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) throws Exception {
        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[] gcd_left = new int[N];
        int[] gcd_right = new int[N];
        gcd_left[0] = A[0];
        gcd_right[N-1] = A[N-1];
        for(int i = 0; i < N-1; i++){
            gcd_left[i+1] = gcd(gcd_left[i],A[i+1]);
            gcd_right[N-2-i] = gcd(gcd_right[N-1-i],A[N-2-i]);
        }
        
        int max_gcd = 1;
        int tmp_left = 0;
        int tmp_right = 0;
        if(N>2){
            if(max_gcd < gcd_right[1]){
                max_gcd = gcd_right[1];}
            if(max_gcd < gcd_left[N-2]){
                max_gcd = gcd_left[N-2];}
            for(int i = 0; i < N-2; i++){
                tmp_left = gcd_left[i];
                tmp_right = gcd_right[i+2];
                int tmp = gcd(tmp_left,tmp_right);
                if(tmp > max_gcd){
                    max_gcd = tmp;}
            }
        } else{
            max_gcd = Math.max(A[0],A[1]);
        }
        System.out.println(max_gcd);
        
 
    }
    static int gcd (int a, int b) {return b>0?gcd(b,a%b):a;}
}