#include<bits/stdc++.h>
#define ll long long int
#define nl "\n"
#define vec vector<ll>
#define pb push_back
#define MOD 1000000007
#define test ll testc;cin>>testc;while(testc--)
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL);
using namespace std;
int main()
{
	test
	{
		ll n; cin>>n;
		ll a[n];
		for(int i=0;i<n;i++) cin>>a[i];
		sort(a,a+n);
		map <ll,ll> m;
		ll cn=1;
		for (int i=1;i<n;i++)
		{
			if (a[i]==a[i-1]) cn++;
			else
			{
				m[cn]++;
				cn=1;
			}
		}
		m[cn]++;
		map <ll,ll> :: iterator it;
		ll ans=1e18;
		for (it=m.begin();it!=m.end();it++)
		{
			map <ll,ll> ::iterator tt;
			ll z= (*it).first;
			ll x=0;
			for (tt=m.begin();tt!=m.end();tt++)
			{
				ll k=(*tt).first;
				if (k>=z)
				{
					x+=(k-z)*((*tt).second);
				}
				else
				x+=k*((*tt).second);
			}
			ans=min(ans,x);
		}
		cout<<ans<<nl;
	}
}

### 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>
#define ll long long int
#define nl "\n"
#define vec vector<ll>
#define pb push_back
#define MOD 1000000007
#define test ll testc;cin>>testc;while(testc--)
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL);
using namespace std;
int main()
{
	test
	{
		ll n; cin>>n;
		ll a[n];
		for(int i=0;i<n;i++) cin>>a[i];
		sort(a,a+n);
		map <ll,ll> m;
		ll cn=1;
		for (int i=1;i<n;i++)
		{
			if (a[i]==a[i-1]) cn++;
			else
			{
				m[cn]++;
				cn=1;
			}
		}
		m[cn]++;
		map <ll,ll> :: iterator it;
		ll ans=1e18;
		for (it=m.begin();it!=m.end();it++)
		{
			map <ll,ll> ::iterator tt;
			ll z= (*it).first;
			ll x=0;
			for (tt=m.begin();tt!=m.end();tt++)
			{
				ll k=(*tt).first;
				if (k>=z)
				{
					x+=(k-z)*((*tt).second);
				}
				else
				x+=k*((*tt).second);
			}
			ans=min(ans,x);
		}
		cout<<ans<<nl;
	}
}

```