A9999 | GCD Table

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

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 . For example, for array $a={4,3,6,2}$ of length 4 the GCD table will look as follows:

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

The first line contains number $n$ ( $1<=n<=500$ ) — the length of array $a$ . The second line contains $n^{2}$ 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 $10^{9}$ . Note that the elements are given in an arbitrary order. It is guaranteed that the set of the input data corresponds to some array $a$ .

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.