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 javafx.collections.ObservableArray;
import javafx.collections.ObservableList;
import javafx.collections.transformation.SortedList;

import java.io.*;
import java.util.*;

public class Task229A {
    private static InputStreamReader INPUT = new InputStreamReader(System.in);
    private static InputStreamReader INPUT_FILE = null;

    static {
        try {
            INPUT_FILE = new FileReader("input.txt");
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    private static int[] getArrayOfIntegers(String line) {
        String[] nn = line.split(" ");
        int[] nnint = new int[nn.length];
        for (int i = 0; i < nnint.length; i++)
            nnint[i] = Integer.parseInt(nn[i]);
        return nnint;
    }

    private static List<Integer> getListOfIntegers(String line) {
        List<Integer> nn = new LinkedList<>();
        String[] ss = line.split(" ");
        int[] nnint = new int[ss.length];
        for (int i = 0; i < ss.length; i++)
            nn.add(Integer.parseInt(ss[i]));
        return nn;
    }

    public static void main(String[] args) {
        try (BufferedReader BR = new BufferedReader(INPUT)) {
            int n = getArrayOfIntegers(BR.readLine())[0];
            int[] array = getArrayOfIntegers(BR.readLine());
            System.out.println(getResult(array));
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    private static int getResult(int[] array) {
        int min = getMin(array);
        for (int i = 0; i < array.length; i++)
            if (array[i] % min != 0)
                return -1;
        return min;
    }

    private static int getMin(int[] array) {
        int min = array[0];
        for (int i = 1; i < array.length; i++) {
            if (array[i] < min)
                min = array[i];
        }
        return min;
    }
}
