#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int st[200005];
map<int,int> mp;
int sum1[200005],sum[200005];
int main()
{
    int t;
    cin>>t; 
	while(t--)
	{
	    mp.clear();
	    memset(st,0,sizeof(st));
	    memset(sum,0,sizeof(sum));
	    memset(sum1,0,sizeof(sum1));
		int n;
		cin>>n;
		int max1=0;
		for(int i=0;i<n;i++)
		{
			int k;
			cin>>k;
			mp[k]++;
			max1=max(max1,mp[k]);
		}
		for(auto p:mp)
		{
			st[p.second]++;
		}
		int min1=1e9;
		for(int i=1;i<=max1;i++)
		{
			sum[i]=sum[i-1]+st[i];
			sum1[i]=sum1[i-1]+st[i]*i;
		}
		for(int i=1;i<=max1;i++)
		{
		    min1=min(min1,(sum1[i-1]+(sum1[max1]-sum1[i]-(i*(sum[max1]-sum[i])))));
		}
		cout<<min1<<endl;
	} 
    return 0;
}
### 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
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int st[200005];
map<int,int> mp;
int sum1[200005],sum[200005];
int main()
{
    int t;
    cin>>t; 
	while(t--)
	{
	    mp.clear();
	    memset(st,0,sizeof(st));
	    memset(sum,0,sizeof(sum));
	    memset(sum1,0,sizeof(sum1));
		int n;
		cin>>n;
		int max1=0;
		for(int i=0;i<n;i++)
		{
			int k;
			cin>>k;
			mp[k]++;
			max1=max(max1,mp[k]);
		}
		for(auto p:mp)
		{
			st[p.second]++;
		}
		int min1=1e9;
		for(int i=1;i<=max1;i++)
		{
			sum[i]=sum[i-1]+st[i];
			sum1[i]=sum1[i-1]+st[i]*i;
		}
		for(int i=1;i<=max1;i++)
		{
		    min1=min(min1,(sum1[i-1]+(sum1[max1]-sum1[i]-(i*(sum[max1]-sum[i])))));
		}
		cout<<min1<<endl;
	} 
    return 0;
}
```