Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., 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 ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, ..., a**n (1 ≤ a**i ≤ 109) — 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.

Samples

3
2 2 4

2

5
2 1 3 1 6

1

3
2 3 5

-1