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.io.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Scanner;

public class Main {

	private static final boolean TEST = false;

	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int n = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		System.out.println(solve(a));
		in.close();
	}

	private static int solve(int[] a) {
		int ans = 0;
		int[] l = new int[a.length];
		int[] r = new int[a.length];

		l[0] = a[0];
		for (int i = 1; i < a.length - 1; i++)
			l[i] = gcm(l[i - 1], a[i]);

		r[r.length - 1] = a[a.length - 1];
		for (int i = r.length - 2; i > 0; i--)
			r[i] = gcm(r[i + 1], a[i]);

		ans = Math.max(r[1], l[l.length - 2]);
		for (int i = 1; i < a.length - 1; i++)
			ans = Math.max(ans, gcm(l[i - 1], r[i + 1]));

		return ans;
	}

	private static int gcm(int a, int b) {
		if (a == b)
			return a;
		if (b == 0)
			return a;
		if (a == 0)
			return b;
		if (a > b)
			return gcm(a % b, b);
		else
			return gcm(a, b % a);
	}
}