#define _USE_MATH_DEFINES
#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int MAX = 2e5;
int t;
int n;
int arr[MAX+5];

int main(void){
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    cin >> t;
    while(t--){
        cin >> n;
        for(int i=0;i<n;i++){
            cin >> arr[i];
        }
        sort(arr,arr+n);
        vector<int> v;
        int cnt = 0;
        for(int i=0;i<n;i++){
            cnt++;
            if(i==n-1||arr[i]!=arr[i+1]){
                v.push_back(cnt);
                cnt = 0;
            }
        }
        sort(v.begin(),v.end());
        int m = v.size();
        ll sum = 0;
        ll acc = 0;
        for(int i=0;i<m;i++){
            sum += v[i];
        }
        ll ans = LLONG_MAX;
        for(int i=0;i<m;i++){
            ll diff = (i==0? v[i] : v[i]-v[i-1]);
            sum -= diff*(m-i);
            ans = min(ans,acc+sum);
            acc+=v[i];
        }
        cout << ans << '\n';
    }

    return 0;
}
### Prompt

In cpp, your task is to solve 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
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int MAX = 2e5;
int t;
int n;
int arr[MAX+5];

int main(void){
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    cin >> t;
    while(t--){
        cin >> n;
        for(int i=0;i<n;i++){
            cin >> arr[i];
        }
        sort(arr,arr+n);
        vector<int> v;
        int cnt = 0;
        for(int i=0;i<n;i++){
            cnt++;
            if(i==n-1||arr[i]!=arr[i+1]){
                v.push_back(cnt);
                cnt = 0;
            }
        }
        sort(v.begin(),v.end());
        int m = v.size();
        ll sum = 0;
        ll acc = 0;
        for(int i=0;i<m;i++){
            sum += v[i];
        }
        ll ans = LLONG_MAX;
        for(int i=0;i<m;i++){
            ll diff = (i==0? v[i] : v[i]-v[i-1]);
            sum -= diff*(m-i);
            ans = min(ans,acc+sum);
            acc+=v[i];
        }
        cout << ans << '\n';
    }

    return 0;
}
```