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;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			long[] a = IntStream.range(0, n).mapToLong(i -> scanner.nextLong()).toArray();
			// l[i]=gcd(a_0,..,a_(i-1))
			long[] l = new long[n + 1];
			l[0] = 0L;
			IntStream.rangeClosed(1, n).forEach(i -> l[i] = gcd(l[i - 1], a[i - 1]));
			// r[i]=gcd(a_i,...a_(n-1))
			long[] r = new long[n + 1];
			r[n] = 0L;
			IntStream.rangeClosed(1, n).map(i -> n - i).forEach(i -> r[i] = gcd(r[i + 1], a[i]));
			System.out.println(IntStream.range(0, n).mapToLong(i -> gcd(l[i], r[i + 1])).max().getAsLong());
		}
	}

	/**
	 * mとnの最大公約数を返す
	 * 
	 * @param m
	 * @param n
	 * @return mとnの最大公約数
	 */
	private static long gcd(long m, long n) {
		if (0L == n) {
			return m;
		}
		return gcd(n, m % n);
	}
}
