#include <bits/stdc++.h>

using namespace std;

int n;
int a[200100];
map<int, int>   c1, c2;

void solve() {
    cin >> n;
    c1.clear();
    c2.clear();

    for (int i=0; i<n; i++) {
        cin >> a[i];
        c1[a[i]]++;
    }
    map<int, int>::iterator j;

    for (j=c1.begin(); j!=c1.end(); j++) {
        c2[j->second]++;
    }

    map<int, int>::reverse_iterator p;
    int c = 0, res = 0;

    for (p=c2.rbegin(); p!=c2.rend(); p++) {
        //cout << p->first << ' ' << p->second << '\n';
        if (c == 0) {
            res = p->second * p->first;
        } else {
            res = max(res, (p->second + c) * p->first);
        }
        c += p->second;
    }
    cout << n - res << '\n';
}

int main() {
    int nt;
    cin >> nt;

    for (int it=0; it<nt; it++) {
        solve();
    }
}

### 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;

int n;
int a[200100];
map<int, int>   c1, c2;

void solve() {
    cin >> n;
    c1.clear();
    c2.clear();

    for (int i=0; i<n; i++) {
        cin >> a[i];
        c1[a[i]]++;
    }
    map<int, int>::iterator j;

    for (j=c1.begin(); j!=c1.end(); j++) {
        c2[j->second]++;
    }

    map<int, int>::reverse_iterator p;
    int c = 0, res = 0;

    for (p=c2.rbegin(); p!=c2.rend(); p++) {
        //cout << p->first << ' ' << p->second << '\n';
        if (c == 0) {
            res = p->second * p->first;
        } else {
            res = max(res, (p->second + c) * p->first);
        }
        c += p->second;
    }
    cout << n - res << '\n';
}

int main() {
    int nt;
    cin >> nt;

    for (int it=0; it<nt; it++) {
        solve();
    }
}

```