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.*;

class Main{

    static int gcd(int x, int y){
        if( x < y ){
            int t = x;
            x = y;
            y = t;
        }
        if(y == 0) return x;
        return gcd(x % y, y);
    }
    public static void main(String[] args) {       
    Scanner stdIn = new Scanner(System.in);
    int n = stdIn.nextInt();
    int a[] = new int [n];
    Arrays.setAll(a, i -> stdIn.nextInt());
    int l[] = new int [n];
    int r[] = new int [n];
    int ans = 1;
    for(int i = 1 ; i < n; i++) l[i] = gcd(l[i-1], a[i-1]);
    for(int i = n - 2; i >= 0; i--) r[i] = gcd(r[i+1], a[i+1]);

    for(int i = 0; i < n; i++) ans = Math.max(ans, gcd(l[i], r[i]));
    System.out.println(ans);
   }
}
