#include<bits/stdc++.h>
using namespace std;
long long q,n,c[400005],z,ans,mn=1e14,d,x;
map<long long,long long>las,ll;
vector<long long>v;
struct am{
long long va,ind;
};
am a[400005];
bool cmp(am zz,am y){
return zz.ind<y.ind;
}
set<long long>st;
int main(){
ios::sync_with_stdio(NULL);
cin.tie(0);
cout.tie(0);
cin>>q;

while (q--){
cin>>n;
st.clear();
v.clear();
las.clear();
ll.clear();
mn=1e14;
for (long long i=1;i<=n;i++){
    cin>>x;
    las[x]++;
}
z=1;
for (auto it=las.begin();it!=las.end();it++){
a[z].va=it->first;
a[z].ind=it->second;
z++;
}

sort (a+1,a+z,cmp);
for (long long i=z-1;i>=1;i--){
        x=st.size();
    mn=min(mn,n-(a[i].ind + a[i].ind*x));
st.insert(a[i].va);
}


cout<<mn<<"\n";
}


}

### Prompt

Your challenge is to write a cpp solution 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>
using namespace std;
long long q,n,c[400005],z,ans,mn=1e14,d,x;
map<long long,long long>las,ll;
vector<long long>v;
struct am{
long long va,ind;
};
am a[400005];
bool cmp(am zz,am y){
return zz.ind<y.ind;
}
set<long long>st;
int main(){
ios::sync_with_stdio(NULL);
cin.tie(0);
cout.tie(0);
cin>>q;

while (q--){
cin>>n;
st.clear();
v.clear();
las.clear();
ll.clear();
mn=1e14;
for (long long i=1;i<=n;i++){
    cin>>x;
    las[x]++;
}
z=1;
for (auto it=las.begin();it!=las.end();it++){
a[z].va=it->first;
a[z].ind=it->second;
z++;
}

sort (a+1,a+z,cmp);
for (long long i=z-1;i>=1;i--){
        x=st.size();
    mn=min(mn,n-(a[i].ind + a[i].ind*x));
st.insert(a[i].va);
}


cout<<mn<<"\n";
}


}

```