#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int sz = 3e5+5;

int a[sz];

void solve() {
   int n;
   scanf("%d", &n);
   map <int,int> mp;
   for(int i=0; i<n; i++) {
      int x;
      scanf("%d", &x);
      mp[x]++;
   }
   int ans = n, z = mp.size(), cut = 0;
   vector <int> ara;
   for(auto it : mp) ara.push_back(it.second);
   sort(ara.begin(), ara.end());
   for(int x : ara) {
      int now = cut + (n - cut) - z * x;
      ans = min(ans, now);
      z--;
      cut += x;
   }
   printf("%d\n", ans);
}

int main() {
   int t;
   cin >> t;
   while(t--) solve();
}

### 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;
typedef long long ll;
const int sz = 3e5+5;

int a[sz];

void solve() {
   int n;
   scanf("%d", &n);
   map <int,int> mp;
   for(int i=0; i<n; i++) {
      int x;
      scanf("%d", &x);
      mp[x]++;
   }
   int ans = n, z = mp.size(), cut = 0;
   vector <int> ara;
   for(auto it : mp) ara.push_back(it.second);
   sort(ara.begin(), ara.end());
   for(int x : ara) {
      int now = cut + (n - cut) - z * x;
      ans = min(ans, now);
      z--;
      cut += x;
   }
   printf("%d\n", ans);
}

int main() {
   int t;
   cin >> t;
   while(t--) solve();
}

```