#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <string>
#include <iostream>
#include <map>
#include <set>
#include <vector>
#include <math.h>
#include <queue>
#include <bitset>
#include <unordered_map>
#include <complex>
using namespace std;
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int long long
#define double long double
#define sqr(x) (x)*(x)
#define pb push_back
typedef int C;
typedef complex<C>P;
#define X real()
#define Y imag()
int32_t main()
{
	IOS;
	int t;
	cin >> t;
	while (t--) {
		int n;
		cin >> n;
		vector<int>a(n);
		unordered_map<int, int>m;
		m.max_load_factor(0.25);
		for (int i = 0; i < n; i++) {
			cin >> a[i];
			m[a[i]]++;
		}
		map<int, int>res;
		for (auto&c : m) {
			res[c.second]++;
		}
		int ans = 1e18;
		int add = 0;
		int i = 1;
		int cc = m.size();
		for (auto&c : res) {
			ans = min(ans, n-cc*c.first);
			//add += c.second*c.first;
			cc -= c.second;
		}
		cout << ans << "\n";
	}
}
### Prompt

Your challenge is to write 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
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <string>
#include <iostream>
#include <map>
#include <set>
#include <vector>
#include <math.h>
#include <queue>
#include <bitset>
#include <unordered_map>
#include <complex>
using namespace std;
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int long long
#define double long double
#define sqr(x) (x)*(x)
#define pb push_back
typedef int C;
typedef complex<C>P;
#define X real()
#define Y imag()
int32_t main()
{
	IOS;
	int t;
	cin >> t;
	while (t--) {
		int n;
		cin >> n;
		vector<int>a(n);
		unordered_map<int, int>m;
		m.max_load_factor(0.25);
		for (int i = 0; i < n; i++) {
			cin >> a[i];
			m[a[i]]++;
		}
		map<int, int>res;
		for (auto&c : m) {
			res[c.second]++;
		}
		int ans = 1e18;
		int add = 0;
		int i = 1;
		int cc = m.size();
		for (auto&c : res) {
			ans = min(ans, n-cc*c.first);
			//add += c.second*c.first;
			cc -= c.second;
		}
		cout << ans << "\n";
	}
}
```