Strange Beauty

5000ms

262144K

Description:

Polycarp found on the street an array $$$a$$$ of $$$n$$$ elements.

Polycarp invented his criterion for the beauty of an array. He calls an array $$$a$$$ beautiful if at least one of the following conditions must be met for each different pair of indices $$$i \ne j$$$:

$$$a_i$$$ is divisible by $$$a_j$$$;
or $$$a_j$$$ is divisible by $$$a_i$$$.

For example, if:

$$$n=5$$$ and $$$a=[7, 9, 3, 14, 63]$$$, then the $$$a$$$ array is not beautiful (for $$$i=4$$$ and $$$j=2$$$, none of the conditions above is met);
$$$n=3$$$ and $$$a=[2, 14, 42]$$$, then the $$$a$$$ array is beautiful;
$$$n=4$$$ and $$$a=[45, 9, 3, 18]$$$, then the $$$a$$$ array is not beautiful (for $$$i=1$$$ and $$$j=4$$$ none of the conditions above is met);

Ugly arrays upset Polycarp, so he wants to remove some elements from the array $$$a$$$ so that it becomes beautiful. Help Polycarp determine the smallest number of elements to remove to make the array $$$a$$$ beautiful.

Input:

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

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

The second line of each test case contains $$$n$$$ numbers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 2 \cdot 10^5$$$) — elements of the array $$$a$$$.

Output:

For each test case output one integer — the minimum number of elements that must be removed to make the array $$$a$$$ beautiful.

Sample Input:

4
5
7 9 3 14 63
3
2 14 42
4
45 9 3 18
3
2 2 8

Sample Output:

Note:

In the first test case, removing $$$7$$$ and $$$14$$$ will make array $$$a$$$ beautiful.

In the second test case, the array $$$a$$$ is already beautiful.

In the third test case, removing one of the elements $$$45$$$ or $$$18$$$ will make the array $$$a$$$ beautiful.

In the fourth test case, the array $$$a$$$ is beautiful.

Informação

Provedor Codeforces

Código CF1475G