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 N = 100000;
    static int[] L = new int[N+1];
    static int[] R = new int[N+1];
    static int num;
    static int[] nums = new int[N+1];

    static int left(int i){
        if(L[i] != -1)return L[i];
        if(i == 0){
            L[i] = 0;
            return 0;
        }
        L[i] = gcd(nums[i-1], left(i-1));
        return L[i];
    }
    static int right(int i){
        if(R[i] != -1)return R[i];
        if(i == num-1){
            R[i] = 0;
            return 0;
        }
        R[i] = gcd(nums[i+1], right(i+1));
        return R[i];
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        num = sc.nextInt();

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

        for(int i = 0; i <= num; i++){
            L[i] = -1;
            R[i] = -1;
        }

        int ans = 0;
        for(int i = 0; i < num; i++){
            //i番目以外の公約数
            int gcd = gcd(left(i),right(i));
            if(gcd > ans)ans = gcd;
        }

        System.out.println(ans);

    }

    static int gcd(int a, int b){
        if(b == 0)return a;
        if(a == 0)return b;
        return gcd(b, a % b);
    }
}