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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

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