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.math.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] As = new int[N];
        for (int i=0; i<N; i++) {
            As[i] = sc.nextInt();
        }

        int[] left = new int[N+1];
        int[] right = new int[N+1];

        for (int i=0; i<N; i++) {
            left[i+1] = gcd(left[i], As[i]);
        }
        for (int i=N-1; i>=0; i--) {
            right[i] = gcd(right[i+1], As[i]);
        }

        int res = 0;
        for (int i=0; i<N; i++) {
            int l = left[i];
            int r = right[i+1];

            if (res < gcd(l, r)) {
                res = gcd(l, r);
            }
        }
        System.out.println(res);
    }
    
    public static int gcd(int a, int b) {
        return b > 0 ? gcd(b, a%b) : a;
    }
}
