#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int max_n = 200000;
int n, arr[max_n + 5], cnt2[max_n + 5];
ll psum[max_n + 5];

void solve(void);

int main(void) {
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
	int t;
	cin >> t;
	while (t--) solve();
	return 0;
}

void solve(void) {
	cin >> n;
	int i, j;
	for (i = 0; i < n; i++) { cin >> arr[i]; }

	memset(cnt2, 0, (n + 1) * sizeof(int));

	sort(arr, arr + n);
	i = 0;
	while (i < n) {
		j = i;
		while (j < n && arr[j] == arr[i]) j++;
		cnt2[j - i]++;
		i = j;
	}

	psum[0] = 0LL;
	for (i = 1; i <= n; i++) psum[i] = psum[i - 1] + i * cnt2[i];

	ll ans = (ll)n;
	ll tmp = 0LL, tsum = 0LL;
	for (i = n; i > 0; i--) {
		ans = min(ans, tmp + psum[i - 1]);
		// tmp += cnt2[i];
		tsum += cnt2[i];
		tmp += tsum;
	}

	cout << ans << '\n';
}

### 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>

using namespace std;

typedef long long ll;

const int max_n = 200000;
int n, arr[max_n + 5], cnt2[max_n + 5];
ll psum[max_n + 5];

void solve(void);

int main(void) {
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
	int t;
	cin >> t;
	while (t--) solve();
	return 0;
}

void solve(void) {
	cin >> n;
	int i, j;
	for (i = 0; i < n; i++) { cin >> arr[i]; }

	memset(cnt2, 0, (n + 1) * sizeof(int));

	sort(arr, arr + n);
	i = 0;
	while (i < n) {
		j = i;
		while (j < n && arr[j] == arr[i]) j++;
		cnt2[j - i]++;
		i = j;
	}

	psum[0] = 0LL;
	for (i = 1; i <= n; i++) psum[i] = psum[i - 1] + i * cnt2[i];

	ll ans = (ll)n;
	ll tmp = 0LL, tsum = 0LL;
	for (i = n; i > 0; i--) {
		ans = min(ans, tmp + psum[i - 1]);
		// tmp += cnt2[i];
		tsum += cnt2[i];
		tmp += tsum;
	}

	cout << ans << '\n';
}

```