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;
const int N = 200005;
int good[N];
int cnt[N];
vector<int> types[N];
void go() {
  int n;
  cin >> n;
  for (int i = (int)(1); i <= (int)(n); i++) {
    good[i] = 0;
    cnt[i] = 0;
    types[i].clear();
  }
  for (int i = 0; i < (int)(n); i++) {
    int t, f;
    cin >> t >> f;
    cnt[t]++;
    if (f == 1) good[t]++;
  }
  for (int i = (int)(1); i <= (int)(n); i++) {
    types[cnt[i]].push_back(good[i]);
  }
  multiset<int> m;
  int a1 = 0, a2 = 0;
  for (int i = n; i >= 1; i--) {
    for (auto x : types[i]) m.insert(x);
    if (!m.empty()) {
      int r = *m.rbegin();
      a1 += i;
      a2 += min(r, i);
      m.erase(m.find(r));
    }
  }
  cout << a1 << " " << a2 << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  int T;
  cin >> T;
  while (T--) go();
  return 0;
}