#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
#define MAX 110000
#define FOR(i, a, b) for (int i = a; i < (b); i++)
#define range(a) a.begin(), a.end()
#define endl "\n"
#define Yes() cout << "Yes" << endl
#define No() cout << "No" << endl
#define MP make_pair
using P = pair<ll, int>;
const unsigned long long mod = 1e9 + 7;
const long long INF = 1LL<<60;
void chmin(long long &a, long long b) { if (a > b) a = b; }
void chmax(long long &a, long long b) { if (a < b) a = b; }


void solve(){
	int size;
    cin >> size;
	map<ll, int> mp;
	FOR(i,0,size){
		int a;
		cin >> a;
		mp[a]++;
	}
	vector<ll> a;
	int sum = 0;
	for(auto itr = mp.begin(); itr != mp.end(); ++itr) {
		a.push_back(itr->second);
		sum += itr->second;
	}
	sort(range(a));
	int asize = a.size();
	ll ans = 0;
	FOR(i, 0, a.size()){
		ans = max(ans, a.at(i) * asize);
		--asize;
	}
	cout << sum - ans << endl;
}

int main(void){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int T;
	cin >> T;
	while(T--){
		solve();
	}

	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
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
#define MAX 110000
#define FOR(i, a, b) for (int i = a; i < (b); i++)
#define range(a) a.begin(), a.end()
#define endl "\n"
#define Yes() cout << "Yes" << endl
#define No() cout << "No" << endl
#define MP make_pair
using P = pair<ll, int>;
const unsigned long long mod = 1e9 + 7;
const long long INF = 1LL<<60;
void chmin(long long &a, long long b) { if (a > b) a = b; }
void chmax(long long &a, long long b) { if (a < b) a = b; }


void solve(){
	int size;
    cin >> size;
	map<ll, int> mp;
	FOR(i,0,size){
		int a;
		cin >> a;
		mp[a]++;
	}
	vector<ll> a;
	int sum = 0;
	for(auto itr = mp.begin(); itr != mp.end(); ++itr) {
		a.push_back(itr->second);
		sum += itr->second;
	}
	sort(range(a));
	int asize = a.size();
	ll ans = 0;
	FOR(i, 0, a.size()){
		ans = max(ans, a.at(i) * asize);
		--asize;
	}
	cout << sum - ans << endl;
}

int main(void){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int T;
	cin >> T;
	while(T--){
		solve();
	}

	return 0;
}


```