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.Scanner;

public class Main {

	public static void main(String[] args) {
		int N = 0;
		Scanner sc = new Scanner(System.in);
		N = Integer.parseInt(sc.next());
		int i;
		long[] A = new long[N];
		long[] ls = new long[N + 1];
		long[] rs = new long[N + 1];

		long max = 0;
		long gcd = 0;
		for (i = 0; i < N; i++) {
			A[i] = Integer.parseInt(sc.next());
		}
		int j;
		for (i = 0; i < N; i++) {
			j = (N - 1) - i;
			ls[i + 1] = gcd(ls[i], A[i]);
			rs[j] = gcd(rs[j + 1], A[j]);
		}
		for (i = 0; i < N; i++) {
			gcd = gcd(ls[i], rs[i + 1]);
			if (max < gcd) {
				max = gcd;
			}
		}
		System.out.println(max);
	}

	private static long gcd(long m, long n) {
		if (m < n)
			return gcd(n, m);
		if (n == 0)
			return m;
		return gcd(n, m % n);
	}

}