1490F · Equalize the Array

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 Format: 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 $2 \cdot 10^5$.

Output Format: 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.