#include<bits/stdc++.h>
using namespace std;
#define fast ios::sync_with_stdio(0);cin.tie(0);
typedef long long int ll;
int main()
{
    fast;
    int t;cin>>t;
    while(t)
    {
       int n;cin>>n;
       map<int,int>mp;int a_m=n;
       for(int i=0;i<n;i++)
       {
           int r;cin>>r;
           mp[r]++;
       }
       int c[n+1];memset(c,0,sizeof(c));
       for(auto i:mp)
       {
           c[i.second]++;
       }
       //for(int i=0;i<n+1;i++)
        //cout<<c[i]<<endl;
       int ld[n+1],rd[n+1];
       memset(ld,0,sizeof(ld));
       memset(rd,0,sizeof(rd));
       for(int i=1;i<=n;i++)
        ld[i]=ld[i-1]+c[i-1]*(i-1);
       int s[n+1];memset(s,0,sizeof(s));
       s[n]=0;
       for(int i=n-1;i>=1;i--)
        s[i]=s[i+1]+c[i+1];
       for(int i=n-1;i>=1;i--)
        rd[i]=rd[i+1]+s[i];
       int am=n;
       for(int i=1;i<=n;i++)
        am=min(am,ld[i]+rd[i]);
       cout<<am<<endl;
       t--;
    }
}

### Prompt

Create a solution in Cpp for 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>
using namespace std;
#define fast ios::sync_with_stdio(0);cin.tie(0);
typedef long long int ll;
int main()
{
    fast;
    int t;cin>>t;
    while(t)
    {
       int n;cin>>n;
       map<int,int>mp;int a_m=n;
       for(int i=0;i<n;i++)
       {
           int r;cin>>r;
           mp[r]++;
       }
       int c[n+1];memset(c,0,sizeof(c));
       for(auto i:mp)
       {
           c[i.second]++;
       }
       //for(int i=0;i<n+1;i++)
        //cout<<c[i]<<endl;
       int ld[n+1],rd[n+1];
       memset(ld,0,sizeof(ld));
       memset(rd,0,sizeof(rd));
       for(int i=1;i<=n;i++)
        ld[i]=ld[i-1]+c[i-1]*(i-1);
       int s[n+1];memset(s,0,sizeof(s));
       s[n]=0;
       for(int i=n-1;i>=1;i--)
        s[i]=s[i+1]+c[i+1];
       for(int i=n-1;i>=1;i--)
        rd[i]=rd[i+1]+s[i];
       int am=n;
       for(int i=1;i<=n;i++)
        am=min(am,ld[i]+rd[i]);
       cout<<am<<endl;
       t--;
    }
}

```