#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<bool> vb;

#define rep(i, a, n) for (int i = a; i < n; i++)
#define show_vi(a)        \
    cout << #a << "-->";  \
    for (auto x : a)      \
        cout << x << " "; \
    cout << endl;

int mod = (int)1e9 + 7;

void solve()
{
    int n;
    cin >> n;
    vi a(n), count(n+1);

    rep(i, 0, n) cin >> a[i];
    sort(a.begin(), a.end());

    int len=1;
    rep(i, 1, n)
    {
        if(a[i]==a[i-1])
            len++;
        else
        {
            count[len]++;
            len=1;
        }
    }
    count[len]++;

    //show_vi(count);

    int m=0, x=0;
    for(int i=n; i>0; i--)
    {
        m=max(m, i*(count[i]+x));
        x+=count[i];
    }
    
    cout<<n-m<<"\n";
}

int main()
{
    cin.tie(0), cout.tie(0)->sync_with_stdio(0);
    int tc;
    cin >> tc;
    while (tc--)
    {
        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;

typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<bool> vb;

#define rep(i, a, n) for (int i = a; i < n; i++)
#define show_vi(a)        \
    cout << #a << "-->";  \
    for (auto x : a)      \
        cout << x << " "; \
    cout << endl;

int mod = (int)1e9 + 7;

void solve()
{
    int n;
    cin >> n;
    vi a(n), count(n+1);

    rep(i, 0, n) cin >> a[i];
    sort(a.begin(), a.end());

    int len=1;
    rep(i, 1, n)
    {
        if(a[i]==a[i-1])
            len++;
        else
        {
            count[len]++;
            len=1;
        }
    }
    count[len]++;

    //show_vi(count);

    int m=0, x=0;
    for(int i=n; i>0; i--)
    {
        m=max(m, i*(count[i]+x));
        x+=count[i];
    }
    
    cout<<n-m<<"\n";
}

int main()
{
    cin.tie(0), cout.tie(0)->sync_with_stdio(0);
    int tc;
    cin >> tc;
    while (tc--)
    {
        solve();
    }

    return 0;
}
```