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>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target(sse, sse2, sse3, ssse3, sse4, popcnt, tune = native)
using namespace std;
const int inf = 1e18 + 239;
signed main() {
  int n;
  cin >> n;
  vector<int> a(n), cnt(101, 0);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    cnt[a[i]]++;
  }
  vector<int> uniq, nuq;
  for (int i = 0; i < int(cnt.size()); i++) {
    if (cnt[i] == 1) uniq.push_back(i);
    if (cnt[i] > 2) nuq.push_back(i);
  }
  if (int(uniq.size()) % 2 == 1 && int(nuq.size()) == 0) {
    cout << "NO"
         << "\n";
    return 0;
  }
  vector<int> color(101, -1);
  for (int i = 0; i < int(uniq.size()); i++) {
    color[uniq[i]] = (i % 2);
  }
  int paint = -2;
  if (int(uniq.size()) % 2 == 1) {
    paint = nuq[0];
  }
  for (int i = 0; i < nuq.size(); i++) {
    color[nuq[i]] = 0;
  }
  string ans;
  for (int i = 0; i < n; i++) {
    if (a[i] == paint) {
      a[i] = 1;
      paint = -2;
      continue;
    }
    a[i] = color[a[i]];
  }
  cout << "YES"
       << "\n";
  for (int i = 0; i < a.size(); i++) {
    char vr = 'A';
    if (a[i] == 1) vr = 'B';
    ans.push_back(vr);
  }
  cout << "\n";
  cout << ans << "\n";
}