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 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] a = new int[N];
        for(int i = 0; i<N; i++) {
            a[i] = Integer.parseInt(sc.next());
        }
        if(N==2) {
            System.out.println(Math.max(a[0],a[1]));
            return;
        }
	int[] left = new int[N+2];
	int[] right = new int[N+2];
        for(int i = 1; i<N; i++) {
	    left[i] = gcd(a[i-1],left[i-1]);
	    right[N+1-i] = gcd(a[N-i],right[N+2-i]);
        }
	int max = Integer.MIN_VALUE;
	for(int i = 1; i<N+1; i++) {
	    max = Math.max(max, gcd(left[i-1], right[i+1]));
	}
	System.out.println(max);
    }

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