#include <cstdio>
#include <map>
#include <vector>
#include <algorithm>
using namespace std;

int tcase,n,ans;

map<int,int> mp;
vector<int> vec,sum;

int main()
{
    scanf("%d",&tcase);
    while(tcase--)
    {
        scanf("%d",&n); mp.clear();
        for(int i=1;i<=n;i++)
        {
            int x; scanf("%d",&x);
            mp[x]++;
        }

        vec.clear(); sum.clear();
        for(auto p : mp) vec.push_back(p.second);
        sort(vec.begin(), vec.end());
        for(int i=0;i<vec.size();i++)
        {
            sum.push_back(vec[i]);
            if(i) sum[i] += sum[i-1];
        }

        ans = n;
        for(int i=0;i<vec.size();i++)
        {
            int x = sum.back() - sum[i] - vec[i] * (vec.size() - 1 - i);
            if(i) x += sum[i-1];
            ans = min(ans, x);
        }
        printf("%d\n",ans);
    }
    return 0;
}

### Prompt

Please create a solution in CPP 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 <cstdio>
#include <map>
#include <vector>
#include <algorithm>
using namespace std;

int tcase,n,ans;

map<int,int> mp;
vector<int> vec,sum;

int main()
{
    scanf("%d",&tcase);
    while(tcase--)
    {
        scanf("%d",&n); mp.clear();
        for(int i=1;i<=n;i++)
        {
            int x; scanf("%d",&x);
            mp[x]++;
        }

        vec.clear(); sum.clear();
        for(auto p : mp) vec.push_back(p.second);
        sort(vec.begin(), vec.end());
        for(int i=0;i<vec.size();i++)
        {
            sum.push_back(vec[i]);
            if(i) sum[i] += sum[i-1];
        }

        ans = n;
        for(int i=0;i<vec.size();i++)
        {
            int x = sum.back() - sum[i] - vec[i] * (vec.size() - 1 - i);
            if(i) x += sum[i-1];
            ans = min(ans, x);
        }
        printf("%d\n",ans);
    }
    return 0;
}

```