A14118 | 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.

The first line contains one integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The first line of each test case consists of one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of the array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ) — array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

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.