#include <iostream>
#include <fstream>
#include <algorithm>
using namespace std;
ifstream fin("date.in");
ofstream fout("date.out");
long long v[200005], sum[200005], cnt[200005], w[200005];
int main()
{
    ios_base::sync_with_stdio(false); cin.tie(0);
    int t; cin >> t;
    for(int j=1; j<=t; j++)
    {
        int n, num=0; cin >> n;
        for(int i=1; i<=n; i++)  cin >> v[i];
        sort(v+1, v+n+1);
        for(int i=1; i<=n; i++)
        {
            int nr=0;
            while(v[i]==v[i+1] && i<n)
            {
                nr++;
                i++;
            }
            num++; cnt[num]=nr+1;
        }
        int MIN=n;
        for(int i=1; i<=num; i++)
        {
            if(w[cnt[i]]==0)
            {
                w[cnt[i]]=1;
                int c=cnt[i], rez=0;
                for(int k=1; k<=num; k++)
                {
                    if(cnt[k]<c)  rez+=cnt[k];
                    else   rez+=cnt[k]-c;
                }
                if(rez<MIN)  MIN=rez;
            }

        }
        for(int i=1; i<=n; i++)  w[i]=0;
        cout << MIN << "\n";
    }
    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 <iostream>
#include <fstream>
#include <algorithm>
using namespace std;
ifstream fin("date.in");
ofstream fout("date.out");
long long v[200005], sum[200005], cnt[200005], w[200005];
int main()
{
    ios_base::sync_with_stdio(false); cin.tie(0);
    int t; cin >> t;
    for(int j=1; j<=t; j++)
    {
        int n, num=0; cin >> n;
        for(int i=1; i<=n; i++)  cin >> v[i];
        sort(v+1, v+n+1);
        for(int i=1; i<=n; i++)
        {
            int nr=0;
            while(v[i]==v[i+1] && i<n)
            {
                nr++;
                i++;
            }
            num++; cnt[num]=nr+1;
        }
        int MIN=n;
        for(int i=1; i<=num; i++)
        {
            if(w[cnt[i]]==0)
            {
                w[cnt[i]]=1;
                int c=cnt[i], rez=0;
                for(int k=1; k<=num; k++)
                {
                    if(cnt[k]<c)  rez+=cnt[k];
                    else   rez+=cnt[k]-c;
                }
                if(rez<MIN)  MIN=rez;
            }

        }
        for(int i=1; i<=n; i++)  w[i]=0;
        cout << MIN << "\n";
    }
    return 0;
}

```