#include <bits/stdc++.h>

using namespace std;


using ll = int;
using ld = long double;
using pl = pair<ll, ll>;
const ll INF = 1e9 + 7;
const ld eps = 1e-9;
const ld PI = acos(-1);

void solve(){
    ll n;
    cin >> n;
    vector<ll> a(n);
    for(ll &i : a){
        cin >> i;
    }
    sort(a.begin(),a.end());
    ll l=0;
    vector<ll> cnt(n + 1);
    unordered_set<ll> nums;
    while(l < n){
        ll r = upper_bound(a.begin(),a.end(),a[l]) - a.begin();
        cnt[(r-l)]++;
        nums.insert(r-l);
        l = r;
    }
    vector<pl> z;
    for(auto nn : nums){
        z.push_back({nn,cnt[nn]});
    }
    ll ans = INF;
    for(ll i=0;i<z.size();i++){
        ll cnt=0;
        for(ll j=0;j<z.size();j++){
            if(z[j].first < z[i].first)cnt+=z[j].second*z[j].first;
            else cnt+=(z[j].first - z[i].first)*z[j].second;
        }
        ans = min(cnt,ans);
    }
    cout << ans << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    ll t;
    cin >> t;
    while(t--)solve();
    return 0;
}
### 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;


using ll = int;
using ld = long double;
using pl = pair<ll, ll>;
const ll INF = 1e9 + 7;
const ld eps = 1e-9;
const ld PI = acos(-1);

void solve(){
    ll n;
    cin >> n;
    vector<ll> a(n);
    for(ll &i : a){
        cin >> i;
    }
    sort(a.begin(),a.end());
    ll l=0;
    vector<ll> cnt(n + 1);
    unordered_set<ll> nums;
    while(l < n){
        ll r = upper_bound(a.begin(),a.end(),a[l]) - a.begin();
        cnt[(r-l)]++;
        nums.insert(r-l);
        l = r;
    }
    vector<pl> z;
    for(auto nn : nums){
        z.push_back({nn,cnt[nn]});
    }
    ll ans = INF;
    for(ll i=0;i<z.size();i++){
        ll cnt=0;
        for(ll j=0;j<z.size();j++){
            if(z[j].first < z[i].first)cnt+=z[j].second*z[j].first;
            else cnt+=(z[j].first - z[i].first)*z[j].second;
        }
        ans = min(cnt,ans);
    }
    cout << ans << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    ll t;
    cin >> t;
    while(t--)solve();
    return 0;
}
```