GCD Table

2000ms

262144K

Description:

The GCD table G of size n × n for an array of positive integers a of length n is defined by formula

$\text{[math]}$

Let us remind you that the greatest common divisor (GCD) of two positive integers x and y is the greatest integer that is divisor of both x and y, it is denoted as $\text{[math]}$ . For example, for array a = {4, 3, 6, 2} of length 4 the GCD table will look as follows:

$\text{[math]}$

Given all the numbers of the GCD table G, restore array a.

Input:

The first line contains number n (1 ≤ n ≤ 500) — the length of array a. The second line contains n² space-separated numbers — the elements of the GCD table of G for array a.

All the numbers in the table are positive integers, not exceeding 10⁹. Note that the elements are given in an arbitrary order. It is guaranteed that the set of the input data corresponds to some array a.

Output:

In the single line print n positive integers — the elements of array a. If there are multiple possible solutions, you are allowed to print any of them.

Sample Input:

4
2 1 2 3 4 3 2 6 1 1 2 2 1 2 3 2

Sample Output:

4 3 6 2

Sample Input:

1
42

Sample Output:

Sample Input:

2
1 1 1 1

Sample Output:

1 1

Informação

Provedor Codeforces

Código CF582A