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.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
 
public class Main{
 
    public static Scanner input = new Scanner(System.in);
    public static void main(String[] args)
            throws IOException {
    
       
   //  BufferedReader buffer=new BufferedReader(new InputStreamReader(System.in));
   //  String str;
    //  while((str=buffer.readLine())!=null){
      
    int n=input.nextInt();
    int []a=new int[n];
   
    for(int i=0;i<n;i++){
        a[i]=input.nextInt();
        
    }
    Arrays.sort(a);
    for(int i=0;i<a.length;i++){
        if(a[i]%a[0]!=0)
        {
            System.out.println("-1");
            return;
        }
    }
        System.out.println(a[0]);
    }
}