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.Arrays;
import java.util.Comparator;
import java.util.Scanner;


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