#include <bits/stdc++.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <algorithm>
#include <vector>
#include <map>
#include <cmath>
#include <random>
#include <unordered_map>
#include <set>
#include <queue>
#include <stack>
using namespace std;
#define pb push_back
#define INF 2e15
#define mod 998244353
#define eps 1e-9
#define abs(x) ((x)>=0?(x):-(x))
#define y1 solai
#define fi first
#define se second
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
typedef pair<double,double> pdd;
const ll N=200100;
ll te,n,x,ans,k,s[N],a[N];
map<ll,ll>v;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin>>te;
	for(;te--;)
	{
		cin>>n;
		ans=n;
		v.clear();
		for(ll i=1;i<=n;i++)
			cin>>x,v[x]++;
		k=0;
		for(auto cur:v)
			a[++k]=cur.se;
		sort(a+1,a+k+1);
		for(ll i=1;i<=k;i++)
			s[i]=s[i-1]+a[i];
		for(ll i=1;i<=k;i++)
			ans=min(ans,s[k]-(k-i+1)*a[i]);
		cout<<ans<<"\n";
	}
}
/*
5
LRLDD
*/
### Prompt

Please create a solution in CPP 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
#include <bits/stdc++.h>
#include <iostream>
#include <iomanip>
#include <fstream>
#include <algorithm>
#include <vector>
#include <map>
#include <cmath>
#include <random>
#include <unordered_map>
#include <set>
#include <queue>
#include <stack>
using namespace std;
#define pb push_back
#define INF 2e15
#define mod 998244353
#define eps 1e-9
#define abs(x) ((x)>=0?(x):-(x))
#define y1 solai
#define fi first
#define se second
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
typedef pair<double,double> pdd;
const ll N=200100;
ll te,n,x,ans,k,s[N],a[N];
map<ll,ll>v;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin>>te;
	for(;te--;)
	{
		cin>>n;
		ans=n;
		v.clear();
		for(ll i=1;i<=n;i++)
			cin>>x,v[x]++;
		k=0;
		for(auto cur:v)
			a[++k]=cur.se;
		sort(a+1,a+k+1);
		for(ll i=1;i<=k;i++)
			s[i]=s[i-1]+a[i];
		for(ll i=1;i<=k;i++)
			ans=min(ans,s[k]-(k-i+1)*a[i]);
		cout<<ans<<"\n";
	}
}
/*
5
LRLDD
*/
```