#include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define ld long double
#define LLMax LLONG_MAX
#define LLMin LLONG_MIN
#define Max INT_MAX
#define Min INT_MIN
#define f1(i,a,b) for(int i=(a);i<(b);i++)
#define f(i,a,b) for(int i=(a);i<=(b);i++)
#define DWN(j,b,a) for(int j=(b);j>=(a);j--)
#define ste1(a) memset(a,-1,sizeof(a))
#define set0(a) memset(a,0,sizeof(a))
#define IOS ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0)
using namespace std;
const int maxn=2e5+50;
int a[200005];
int c[200005];
signed main() {
  IOS;
  int t;
  cin>>t;
  while(t--)
  {
            int n, flag = 0;
    cin >> n;
    set0(c);
    for (int i = 0; i < n; i++)
    {
        cin>>a[i];
    }
    sort(a, a + n);
    int k = 0;
    int b = a[0];
    for (int i = 0; i < n; i++)
    {
        if (a[i] == b)
        {
            k++;
        }
        else
        {
            c[k]++;
            k = 1;
            b = a[i];
        }
    }
    c[k]++;
 
    int minn = 999999999;
    int nowsum = 0;
    for (int i = 200000; i >= 1; i--)
    {
     
        if (n - c[i] * i < minn)
        {
            minn = n - c[i] * i;
        }
        nowsum += c[i];
        c[i - 1] += c[i];
    }
    cout << minn << 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>
#define ll long long
#define ull unsigned long long
#define ld long double
#define LLMax LLONG_MAX
#define LLMin LLONG_MIN
#define Max INT_MAX
#define Min INT_MIN
#define f1(i,a,b) for(int i=(a);i<(b);i++)
#define f(i,a,b) for(int i=(a);i<=(b);i++)
#define DWN(j,b,a) for(int j=(b);j>=(a);j--)
#define ste1(a) memset(a,-1,sizeof(a))
#define set0(a) memset(a,0,sizeof(a))
#define IOS ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0)
using namespace std;
const int maxn=2e5+50;
int a[200005];
int c[200005];
signed main() {
  IOS;
  int t;
  cin>>t;
  while(t--)
  {
            int n, flag = 0;
    cin >> n;
    set0(c);
    for (int i = 0; i < n; i++)
    {
        cin>>a[i];
    }
    sort(a, a + n);
    int k = 0;
    int b = a[0];
    for (int i = 0; i < n; i++)
    {
        if (a[i] == b)
        {
            k++;
        }
        else
        {
            c[k]++;
            k = 1;
            b = a[i];
        }
    }
    c[k]++;
 
    int minn = 999999999;
    int nowsum = 0;
    for (int i = 200000; i >= 1; i--)
    {
     
        if (n - c[i] * i < minn)
        {
            minn = n - c[i] * i;
        }
        nowsum += c[i];
        c[i - 1] += c[i];
    }
    cout << minn << endl;

  }
return 0;
}



```