1490_F. Equalize the Array
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
```python
def find():
    n = int(input())
    mas = tuple(map(int, input().split()))

    count_numbers = {}
    for j in mas:
        count_numbers[j] = count_numbers.get(j, 0) + 1

    count_set_numb = {}
    for j in count_numbers:
        count_set_numb[count_numbers[j]] = count_set_numb.get(count_numbers[j], 0) + 1

    res = n
    last = 0
    all_next = n
    uniq_next = len(count_numbers)
    for j in sorted(count_set_numb):
        res = min(res, last + all_next - uniq_next * j)
        last += j * count_set_numb[j]
        all_next -= j * count_set_numb[j]
        uniq_next -= count_set_numb[j]
       
    print(res)


for i in range(int(input())):
    find()

```