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

//   A. Ksusha and Array

//   http://codeforces.com/problemset/problem/299/A

import java.util.Arrays;
import java.util.Scanner;

public class A25 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int array[] = new int[n];

		for (int i = 0; i < n; i++) {
			array[i] = sc.nextInt();
		}

		Arrays.sort(array);
		int x = 0;
		for (int i = 0; i < n; i++) {
			if(array[i]%array[0]!=0) {
				x++;
				break;
			}
		}
		if(x==0)
		System.out.println(array[0]);
		else
			System.out.println(-1);
	}
}