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[] a = new int[n];
      for(int i = 0;i < n;i++)a[i]=sc.nextInt();
      int[] l = new int[n+1];
      int[] r = new int[n+1];
      int[] m = new int[n+1];
      int max = 0;
      l[0]=0;
      r[n]=0;
      for(int i = 0;i < n;i++)l[i+1]=gcd(l[i],a[i]);
      for(int i = n-1;i >= 0;i--)r[i]=gcd(r[i+1],a[i]);
      for(int i = 1;i <= n;i++){
        m[i]=gcd(l[i-1],r[i]);
        max = Math.max(m[i],max);
      }
      System.out.println(max);
    }
    public static int lcm(int x, int y){
      return x*y/gcd(x,y);
    }
    public static int gcd(int x, int y){
      if(x < y)return gcd(y,x);
      if(y==0)return x;
      return gcd(y,x%y);
    }
}