Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, ..., an, 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, ..., an (1 ≤ ai ≤ 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.

Examples

Input

3
2 2 4


Output

2


Input

5
2 1 3 1 6


Output

1


Input

3
2 3 5


Output

-1
def gcd(a, b):
    """Return greatest common divisor using Euclid's Algorithm."""
    while b:      
        a, b = b, a % b
    return a


def main():
    n = input()
    nums = map(int, raw_input().split())
    numbers = nums[:]
    nums1 = nums[:]
    while len(nums)!=1:
        nums = nums1[:]
        nums1 = []
        for i in xrange(len(nums)/2):
            nums1.append(gcd(nums[2*i],nums[(2*i)+1]))
        if len(nums)&1:
            nums1.append(nums[-1])
    if nums[0] in numbers:
        print nums[0]
    else:
        print -1
main()
