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.Scanner;
import java.util.Arrays;

public class KshushaAndArray_299A {
    public static void main(String[] arg) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int arr[] = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }
        Arrays.sort(arr);
        boolean flag = true;
        for (int i = 1; i < n; i++) {
            if (arr[i] % arr[0] != 0) {
                flag = false;
            }
        }
        if (flag == true) {
            System.out.println(arr[0]);
        } else {
            System.out.println(-1);
        }
    }
}