#include<bits/stdc++.h>
#define ll long long
#define pb push_back
#define vi vector<ll>
#define s second
#define f first
using namespace std;
const ll mod=1e9+7;
const ll nmod=998244353;
ll check(double p)
{
	for(int i=0;i<5;i++)
	{
		if((ll)p==pow(2,i))
		{
			return 1;
		}
	}
	return 0;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll t;
    cin>>t;
    while(t--)
    {
    	ll n;
    	cin>>n;
    	ll a[n];
    	map<ll,ll> mp;
    	for(int i=0;i<n;i++)
    	{
    		cin>>a[i];
    		mp[a[i]]++;
		}
		map<ll,ll> :: iterator it;
		vi v;
		for(it=mp.begin();it!=mp.end();it++)
		{
			v.pb(it->s);
		}
		sort(v.begin(),v.end());
		ll ans=n;
		ll sum[v.size()];
		sum[0]=v[0];
		for(int i=1;i<v.size();i++)
		{
			sum[i]=(sum[i-1]+v[i]);
		}
		ll m=v.size();
		for(int i=0;i<v.size();i++)
		{
			ll p=n-(m-i)*v[i];
			ans=min(ans,p);
		}
		cout<<ans<<"\n";
	}
    return 0;
}
### 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
#define pb push_back
#define vi vector<ll>
#define s second
#define f first
using namespace std;
const ll mod=1e9+7;
const ll nmod=998244353;
ll check(double p)
{
	for(int i=0;i<5;i++)
	{
		if((ll)p==pow(2,i))
		{
			return 1;
		}
	}
	return 0;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll t;
    cin>>t;
    while(t--)
    {
    	ll n;
    	cin>>n;
    	ll a[n];
    	map<ll,ll> mp;
    	for(int i=0;i<n;i++)
    	{
    		cin>>a[i];
    		mp[a[i]]++;
		}
		map<ll,ll> :: iterator it;
		vi v;
		for(it=mp.begin();it!=mp.end();it++)
		{
			v.pb(it->s);
		}
		sort(v.begin(),v.end());
		ll ans=n;
		ll sum[v.size()];
		sum[0]=v[0];
		for(int i=1;i<v.size();i++)
		{
			sum[i]=(sum[i-1]+v[i]);
		}
		ll m=v.size();
		for(int i=0;i<v.size();i++)
		{
			ll p=n-(m-i)*v[i];
			ans=min(ans,p);
		}
		cout<<ans<<"\n";
	}
    return 0;
}
```