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;
const unsigned long long inf = (unsigned long long)2e18;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  unsigned long long n;
  cin >> n;
  unordered_map<unsigned long long, unsigned long long> mymap;
  unsigned long long m = 0;
  vector<unsigned long long> A(n);
  for (unsigned long long i = 0; i < n; i++) {
    unsigned long long a;
    cin >> a;
    A[i] = a;
    mymap[a]++;
  }
  for (auto it = mymap.begin(); it != mymap.end(); it++) {
    if (it->second == 1) m++;
  }
  vector<unsigned long long> used(n, 0);
  unsigned long long cnt = m / 2;
  if ((m) % 2 == 0) {
    cout << "YES" << endl;
    for (unsigned long long i = 0; i < n; i++) {
      if (cnt == 0) break;
      if (mymap[A[i]] == 1) {
        used[i] = 1;
        cnt--;
      }
    }
    for (unsigned long long i = 0; i < n; i++) {
      if (used[i] == 1) {
        cout << "A";
      } else
        cout << "B";
    }
  } else {
    unsigned long long flag = -1;
    for (unsigned long long i = 0; i < n; i++) {
      if (mymap[A[i]] > 2) {
        flag = 1;
        used[i] = 1;
        break;
      }
    }
    if (flag == -1) {
      cout << "NO";
      return 0;
    } else {
      cout << "YES" << endl;
      unsigned long long cnt1 = (m + 1) / 2;
      cnt1--;
      for (unsigned long long i = 0; i < n; i++) {
        if (cnt1 == 0) break;
        if (mymap[A[i]] == 1) {
          used[i] = 1;
          cnt1--;
        }
      }
      for (unsigned long long i = 0; i < n; i++) {
        if (used[i] == 1) {
          cout << "A";
        } else
          cout << "B";
      }
    }
  }
  return 0;
}