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

using ll = long long;
using ld = long double;

const int N = 2e5;

int n;
pair<int, int> ar[N + 5];
int pre[N + 5];

void solve() {
    cin >> n;
    map<int, int> cnt;
    for (int i = 1; i <= n; i++) {
        int x;
        cin >> x;
        cnt[x]++;
    }
    int idx = 1;
    for (auto e : cnt) {
        ar[idx++] = make_pair(e.second, e.first);
    }
    sort(ar + 1, ar + idx);
    for (int i = 1; i < idx; i++) {
        pre[i] = pre[i - 1] + ar[i].first;
    }
    int ans = n;
    for (int i = 0; i < idx - 1; i++) {
        ans = min(ans, n - (idx - 1 - i) * ar[i + 1].first);
    }
    cout << ans << '\n';
}

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

    int TC = 1;
    cin >> TC;
    for(int i = 1; i <= TC; i++) {
        solve();
    }
  
    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<bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;

const int N = 2e5;

int n;
pair<int, int> ar[N + 5];
int pre[N + 5];

void solve() {
    cin >> n;
    map<int, int> cnt;
    for (int i = 1; i <= n; i++) {
        int x;
        cin >> x;
        cnt[x]++;
    }
    int idx = 1;
    for (auto e : cnt) {
        ar[idx++] = make_pair(e.second, e.first);
    }
    sort(ar + 1, ar + idx);
    for (int i = 1; i < idx; i++) {
        pre[i] = pre[i - 1] + ar[i].first;
    }
    int ans = n;
    for (int i = 0; i < idx - 1; i++) {
        ans = min(ans, n - (idx - 1 - i) * ar[i + 1].first);
    }
    cout << ans << '\n';
}

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

    int TC = 1;
    cin >> TC;
    for(int i = 1; i <= TC; i++) {
        solve();
    }
  
    return 0;
}
```