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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n, cnt[103], i, cnt1 = 0, cnt3 = 0, x, y, z;
  cin >> n;
  long long int arr[n + 3];
  string str;
  for (i = 0; i < n; i++) str += 'x';
  memset(cnt, 0, sizeof(cnt));
  for (i = 0; i < n; i++) {
    cin >> arr[i];
    cnt[arr[i]]++;
  }
  for (i = 1; i <= 100; i++) {
    if (cnt[i] == 1)
      cnt1++;
    else if (cnt[i] >= 3)
      cnt3++;
  }
  if (cnt1 % 2 != 0 && cnt3 == 0)
    cout << "NO" << endl;
  else {
    cout << "YES" << endl;
    if (cnt1 % 2 == 0) {
      x = 0;
      for (i = 0; i < n; i++) {
        if (cnt[arr[i]] == 1 && x < (cnt1 / 2)) {
          str[i] = 'A';
          x++;
        } else if (cnt[arr[i]] >= 2) {
          str[i] = 'A';
        }
      }
      x = 0;
      for (i = 0; i < n; i++) {
        if (str[i] != 'A') str[i] = 'B';
      }
    } else {
      for (i = 0; i < n; i++) {
        if (cnt[arr[i]] >= 3) {
          y = arr[i];
          break;
        }
      }
      x = 0;
      z = 0;
      for (i = 0; i < n; i++) {
        if (cnt[arr[i]] == 1 && x < (cnt1 / 2)) {
          str[i] = 'A';
          x++;
        } else if (arr[i] == y && z == 0) {
          str[i] = 'A';
          z = 1;
        }
      }
      for (i = 0; i < n; i++) {
        if (str[i] != 'A') str[i] = 'B';
      }
    }
    cout << str << endl;
  }
  return 0;
}