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 main() {
  int q;
  scanf("%d", &q);
  while (q--) {
    int n;
    scanf("%d", &n);
    map<int, int> q;
    for (int i = 0; i < n; i++) {
      int x;
      scanf("%d", &x);
      q[x]++;
    }
    vector<int> o;
    for (auto it : q) o.push_back(it.second);
    sort(o.begin(), o.end());
    int ans = 0, sz = o.size();
    int bk = 1;
    while ((bk) * (bk + 1) / 2 <= n) bk++;
    for (int i = 1; i <= bk + 30; i++) {
      vector<int> best;
      for (int j = sz - 1, c = 0; j >= 0 && c < i; j--, c++) {
        best.push_back(o[j]);
      }
      int len = best.size();
      for (int j = 1; j < len; j++) best[j] = min(best[j], best[j - 1] - 1);
      int sum = 0;
      for (int j = 0; j < len; j++)
        if (best[j] > 0) sum += best[j];
      ans = max(ans, sum);
    }
    printf("%d\n", ans);
  }
  return 0;
}