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.*;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class A
{
	public static void main(String [] args) throws IOException
	{
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));
		int n = Integer.parseInt(reader.readLine());

		int [] numbers = new int[n];
		StringTokenizer tokenizer = new StringTokenizer(reader.readLine().trim());
		for(int i = 0 ; i < n ; i++)
			numbers[i] = Integer.parseInt(tokenizer.nextToken());

		Arrays.sort(numbers);

		int res = numbers[0];
		for(int i = 0 ; i < n ; i++)
			if(numbers[i]%res != 0)
			{
				res = -1;
				break;
			}

		writer.println(res);
		writer.flush();
		writer.close();

	}
}
