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() {
  std::vector<std::vector<int> > base;
  int i, n;
  cin >> n;
  map<int, int> mp;
  vector<int> vec;
  vector<char> vec2;
  for (i = 0; i < n; i++) {
    int a;
    cin >> a;
    vec.push_back(a);
    mp[a]++;
  }
  int nice = 0;
  for (i = 0; i < vec.size(); i++) {
    if (mp[vec[i]] == 1) {
      nice++;
    }
  }
  int flag = 0, flag2 = 0;
  if (nice % 2 == 1) {
    flag2 = 1;
  }
  for (i = 0; i < vec.size(); i++) {
    if (mp[vec[i]] == 1 && flag == 0) {
      vec2.push_back('A');
      flag = 1;
    } else if (mp[vec[i]] == 1 && flag == 1) {
      vec2.push_back('B');
      flag = 0;
    } else if (mp[vec[i]] > 2 && flag2 == 1) {
      flag2 = 0;
      vec2.push_back('B');
    } else {
      vec2.push_back('A');
    }
  }
  if (flag2 == 1) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    for (int i = 0; i < vec2.size(); i++) {
      cout << vec2[i];
    }
  }
}