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.*;
import java.io.*;

public class Main
{
  int n, max = 0;
  int[] a, l, r;
  
  Main(Scanner in, PrintWriter out)
  {
    n = in.nextInt();
    a = new int[n];
    l = new int[n+1];
    r = new int[n+1];
    for (int i = 0; i < n; i++)
      a[i] = in.nextInt();
    for (int i = 1; i <= n; i++)
      l[i] = gcd(a[i-1], l[i-1]);
   	for (int i = n-1; i >= 0; i--)
      r[i] = gcd(a[i], r[i+1]);
    for (int i = 0; i < n; i++)
      max = Math.max(max, gcd(l[i], r[i+1]));
    out.println(max);
  }
  
  int gcd(int a, int b)
  {
    return b == 0 ? a : gcd(b, a%b);
  }
  
  public static void main(String[] args)
  {
	Scanner in = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    new Main(in, out);
    out.close();
  }
}
