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) {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt();
		long[] A = new long[N];
		for (int i = 0; i < A.length; i++) {
			A[i] = in.nextLong();
		}
		long[] left = new long[N + 1];
		long[] right = new long[N + 1];
		for (int i = 0; i < N; i++) {
			left[i + 1] = gcd(left[i], A[i]);
		}
		for (int i = N - 1; i >= 0; --i) {
			right[i] = gcd(right[i + 1], A[i]);
		}
		long ans = 0;
		for (int i = 0; i < N; i++) {
			long l = left[i];
			long r = right[i + 1];
			ans = Math.max(ans, gcd(r, l));
		}
		System.out.println(ans);
		in.close();
	}

	static long gcd(long m, long n) {
		if (m < n) {
			long d = n;
			n = m;
			m = d;
		}
		if (n <= 0) {
			return m;
		}
		long temp;
		while (m % n != 0) {
			temp = n;
			n = m % n;
			m = temp;
		}
		return n;
	}
}