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 {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] numbers = new int[n];
        for (int i = 0; i < n; i++) {
            numbers[i] = sc.nextInt();
        }
        
        int[] gcdLeft = new int[n];
        int[] gcdRight = new int[n];
        gcdLeft[0] = numbers[0];
        gcdRight[n - 1] = numbers[n - 1];
        
        for (int i = 1; i < n; i++) {
            gcdLeft[i] = gcd(gcdLeft[i - 1], numbers[i]);
        }
        for (int i = n - 2; i >= 0; i--) {
            gcdRight[i] = gcd(gcdRight[i + 1], numbers[i]);
        }
        
        int max = Math.max(gcdLeft[n - 2], gcdRight[1]);
        for (int i = 1; i < n - 1; i++) {
            max = Math.max(max, gcd(gcdLeft[i - 1], gcdRight[i + 1]));
        }
        
        System.out.println(max);
    }
    
    public static int gcd(int a, int b) {
        if (b == 0) return a;
        
        return gcd(b, a % b);
    }
}
