/**
      --------------------------------------------------
      |   made by Matvey Bunos (@nyashenotik) with <3  |
      |           2020 - Lyceum BSU - 10 IM	       	   |
      |          *** All rights reserved *** 	       |
      --------------------------------------------------
                                                        **/
 
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <climits>
#include <vector>
 
using namespace std;
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
 
    int t;
    cin >> t;
 
    while(t --) {
        int n;
        cin >> n;
 
        vector <int> a(n), cnt;
        int sumOfThis = 0;
        map <int, int> countMap;
        set <int> uniqueCount;
 
        for(int i = 0; i < n; i ++) {
            cin >> a[i];
            countMap[a[i]] ++;
        }
 
        for(auto pr : countMap) {
            cnt.push_back(pr.second);
            uniqueCount.insert(pr.second);
        }
 
        int curAnswer = 0, bestAnswer = INT_MAX;
 
        sort(cnt.begin(), cnt.end());
 
        for(int i = 0; i < cnt.size(); i ++)
            sumOfThis += cnt[i];
 
 
        for(int i : uniqueCount) {
            curAnswer = 0;
            int index = lower_bound(cnt.begin(), cnt.end(), i) - cnt.begin();
 
            curAnswer += sumOfThis;
            curAnswer -= i * (cnt.size() - index);
 
            bestAnswer = min(bestAnswer, curAnswer);
        }
 
        cout << bestAnswer << '\n';
 
 
 
    }
    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
/**
      --------------------------------------------------
      |   made by Matvey Bunos (@nyashenotik) with <3  |
      |           2020 - Lyceum BSU - 10 IM	       	   |
      |          *** All rights reserved *** 	       |
      --------------------------------------------------
                                                        **/
 
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <climits>
#include <vector>
 
using namespace std;
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
 
    int t;
    cin >> t;
 
    while(t --) {
        int n;
        cin >> n;
 
        vector <int> a(n), cnt;
        int sumOfThis = 0;
        map <int, int> countMap;
        set <int> uniqueCount;
 
        for(int i = 0; i < n; i ++) {
            cin >> a[i];
            countMap[a[i]] ++;
        }
 
        for(auto pr : countMap) {
            cnt.push_back(pr.second);
            uniqueCount.insert(pr.second);
        }
 
        int curAnswer = 0, bestAnswer = INT_MAX;
 
        sort(cnt.begin(), cnt.end());
 
        for(int i = 0; i < cnt.size(); i ++)
            sumOfThis += cnt[i];
 
 
        for(int i : uniqueCount) {
            curAnswer = 0;
            int index = lower_bound(cnt.begin(), cnt.end(), i) - cnt.begin();
 
            curAnswer += sumOfThis;
            curAnswer -= i * (cnt.size() - index);
 
            bestAnswer = min(bestAnswer, curAnswer);
        }
 
        cout << bestAnswer << '\n';
 
 
 
    }
    return 0;
}
```