#include <bits/stdc++.h>
#define rep(i, n) for (int i = 1; i <= (n); ++i)
#define debug(a) cout << #a << " = " << a << endl;
using namespace std;
typedef long long ll;
map<int, int> mp1; 
map<int, int, greater<int>> mp2; 
int main()
{
    int t; cin >> t;
    while (t--) {
        mp1.clear(), mp2.clear();
        
        int n; scanf("%d", &n);
        rep(i, n) {
            int x; scanf("%d", &x);
            mp1[x]++;
        }
        for (auto& [x, y] : mp1) mp2[y]++;
        
        int res = 0x3f3f3f3f; 
        int bin = 0;
        for (auto& [cou, num] : mp2) {
            bin += num;
            int del = n - cou * bin;
            res = min(res, del);
        }
        printf("%d\n", res);
    }
    return 0;
}

### Prompt

Please formulate 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>
#define rep(i, n) for (int i = 1; i <= (n); ++i)
#define debug(a) cout << #a << " = " << a << endl;
using namespace std;
typedef long long ll;
map<int, int> mp1; 
map<int, int, greater<int>> mp2; 
int main()
{
    int t; cin >> t;
    while (t--) {
        mp1.clear(), mp2.clear();
        
        int n; scanf("%d", &n);
        rep(i, n) {
            int x; scanf("%d", &x);
            mp1[x]++;
        }
        for (auto& [x, y] : mp1) mp2[y]++;
        
        int res = 0x3f3f3f3f; 
        int bin = 0;
        for (auto& [cou, num] : mp2) {
            bin += num;
            int del = n - cou * bin;
            res = min(res, del);
        }
        printf("%d\n", res);
    }
    return 0;
}

```