#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ull unsigned long long
#define uint unsigned int
#define loop(n) for(int i=1;i<=n;i++)


int main()
{
	ios_base::sync_with_stdio(false);
	cout.tie(NULL);
	cin.tie(NULL);

	uint t;
	cin>>t;
	while(t--)
	{
		int n,temp,tem;
		ll min=INT_MAX;
		cin>>n;
		map<int,int> a;
		vector<int> s;
		set<int> st;
		loop(n)
		{
			cin>>temp;
			tem=a[temp];
			a[temp]=tem+1;
		}
		for(auto i:a)
		{
			//cout<<i.second<<" ";
			s.push_back(i.second);
			st.insert(i.second);
		}
		for(auto mid:st)		
		{
			ll sum=0;
			for(auto i:s)
				if(i<mid)
					sum+=i;
				else
					sum+=i-mid;
			if(min>sum)
				min=sum;
		}
		cout<<min<<endl;
	}
	return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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;
#define ll long long
#define ull unsigned long long
#define uint unsigned int
#define loop(n) for(int i=1;i<=n;i++)


int main()
{
	ios_base::sync_with_stdio(false);
	cout.tie(NULL);
	cin.tie(NULL);

	uint t;
	cin>>t;
	while(t--)
	{
		int n,temp,tem;
		ll min=INT_MAX;
		cin>>n;
		map<int,int> a;
		vector<int> s;
		set<int> st;
		loop(n)
		{
			cin>>temp;
			tem=a[temp];
			a[temp]=tem+1;
		}
		for(auto i:a)
		{
			//cout<<i.second<<" ";
			s.push_back(i.second);
			st.insert(i.second);
		}
		for(auto mid:st)		
		{
			ll sum=0;
			for(auto i:s)
				if(i<mid)
					sum+=i;
				else
					sum+=i-mid;
			if(min>sum)
				min=sum;
		}
		cout<<min<<endl;
	}
	return 0;
}
```