#include <bits/stdc++.h>
#define int long long

using namespace std;


void solve() {
    map <int, int> cnt;

    int n;
    cin >> n;
    for (int i = 0; i < n; i++) {
        int x;
        cin >> x;
        cnt[x]++;
    }

    map <int, int> mp;
    for (auto [x, cn] : cnt) {
        mp[cn]++;
        mp[cn + 1] = mp[cn + 1];
    }

    int lower = 0, now = 0, total = 0;

    for (auto [lo, cnt] : mp) {
        now += lo * cnt;
        total += cnt;
    }

    int ans = now;
    int last = 0;
    for (auto [lo, cnt] : mp) {
        now -= (total - lower) * (lo - last);
        now += mp[lo - 1] * (lo - 1);
        ans = min(ans, now);
        lower += cnt;
        last = lo;
    }
    cout << ans << endl;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int q;
    cin >> q;
    while (q--)
        solve();
    return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#define int long long

using namespace std;


void solve() {
    map <int, int> cnt;

    int n;
    cin >> n;
    for (int i = 0; i < n; i++) {
        int x;
        cin >> x;
        cnt[x]++;
    }

    map <int, int> mp;
    for (auto [x, cn] : cnt) {
        mp[cn]++;
        mp[cn + 1] = mp[cn + 1];
    }

    int lower = 0, now = 0, total = 0;

    for (auto [lo, cnt] : mp) {
        now += lo * cnt;
        total += cnt;
    }

    int ans = now;
    int last = 0;
    for (auto [lo, cnt] : mp) {
        now -= (total - lower) * (lo - last);
        now += mp[lo - 1] * (lo - 1);
        ans = min(ans, now);
        lower += cnt;
        last = lo;
    }
    cout << ans << endl;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int q;
    cin >> q;
    while (q--)
        solve();
    return 0;
}

```