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
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class foijfoiafjdsoa {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		sc.nextLine();
		ArrayList<String> bruh = new ArrayList<String>(Arrays.asList(sc.nextLine().split(" ")));
		ArrayList<Integer> bruh2 = new ArrayList<>();
		for(int i = 0; i < bruh.size(); i++) {
			bruh2.add(Integer.parseInt(bruh.get(i)));
		}
		sc.close();
		int x = Collections.min(bruh2);
		for(int cur : bruh2) {
			if(cur % x != 0) {
				System.out.println(-1);
				return;
			}
		}
		System.out.println(x);
	}
}
