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F. Equalize the Array

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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 $$$t$$$ ($$$1 \le t \le 10^4$$$) — 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

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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