#include <iostream>
#include <algorithm>
using namespace std;

int main() {
long long int t;
cin>>t;
while(t--)
{
 long long int i,j;
 j=0;
 long long int n;
 long long int a[200005];
   long long int b[200005];
 cin>>n;
 for(i=0;i<n;i++)
  {cin>>a[i];b[i]=0;}
  sort(a,a+n);

  b[j]++;
  for(i=1;i<n;i++)
  {
   if(a[i]!=a[i-1])
    {
     j++;
     b[j]++;
    }
    else
    b[j]++;
  }
  sort(b,b+j+1);
  long long int min,s;
  s=0;min=n;
  for(i=0;i<=j;i++)
  {
   s=(n-b[i]*(j-i+1));
   if(s<min)
   min=s;
  }
  cout<<min<<"\n";
}
	return 0;
}

### Prompt

Create a solution in cpp for 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 <iostream>
#include <algorithm>
using namespace std;

int main() {
long long int t;
cin>>t;
while(t--)
{
 long long int i,j;
 j=0;
 long long int n;
 long long int a[200005];
   long long int b[200005];
 cin>>n;
 for(i=0;i<n;i++)
  {cin>>a[i];b[i]=0;}
  sort(a,a+n);

  b[j]++;
  for(i=1;i<n;i++)
  {
   if(a[i]!=a[i-1])
    {
     j++;
     b[j]++;
    }
    else
    b[j]++;
  }
  sort(b,b+j+1);
  long long int min,s;
  s=0;min=n;
  for(i=0;i<=j;i++)
  {
   s=(n-b[i]*(j-i+1));
   if(s<min)
   min=s;
  }
  cout<<min<<"\n";
}
	return 0;
}

```