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.*;
import java.io.*;

public class King{
	public static void main(String[] args) throws Exception{
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		boolean yes = true;
		long[] ar = new long[n];
		for (int i=0;i<n;i++) {
			ar[i] = in.nextLong();
		}
		Arrays.sort(ar);
		long num = ar[0];

		for (int j=1;j<n;j++) {
			if (ar[j] % num != 0) {
				yes = false;
				break;
			}
		}

		if(yes){
			System.out.println(num);//
		}
		else {
			System.out.println(-1);
		}



		

		
		// System.out.println(Arrays.toString(ar));	

		
		

	}
}