#include<bits/stdc++.h>
 
using namespace std;
using ll = long long;

map<int, int> M;
void solve(int TestCase) {
    M.clear();

    int n;
    cin >> n;

    vector<int> A(n);
    for(auto& x : A) cin >> x;

    for(auto x : A) M[x]++;

    vector<int> B;
    for(auto& p : M) B.push_back(p.second);

    sort(B.begin(), B.end());

    auto BS = vector<int>(B.size() + 1);
    for(auto i = 1; i < BS.size(); ++i)
        BS[i] = BS[i-1] + B[i-1];
    
    int ret = INT_MAX;
    for(auto i = 0, j = 0; j < B.size(); i = j) {
        while(j < B.size() && B[i] == B[j]) ++j;
        int candi = BS[i] + BS.back() - BS[j] - B[i] * ((int)B.size() - j);
        ret = min(ret, candi);
    }

    cout << ret << endl;
}
 
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
 
    int t = 1;
    cin >> t;
    for(auto i = 1; i <= t; ++i) {
       // cout << "Case #"<< i << ": ";
        solve(i);
    }
}
### Prompt

Your task is to create 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>
 
using namespace std;
using ll = long long;

map<int, int> M;
void solve(int TestCase) {
    M.clear();

    int n;
    cin >> n;

    vector<int> A(n);
    for(auto& x : A) cin >> x;

    for(auto x : A) M[x]++;

    vector<int> B;
    for(auto& p : M) B.push_back(p.second);

    sort(B.begin(), B.end());

    auto BS = vector<int>(B.size() + 1);
    for(auto i = 1; i < BS.size(); ++i)
        BS[i] = BS[i-1] + B[i-1];
    
    int ret = INT_MAX;
    for(auto i = 0, j = 0; j < B.size(); i = j) {
        while(j < B.size() && B[i] == B[j]) ++j;
        int candi = BS[i] + BS.back() - BS[j] - B[i] * ((int)B.size() - j);
        ret = min(ret, candi);
    }

    cout << ret << endl;
}
 
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
 
    int t = 1;
    cin >> t;
    for(auto i = 1; i <= t; ++i) {
       // cout << "Case #"<< i << ": ";
        solve(i);
    }
}
```