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) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] A = new int[n];
		int[] left = new int[n];
		int[] right = new int[n];
		for(int i = 0; i < n; i++) {
			A[i] = sc.nextInt();
		}
		int ans = 0;
		left[0] = 0;
		for(int i = 1; i < n; i++) {
			left[i] = gcd(left[i-1], A[i-1]);
		}
		right[n-1] = 0;
		for(int i = n-2; i >= 0; i--) {
			right[i] = gcd(right[i+1], A[i+1]);
		}
		for(int i = 0; i < n; i++) {
			ans = Math.max(ans, gcd(left[i], right[i]));
		}
		//クラスにしないでL、Rをmain内に配列として入れるプランに変更
		
		System.out.println(ans);
		sc.close();
	}
	private static int gcd(int m, int n) {
	    if(m < n) return gcd(n, m);
	    if(n == 0) return m;
	    return gcd(n, m % n);
	}
	
}