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.math.BigInteger;
import java.util.*;
import java.io.*;



public class Mohsmednsbil2 {

    
    public static void main(String[] args) throws IOException {
        Scanner in=new Scanner(System.in);
        BufferedReader k=new BufferedReader(new InputStreamReader(System.in));
        int test=Integer.parseInt(k.readLine());
        int[]array=new int[test];
        StringTokenizer str=new StringTokenizer(k.readLine());
        for (int i = 0; i < array.length; i++) {
            array[i]=Integer.parseInt(str.nextToken());
        }
        Arrays.sort(array);
        int m=0;
        for (int i = 1; i < array.length; i++) {
            if (array[i]%array[0]!=0) {
                System.out.println("-1");
                m++;
                break;
            }
        }
        if (m==0) {
            System.out.println(array[0]);
        }

    }


}