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.*;
public class cf299a {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    int[] v = new int[n];
    for(int i=0; i<n; i++)
      v[i] = in.nextInt();
    int ans = v[0];
    for(int i=1; i<n; i++)
      ans = gcd(ans,v[i]);
    for(int i=0; i<n; i++) {
      if(ans%v[i] == 0) {
        System.out.println(v[i]);
        return;
      }
    }
    System.out.println(-1);
  }
  static int gcd(int a, int b) {
    return b==0?a:gcd(b,a%b);
  }
}
