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{
  static int gcd (int a, int b) {return b>0?gcd(b,a%b):a;}

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] array = new int[n];

    for(int i=0; i<n; i++){
      array[i] = sc.nextInt();
    }

    int ans =0;
    int max_ans = 0;
    int pp;
    int ss;

    int[] l_gcd = new int[n];
    l_gcd[0] = array[0];
    for(int i=1; i<n-1; i++){
      l_gcd[i] = gcd(l_gcd[i-1],array[i]);
    }

    int[] r_gcd = new int[n];
    r_gcd[n-1] = array[n-1];

    for(int i=n-2; i>0; i--){
      r_gcd[i] = gcd(r_gcd[i+1],array[i]);
    }

    if(r_gcd[1]>max_ans){
      max_ans = r_gcd[1];
    }
    for(int i=0; i<n-2; i++){
      ans = gcd(l_gcd[i],r_gcd[i+2]);
      if(ans>max_ans){
        max_ans = ans;
      }
    }
    if(l_gcd[n-2]>max_ans){
      max_ans = l_gcd[n-2];
    }
    System.out.println(max_ans);






  }
}