#include <map>
#include <ctime>
#include <stack>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define int long long
using namespace std;
 
inline int read() {
	int x = 0, w = 1;char ch = getchar();
	while (ch > '9' || ch < '0') { if (ch == '-')w = -1;ch = getchar(); }
	while (ch >= '0' && ch <= '9')x = x * 10 + ch - '0', ch = getchar();
	return x * w;
}
inline void write(int x) {
    if (x < 0) putchar('-'), x = -x;
    if (x > 9) write(x / 10);
    putchar(x % 10 + '0');
}
 
const int maxn = 2e5 + 5;
const int mod = 1e9 + 7;
const int inf = 1e9;
 
inline int min(int x, int y) { return x < y ? x : y; }
inline int max(int x, int y) { return x > y ? x : y; }

int t, n, ans, cnt[maxn];

inline int solve() {
    memset(cnt, 0, sizeof(cnt));
    map<int, int> mp; n = read(), ans = 0;
    for (int i = 1, x;i <= n;i++) 
        x = read(), ++mp[x], ++cnt[mp[x]];
    for (int i = 1;i <= n;i++)
        ans = max(ans, i * cnt[i]);
    return n - ans;
}

signed main() { t = read();
    while (t--) printf("%d\n", solve());
    return 0; 
}
### Prompt

In cpp, your task is to solve 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 <map>
#include <ctime>
#include <stack>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define int long long
using namespace std;
 
inline int read() {
	int x = 0, w = 1;char ch = getchar();
	while (ch > '9' || ch < '0') { if (ch == '-')w = -1;ch = getchar(); }
	while (ch >= '0' && ch <= '9')x = x * 10 + ch - '0', ch = getchar();
	return x * w;
}
inline void write(int x) {
    if (x < 0) putchar('-'), x = -x;
    if (x > 9) write(x / 10);
    putchar(x % 10 + '0');
}
 
const int maxn = 2e5 + 5;
const int mod = 1e9 + 7;
const int inf = 1e9;
 
inline int min(int x, int y) { return x < y ? x : y; }
inline int max(int x, int y) { return x > y ? x : y; }

int t, n, ans, cnt[maxn];

inline int solve() {
    memset(cnt, 0, sizeof(cnt));
    map<int, int> mp; n = read(), ans = 0;
    for (int i = 1, x;i <= n;i++) 
        x = read(), ++mp[x], ++cnt[mp[x]];
    for (int i = 1;i <= n;i++)
        ans = max(ans, i * cnt[i]);
    return n - ans;
}

signed main() { t = read();
    while (t--) printf("%d\n", solve());
    return 0; 
}
```