/*
 * @Author: hesorchen
 * @Date: 2020-11-26 09:12:46
 * @LastEditTime: 2021-02-17 14:39:18
 * @Description: 栽种绝处的花
 */
#include <bits/stdc++.h>
using namespace std;
long long a[200010];
int n;
int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        cin >> n;
        map<long long, long long> mp;
        set<int> st;
        for (int i = 1; i <= n; i++)
        {
            cin >> a[i];
            ++mp[a[i]];
        }

        long long ans = 1000000000000000;
        for (pair<long long, long long> it : mp)
        {
            st.insert(it.second);
        }
        for (long long it : st)
        {
            long long res = 0;
            for (pair<long long, long long> it2 : mp)
            {
                if (it2.second < it)
                    res += it2.second;
                else if (it2.second >= it)
                    res += it2.second - it;
            }
            ans = min(ans, res);
        }
        cout << ans << '\n';
    }

    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
/*
 * @Author: hesorchen
 * @Date: 2020-11-26 09:12:46
 * @LastEditTime: 2021-02-17 14:39:18
 * @Description: 栽种绝处的花
 */
#include <bits/stdc++.h>
using namespace std;
long long a[200010];
int n;
int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        cin >> n;
        map<long long, long long> mp;
        set<int> st;
        for (int i = 1; i <= n; i++)
        {
            cin >> a[i];
            ++mp[a[i]];
        }

        long long ans = 1000000000000000;
        for (pair<long long, long long> it : mp)
        {
            st.insert(it.second);
        }
        for (long long it : st)
        {
            long long res = 0;
            for (pair<long long, long long> it2 : mp)
            {
                if (it2.second < it)
                    res += it2.second;
                else if (it2.second >= it)
                    res += it2.second - it;
            }
            ans = min(ans, res);
        }
        cout << ans << '\n';
    }

    return 0;
}

/*


*/

```