Problem: This problem is actually a subproblem of problem G from the same contest.

There are n candies in a candy box. The type of the i-th candy is a_i (1 ≤ a_i ≤ n).

You have to prepare a gift using some of these candies with the following restriction: the numbers of candies of each type presented in a gift should be all distinct (i. e. for example, a gift having two candies of type 1 and two candies of type 2 is bad). 

It is possible that multiple types of candies are completely absent from the gift. It is also possible that not all candies of some types will be taken to a gift.

Your task is to find out the maximum possible size of the single gift you can prepare using the candies you have.

You have to answer q independent queries.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries. Each query is represented by two lines.

The first line of each query contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of candies.

The second line of each query contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n), where a_i is the type of the i-th candy in the box.

It is guaranteed that the sum of n over all queries does not exceed 2 ⋅ 10^5.

Output

For each query print one integer — the maximum possible size of the single gift you can compose using candies you got in this query with the restriction described in the problem statement.

Example

Input


3
8
1 4 8 4 5 6 3 8
16
2 1 3 3 4 3 4 4 1 3 2 2 2 4 1 1
9
2 2 4 4 4 7 7 7 7


Output


3
10
9

Note

In the first query, you can prepare a gift with two candies of type 8 and one candy of type 5, totalling to 3 candies.

Note that this is not the only possible solution — taking two candies of type 4 and one candy of type 6 is also valid.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int t, n, a, type;
long long ans1, ans2;
multiset<int> m;
int main(void) {
  ios ::sync_with_stdio(0);
  cin.tie(0);
  cin >> t;
  for (int z = 1; z <= t; ++z) {
    m.clear();
    ans1 = ans2 = 0;
    cin >> n;
    vector<int> cnt(n + 5, 0), one(n + 5, 0);
    vector<multiset<int> > s(n + 5);
    for (int i = 1; i <= n; ++i) {
      cin >> a >> type;
      ++cnt[a];
      if (type) {
        ++one[a];
      }
    }
    for (int i = 1; i <= n; ++i) {
      if (cnt[i]) {
        s[cnt[i]].insert(one[i]);
      }
    }
    for (int i = n; i >= 1; --i) {
      for (int num : s[i]) {
        m.insert(num);
      }
      if (m.size()) {
        ans1 += i;
        a = *(m.rbegin());
        ans2 += min(i, a);
        m.erase(m.find(a));
      }
    }
    cout << ans1 << " " << ans2 << "\n";
  }
  return 0;
}