There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Examples

Input

3
7 6 8


Output

2


Input

3
12 15 18


Output

6


Input

2
1000000000 1000000000


Output

1000000000
import java.util.*;

public class Main {
    public static long gcd(long a, long b) {
        while (b != 0) {
            long tmp = b;
            b = a % b;
            a = tmp;
        }

        return a;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int[] nums = new int[n];

        HashMap<Integer, Integer> divs = new HashMap<>();

        for (int i = 0; i < n; i++) {
            nums[i] = sc.nextInt();
        }

        int[] prefixGCD = new int[n - 1];

        prefixGCD[0] = nums[0];

        for (int i = 1; i < n - 1; i++) {
            prefixGCD[i] = (int) gcd(prefixGCD[i - 1], nums[i]);
        }

        int best = prefixGCD[n - 2];
        int runningGCDsuffix = nums[n - 1];

        for (int i = n - 2; i > 0; i--) {
            best = Math.max(best, (int) gcd(runningGCDsuffix, prefixGCD[i - 1]));
            runningGCDsuffix = (int) gcd(runningGCDsuffix, nums[i]);
        }

        best = Math.max(best, runningGCDsuffix);

        System.out.println(best);
    }
}
