/*
    ******** ****** **     ** ****  **       ***   ******** ******
       **    **     ***   *** **  * **     **   **    **    **
       **    ****   ** * * ** ****  **     *******    **    ****
       **    **     **  *  ** **    **     **   **    **    **
       **    ****** **     ** **    ****** **   **    **    ******
*/

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;

const int MOD = 1e9+7;

#define F first
#define S second
#define PB push_back
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()

int t;
int n;
map<int, int> Cnt;

void solve()
{
    Cnt.clear();
    scanf("%d", &n);

    for(int i = 0; i < n; i++)
    {
        int temp;
        scanf("%d", &temp);
        Cnt[temp]++;
    }

    vector<int> C;

    for(auto it = Cnt.begin(); it != Cnt.end(); it++)
    {
        C.PB(it->second);
    }

    sort(all(C));

    int m = C.size();
    int ans = 0;

    for(int i = 0; i < m; i++)
    {
        ans = max(ans, C[i]*(m-i));
    }

    printf("%d\n", n - ans);
}

int main()
{
    //t = 1;
    scanf("%d", &t);
    while(t--)
    {
        solve();
    }
    return 0;
}

/* INPUT



*/

### 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 pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;

const int MOD = 1e9+7;

#define F first
#define S second
#define PB push_back
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()

int t;
int n;
map<int, int> Cnt;

void solve()
{
    Cnt.clear();
    scanf("%d", &n);

    for(int i = 0; i < n; i++)
    {
        int temp;
        scanf("%d", &temp);
        Cnt[temp]++;
    }

    vector<int> C;

    for(auto it = Cnt.begin(); it != Cnt.end(); it++)
    {
        C.PB(it->second);
    }

    sort(all(C));

    int m = C.size();
    int ans = 0;

    for(int i = 0; i < m; i++)
    {
        ans = max(ans, C[i]*(m-i));
    }

    printf("%d\n", n - ans);
}

int main()
{
    //t = 1;
    scanf("%d", &t);
    while(t--)
    {
        solve();
    }
    return 0;
}

/* INPUT



*/

```