#include <bits/stdc++.h>
#define ll long long
using namespace std;
int t, n, ma[200010];
ll a[200010];
map <ll, ll> m, flag;
int main(){
	scanf("%d", &t);
	while(t--){
		int maxn = 0;
		scanf("%d", &n);
		for(int i = 1; i <= n; i++){
			scanf("%lld", &a[i]);
			m[a[i]]++;
			if(m[a[i]] > maxn) maxn = m[a[i]];
		}
		
		for(int i = 1; i <= n; i++){
			if(!flag[a[i]]){
				flag[a[i]] = 1;
				ma[m[a[i]]]++;
			}
		}
		ll minn = 1e18, cnt = 0, cnt1 = 0;
		for(int i = maxn; i >= 0; i--){
			minn = min(minn, n - cnt - (ma[i] * i) + (cnt - cnt1 * i));
			cnt += ma[i] * i;
			cnt1 += ma[i];
		}
		for(int i = 1; i <= n; i++){
			ma[m[a[i]]] = 0;
			flag[a[i]] = 0;
			m[a[i]] = 0;
		}
		printf("%lld\n", minn);
	}
	return 0;
}
### Prompt

Please create a solution in CPP 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 ll long long
using namespace std;
int t, n, ma[200010];
ll a[200010];
map <ll, ll> m, flag;
int main(){
	scanf("%d", &t);
	while(t--){
		int maxn = 0;
		scanf("%d", &n);
		for(int i = 1; i <= n; i++){
			scanf("%lld", &a[i]);
			m[a[i]]++;
			if(m[a[i]] > maxn) maxn = m[a[i]];
		}
		
		for(int i = 1; i <= n; i++){
			if(!flag[a[i]]){
				flag[a[i]] = 1;
				ma[m[a[i]]]++;
			}
		}
		ll minn = 1e18, cnt = 0, cnt1 = 0;
		for(int i = maxn; i >= 0; i--){
			minn = min(minn, n - cnt - (ma[i] * i) + (cnt - cnt1 * i));
			cnt += ma[i] * i;
			cnt1 += ma[i];
		}
		for(int i = 1; i <= n; i++){
			ma[m[a[i]]] = 0;
			flag[a[i]] = 0;
			m[a[i]] = 0;
		}
		printf("%lld\n", minn);
	}
	return 0;
}
```