#include <bits/stdc++.h>
#define ll long long

using namespace std;

int main()
{
	int t, temp, n;
	cin>>t;
	while(t--)
	{
		cin>>n;
		vector<int> v;
		map<int, int> mp;
		for(int i = 0; i<n; i++)
		{
			cin>>temp;
			mp[temp]++;
		}

		for(auto i = mp.begin(); i != mp.end(); i++)
		{
			v.push_back(i->second);

		}		

		sort(v.begin(), v.end());

		int n = v.size();
		vector<int> s(n);
		ll prev = 0;

		for(int i = 0; i < n; i++)
		{
			s[i] = prev + v[i];
			prev = s[i];
		
		}
		ll ans = INT_MAX, cost;

		for(int i = 0; i < n; i++)
		{
			int num = v[i];
			int start = i;

			while(i+1 < n && v[i+1]==num) i++;

			cost = start > 0 ? s[start-1]: 0;
			
			cost += i < n ? (s[n-1] - s[i]) - ((n-1 - i) * num) : 0;
			//cout << start << " " << i << " " << cost << "\n";
			ans = min(cost, ans);
		}

		cout << ans <<  endl;

	}
}
### Prompt

Your task is to create 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>
#define ll long long

using namespace std;

int main()
{
	int t, temp, n;
	cin>>t;
	while(t--)
	{
		cin>>n;
		vector<int> v;
		map<int, int> mp;
		for(int i = 0; i<n; i++)
		{
			cin>>temp;
			mp[temp]++;
		}

		for(auto i = mp.begin(); i != mp.end(); i++)
		{
			v.push_back(i->second);

		}		

		sort(v.begin(), v.end());

		int n = v.size();
		vector<int> s(n);
		ll prev = 0;

		for(int i = 0; i < n; i++)
		{
			s[i] = prev + v[i];
			prev = s[i];
		
		}
		ll ans = INT_MAX, cost;

		for(int i = 0; i < n; i++)
		{
			int num = v[i];
			int start = i;

			while(i+1 < n && v[i+1]==num) i++;

			cost = start > 0 ? s[start-1]: 0;
			
			cost += i < n ? (s[n-1] - s[i]) - ((n-1 - i) * num) : 0;
			//cout << start << " " << i << " " << cost << "\n";
			ans = min(cost, ans);
		}

		cout << ans <<  endl;

	}
}
```