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
#!/usr/bin/env python

N = int(raw_input())
s = [int(si) for si in str(raw_input()).split()]

def gcd(a, b):
	if a < b:
	   a, b = b, a
	if a % b != 0:
		return gcd(b, a % b)
	else:
		return b

r, n = 0, -1

if len(s) > 2:
	r = gcd(s[0], s[1])
else:
	r = s[0]

for si in s:
	r = gcd(r, si)

for si in s:
	if r % si == 0:
		n = si

print n