#include<bits/stdc++.h>
using namespace std;
 
#define int long long
#define mod 1000000007
#define pii pair<int,int>
#define pb push_back
#define ff first
#define ss second
#define endl '\n'
#define PI 3.14159265358979323846
 
#define maxn 2000005
 
int32_t main()
{
 
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
 
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        vector<int> a(n);
        map<int,int> freq;
        for(int i=0;i<n;i++){
            cin>>a[i];
            freq[ a[i] ]++;
        }
        vector<pii> b;
        for(auto x: freq){
            b.pb( {x.ss,x.ff} );
        }
        sort(b.begin(),b.end());
        int ans = INT_MAX;
        int sz = b.size();
        for(int i=0;i<b.size();i++){
            ans = min( ans, n-((sz-i)*b[i].first) );
        }
        cout<<ans<<endl;
    }
 
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 int long long
#define mod 1000000007
#define pii pair<int,int>
#define pb push_back
#define ff first
#define ss second
#define endl '\n'
#define PI 3.14159265358979323846
 
#define maxn 2000005
 
int32_t main()
{
 
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
 
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        vector<int> a(n);
        map<int,int> freq;
        for(int i=0;i<n;i++){
            cin>>a[i];
            freq[ a[i] ]++;
        }
        vector<pii> b;
        for(auto x: freq){
            b.pb( {x.ss,x.ff} );
        }
        sort(b.begin(),b.end());
        int ans = INT_MAX;
        int sz = b.size();
        for(int i=0;i<b.size();i++){
            ans = min( ans, n-((sz-i)*b[i].first) );
        }
        cout<<ans<<endl;
    }
 
}
```