/**
*    author:  Mohamed AboOkail
*    created: 16/02/2O21
**/
#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
 
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	int t;
	cin >> t;
	while(t--) {
		int n;
		cin >> n;
		vector < long long > a(n);
		map < long long , int > mp;
		for (int i = 0; i < n; i++) {
			cin >> a[i];
			mp[a[i]]++;
		}
		vector < long long > x;
		for(auto it : mp) {
			x.push_back(it.second);
		}
		vector < long long > ans;
		sort(x.begin(), x.end());
		for (int i = 0; i < x.size(); i++) {
			ans.push_back(n - (x.size() - i) * x[i]);
		}
		cout << *min_element(ans.begin(), ans.end()) << "\n";
	}
}
### Prompt

Please formulate 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
/**
*    author:  Mohamed AboOkail
*    created: 16/02/2O21
**/
#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
 
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	int t;
	cin >> t;
	while(t--) {
		int n;
		cin >> n;
		vector < long long > a(n);
		map < long long , int > mp;
		for (int i = 0; i < n; i++) {
			cin >> a[i];
			mp[a[i]]++;
		}
		vector < long long > x;
		for(auto it : mp) {
			x.push_back(it.second);
		}
		vector < long long > ans;
		sort(x.begin(), x.end());
		for (int i = 0; i < x.size(); i++) {
			ans.push_back(n - (x.size() - i) * x[i]);
		}
		cout << *min_element(ans.begin(), ans.end()) << "\n";
	}
}
```