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.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
		    arr[i] = sc.nextInt();
		}
		int[] lefts = new int[n];
		int[] rights = new int[n];
		lefts[1] = arr[0];
		rights[n - 2] = arr[n - 1];
		for (int i = 2; i < n; i++) {
		    lefts[i] = gcd(lefts[i - 1], arr[i - 1]);
		    rights[n - i - 1] = gcd(rights[n - i], arr[n - i]);
		}
		int max = 1;
		for (int i = 1; i < n - 1; i++) {
		    max = Math.max(max, gcd(lefts[i], rights[i]));
		}
		max = Math.max(max, lefts[n - 1]);
		max = Math.max(max, rights[0]);
		System.out.println(max);
   }
   
   static int gcd(int x, int y) {
       if (x % y == 0) {
           return y;
       } else {
           return gcd(y, x % y);
       }
   }
}
