#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pi pair<int,int>
#define pl pair<ll,ll>
#define pd pair<double,double>
#define F first
#define S second
#define pb push_back
#define all(v) v.begin(),v.end()
#define mod 1000000007

int main(){
    //cout<<ceil((double)log2(3));
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        int a[n];
        map<int,int>m;
        for(int i=0;i<n;i++){
            cin>>a[i];
            m[a[i]]++;
        }
        map<int,int>im;
        for(auto x:m){
            im[x.S]++;
        }
        vector<pi>v;
        for(auto x:im){
            v.pb({x.F,x.S});
        }
        int ans=INT_MAX;
        int p=v.size();
        assert(p<=1000);
        for(int i=0;i<p;i++){
            int s=0;
            for(int j=0;j<p;j++){
                if(v[j]>=v[i]){
                    s+=abs(v[j].F-v[i].F)*v[j].S;
                }
                else{
                    s+=v[j].F*v[j].S;
                }
            }
            ans=min(ans,s);
        }
        cout<<ans<<endl;

    }

}

### Prompt

Develop a solution in CPP 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;
#define ll long long
#define pi pair<int,int>
#define pl pair<ll,ll>
#define pd pair<double,double>
#define F first
#define S second
#define pb push_back
#define all(v) v.begin(),v.end()
#define mod 1000000007

int main(){
    //cout<<ceil((double)log2(3));
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        int a[n];
        map<int,int>m;
        for(int i=0;i<n;i++){
            cin>>a[i];
            m[a[i]]++;
        }
        map<int,int>im;
        for(auto x:m){
            im[x.S]++;
        }
        vector<pi>v;
        for(auto x:im){
            v.pb({x.F,x.S});
        }
        int ans=INT_MAX;
        int p=v.size();
        assert(p<=1000);
        for(int i=0;i<p;i++){
            int s=0;
            for(int j=0;j<p;j++){
                if(v[j]>=v[i]){
                    s+=abs(v[j].F-v[i].F)*v[j].S;
                }
                else{
                    s+=v[j].F*v[j].S;
                }
            }
            ans=min(ans,s);
        }
        cout<<ans<<endl;

    }

}

```