        }
      }
    }
    cout << '\n';
  }
  return true;
}
int main() {
  while (resuelveCaso()) {
  }
  return 0;
}