A12580 | Recover it!

Authors guessed an array $a$ consisting of $n$ integers; each integer is not less than $2$ and not greater than $2 \cdot 10^5$ . You don't know the array $a$ , but you know the array $b$ which is formed from it with the following sequence of operations:

1. Firstly, let the array $b$ be equal to the array $a$ ;
2. Secondly, for each $i$ from $1$ to $n$ :
- if $a_i$ is a prime number, then one integer $p_{a_i}$ is appended to array $b$ , where $p$ is an infinite sequence of prime numbers ( $2, 3, 5, \dots$ );
- otherwise (if $a_i$ is not a prime number), the greatest divisor of $a_i$ which is not equal to $a_i$ is appended to $b$ ;
3. Then the obtained array of length $2n$ is shuffled and given to you in the input.

Here $p_{a_i}$ means the $a_i$ -th prime number. The first prime $p_1 = 2$ , the second one is $p_2 = 3$ , and so on.

Your task is to recover any suitable array $a$ that forms the given array $b$ . It is guaranteed that the answer exists (so the array $b$ is obtained from some suitable array $a$ ). If there are multiple answers, you can print any.

The first line of the input contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of elements in $a$ .

The second line of the input contains $2n$ integers $b_1, b_2, \dots, b_{2n}$ ( $2 \le b_i \le 2750131$ ), where $b_i$ is the $i$ -th element of $b$ . $2750131$ is the $199999$ -th prime number.

In the only line of the output print $n$ integers $a_1, a_2, \dots, a_n$ ( $2 \le a_i \le 2 \cdot 10^5$ ) in any order — the array $a$ from which the array $b$ can be obtained using the sequence of moves given in the problem statement. If there are multiple answers, you can print any.