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.Scanner;

public class KsushaAndArray {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int[] arr=new int[n];
		for(int i=0;i<n;i++){
			arr[i]=s.nextInt();
		}
		int gcd=findGCD(arr, n);
		for(int i=0;i<n;i++){
			if(gcd==arr[i]){
				System.out.println(arr[i]);
				return;
			}
		}
		System.out.println(-1);
	}
	 static int gcd(int a, int b) 
	    { 
	        if (a == 0) 
	            return b; 
	        return gcd(b % a, a); 
	    } 
	  
	    // Function to find gcd of array of 
	    // numbers 
	    static int findGCD(int arr[], int n) 
	    { 
	        int result = 0; 
	        for (int element: arr){ 
	            result = gcd(result, element); 
	  
	            if(result == 1) 
	            { 
	               return 1; 
	            } 
	        } 
	  
	        return result; 
	    } 

}
