#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define mp make_pair
#define f first
#define s second
#define mod 1000000007
#define vll vector<ll>
#define pll vector<pair<ll,ll>>

ll gr[200001];
 ll pref[200001];


int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll t;
	t=1;
	cin>>t;
	start:
	while(t--){

	    ll n;
        cin>>n;

        ll arr[n+1];
        map<ll,ll> ct;
        for(ll i=1;i<=n;i++){
            cin>>arr[i];
            ct[arr[i]]++;
        }

        memset(gr,0,sizeof gr);
        memset(pref,0,sizeof pref);
        set<ll> st;

        for(auto i:ct){
            gr[i.s]++;
            st.insert(i.s);
        }

        ll pr=0;
        for(auto i=st.rbegin();i!=st.rend();i++){
                pr+=gr[*i];
            pref[*i]=pr;
        }

        ll mn=1e8;

        for(ll i=0;i<=*st.rbegin();i++){
              ll val=i*pref[i];
              mn=min(mn,n-val);
        }

        cout<<mn<<endl;






	}
	return 0;
}

### 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 pb push_back
#define mp make_pair
#define f first
#define s second
#define mod 1000000007
#define vll vector<ll>
#define pll vector<pair<ll,ll>>

ll gr[200001];
 ll pref[200001];


int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll t;
	t=1;
	cin>>t;
	start:
	while(t--){

	    ll n;
        cin>>n;

        ll arr[n+1];
        map<ll,ll> ct;
        for(ll i=1;i<=n;i++){
            cin>>arr[i];
            ct[arr[i]]++;
        }

        memset(gr,0,sizeof gr);
        memset(pref,0,sizeof pref);
        set<ll> st;

        for(auto i:ct){
            gr[i.s]++;
            st.insert(i.s);
        }

        ll pr=0;
        for(auto i=st.rbegin();i!=st.rend();i++){
                pr+=gr[*i];
            pref[*i]=pr;
        }

        ll mn=1e8;

        for(ll i=0;i<=*st.rbegin();i++){
              ll val=i*pref[i];
              mn=min(mn,n-val);
        }

        cout<<mn<<endl;






	}
	return 0;
}

```