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() {
  long long int n;
  cin >> n;
  long long int a[n];
  long long int f[101] = {0};
  for (long long int i = 0; i < n; i++) {
    cin >> a[i];
    f[a[i]]++;
  }
  long long int nice[101] = {0};
  long long int nc = 0;
  for (long long int i = 0; i < n; i++) {
    if (f[a[i]] == 1) {
      nice[a[i]] = 1;
      nc++;
    }
  }
  if (nc % 2 == 0) {
    cout << "YES" << endl;
    long long int prev = 1;
    for (long long int i = 0; i < n; i++) {
      if (nice[a[i]] and prev == 1) {
        cout << "A";
        prev = 0;
      } else if (nice[a[i]] and prev == 0) {
        cout << "B";
        prev = 1;
      } else if (!nice[a[i]])
        cout << "A";
    }
  } else {
    long long int ind = -1;
    for (long long int i = 0; i < n; i++) {
      if (!nice[a[i]] and f[a[i]] > 2) {
        ind = i;
        break;
      }
    }
    if (ind == -1) {
      cout << "NO";
    } else {
      cout << "YES" << endl;
      long long int prev = 1;
      for (long long int i = 0; i < n; i++) {
        if (nice[a[i]] and prev == 1) {
          cout << "A";
          prev = 0;
        } else if (nice[a[i]] and prev == 0) {
          cout << "B";
          prev = 1;
        } else if (!nice[a[i]] and i == ind)
          cout << "B";
        else if (!nice[a[i]] and i != ind)
          cout << "A";
      }
    }
  }
}