Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Ksusha and Array

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKsusha is a beginner coder. Today she starts studying arrays. She has array *a* _{1}, *a* _{2}, ..., *a* _{ n}, consisting of *n* positive integers.

Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number!

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}), showing how many numbers the array has. The next line contains integers *a* _{1}, *a* _{2}, ..., *a* _{ n} (1 ≤ *a* _{ i} ≤ 10^{9}) — the array elements.

Output

Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn't exist, print -1.

If there are multiple answers, you are allowed to print any of them.

Examples

Input

3

2 2 4

Output

2

Input

5

2 1 3 1 6

Output

1

Input

3

2 3 5

Output

-1

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/09/2020 12:23:27 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|