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 codeforces229a {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int size = sc.nextInt();
		int arr[] = new int[size];
		int i;
		
		for(i = 0;i<size;i++) arr[i] = sc.nextInt();
		Arrays.sort(arr);
		for(i =0;i<size;i++) {
			if(arr[i]%arr[0]!=0) {
				System.out.println("-1");
				break;
			}
		}
		if(i==size) {
			System.out.println(arr[0]);
		}
//		for(i = 0;i<size;i++) {
//			if(arr[i]==1) {
//				System.out.println("1");break;
//			}
//			for(j = 0;j<size;j++) {
//				if(arr[j]%arr[i]!=0) {
//					break;
//				}
//			}
//			if(j==size) {
//				System.out.println(arr[i]);
//				break;
//			}
//			
//		}
//		if(i==size) {
//			System.out.println("-1");
//		}
				
	}
}