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 sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		long[] a = new long[n];
		
		long[] start = new long[n];
		long[] end = new long[n];
		
		for(int i = 0; i < n; i++)a[i] = sc.nextLong();

		long res = 0;
		start[0] = 0;
		
		for(int i = 1; i < n; i++) {
			start[i] = gcd(start[i-1],a[i-1]);
		}
		
		end[n-1] = 0;
		
		for(int i = n-2; i >= 0; i--) {
			end[i] = gcd(end[i+1],a[i+1]);
		}
		
		
		for(int i = 0; i < n; i++) {
			res=Math.max(res, gcd(start[i],end[i]));
		}
		System.out.println(res);
		
	}
	
	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);
	}
}