Bruce is given a multiset ~a~ of ~N~ integers. Bruce defines ~f(x)~ to be the set of factors of ~x~, including ~1~ and ~x~. Bruce would like to know ~f(a_1)~ ~\cap f(a_2)~ ~\cap \ldots ~ ~\cap f(a_N)~. That is, Bruce would like to know the common factors that exists in all elements in ~a~.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~.

The second line will contain ~N~ integers, ~a_1, a_2, \ldots, a_N~ ~(1 \le a_i \le 10^6)~.

Output Specification

Output the factors that are common to all elements in ~a~, one factor per line, in sorted order.

Subtasks

For 5/15 of the points, ~N \le 10~.

Sample Input

4
28 12 8 20

Sample Output

1
2
4