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.io.PrintWriter;
import java.util.Scanner;

public class Solution {
    final static int N = 100 * 1000 + 13;
    static int[] a = new int[N];

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        for (int i = 0; i < n; i++)
            a[i] = in.nextInt();

        int minVal = a[0];
        for (int i = 1; i < n; i++)
            if (minVal > a[i])
                minVal = a[i];

        boolean isGoodAnswer = true;
        for (int i = 0; i < n; i++)
            if (a[i] % minVal != 0) {
                isGoodAnswer = false;
                break;
            }

        if (isGoodAnswer)
            out.println(minVal);
        else
            out.println("-1");

        in.close();
        out.close();
    }
}
