Reference: Codeforces 582A — GCD Table

For an array of ~n~ positive integers:

~a_1, a_2, \ldots, a_n~

its GCD table is an ~n \times n~ table defined by:

~G_{i,j} = \gcd(a_i, a_j)~

You are given all ~n^2~ entries of the GCD table in an arbitrary order.

Restore an array that could have produced the given table.

Input

• The first line contains one integer ~n~.
• The second line contains ~n^2~ positive integers: all entries of the GCD table in an arbitrary order.

Output

• Print ~n~ positive integers forming a valid original array.
• If multiple valid arrays exist, print any of them.

Constraints

• ~1 \le n \le 500~
• ~1 \le G_{i,j} \le 10^9~
• It is guaranteed that the input corresponds to at least one valid array.

Example 1

Input:

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

Output:

4 3 6 2