#include <bits/stdc++.h>
using namespace std;

int main(int argc, char **argv) {
  cin.sync_with_stdio(false), cin.tie(nullptr);

  int tests;
  cin >> tests;

  while (tests--) {
    int n;
    cin >> n;

    map<int, int> cnt;

    for (int i = 0; i < n; i++) {
      int x;
      cin >> x;
      cnt[x] += 1;
    }

    const int m = cnt.size();

    vector<int> a;
    a.reserve(m);

    for (auto x : cnt) {
      a.push_back(x.second);
    }
    
    sort(a.begin(), a.end());

    vector<int64_t> sum(m + 1, 0);

    for (int i = 0; i < m; i++) {
      sum[i + 1] = a[i] + sum[i];
    }

    int64_t result = n;

    for (int i = 0; i < m; i++) {
      result = min(result, sum[i] + sum[m] - sum[i + 1] - int64_t(m - i - 1) * a[i]);
    }

    cout << result << "\n";
  }
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

Polycarp was gifted an array a of length n. Polycarp considers an array beautiful if there exists a number C, such that each number in the array occurs either zero or C times. Polycarp wants to remove some elements from the array a to make it beautiful.

For example, if n=6 and a = [1, 3, 2, 1, 4, 2], then the following options are possible to make the array a array beautiful: 

  * Polycarp removes elements at positions 2 and 5, array a becomes equal to [1, 2, 1, 2]; 
  * Polycarp removes elements at positions 1 and 6, array a becomes equal to [3, 2, 1, 4]; 
  * Polycarp removes elements at positions 1, 2 and 6, array a becomes equal to [2, 1, 4]; 



Help Polycarp determine the minimum number of elements to remove from the array a to make it beautiful.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case consists of one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — array a.

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

Output

For each test case, output one integer — the minimum number of elements that Polycarp has to remove from the array a to make it beautiful.

Example

Input


3
6
1 3 2 1 4 2
4
100 100 4 100
8
1 2 3 3 3 2 6 6


Output


2
1
2

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

int main(int argc, char **argv) {
  cin.sync_with_stdio(false), cin.tie(nullptr);

  int tests;
  cin >> tests;

  while (tests--) {
    int n;
    cin >> n;

    map<int, int> cnt;

    for (int i = 0; i < n; i++) {
      int x;
      cin >> x;
      cnt[x] += 1;
    }

    const int m = cnt.size();

    vector<int> a;
    a.reserve(m);

    for (auto x : cnt) {
      a.push_back(x.second);
    }
    
    sort(a.begin(), a.end());

    vector<int64_t> sum(m + 1, 0);

    for (int i = 0; i < m; i++) {
      sum[i + 1] = a[i] + sum[i];
    }

    int64_t result = n;

    for (int i = 0; i < m; i++) {
      result = min(result, sum[i] + sum[m] - sum[i + 1] - int64_t(m - i - 1) * a[i]);
    }

    cout << result << "\n";
  }
}

```