A13982 | Strange Beauty

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.

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 $a$ .

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