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;
map<int, int> m;
int maxi = 0;
int maxNum = -1;
int main() {
  int n;
  cin >> n;
  vector<int> v(n);
  for (int i = 0; i < n; i++) {
    cin >> v[i];
    m[v[i]] += 1;
    if (m[v[i]] > maxi) {
      maxi = m[v[i]];
      maxNum = v[i];
    }
  }
  int count = 0;
  for (int i = 0; i < n; i++) {
    if (m[v[i]] == 1) count++;
  }
  int rem = count % 2;
  if (rem == 0) {
    cout << "YES\n";
    bool turn = true;
    for (int i = 0; i < n; i++) {
      if (m[v[i]] == 1) {
        if (turn)
          cout << "A";
        else
          cout << "B";
        turn = not(turn);
      } else
        cout << "A";
    }
  } else {
    if (maxi > 2) {
      cout << "YES\n";
      bool turn = true;
      bool cond = true;
      for (int i = 0; i < n; i++) {
        if (m[v[i]] == 1) {
          if (turn)
            cout << "A";
          else
            cout << "B";
          turn = not(turn);
        } else if (v[i] == maxNum and cond) {
          cout << "B";
          cond = false;
        } else
          cout << "A";
      }
    } else
      cout << "NO";
  }
  return 0;
}