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.Scanner;

class Solver {
    public void Solve() {
        int n = sc.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = sc.nextInt();
        }
        int[] gcdl = new int[n];
        int[] gcdr = new int[n];
        gcdl[0] = a[0];
        for (int i = 1; i < gcdr.length; i++) {
            gcdl[i] = gcd(gcdl[i - 1], a[i]);
        }
        gcdr[n - 1] = a[n - 1];
        for (int i = n - 2; i >= 0; i--) {
            gcdr[i] = gcd(gcdr[i + 1], a[i]);
        }

        // 端を使わない場合
        int max = Math.max(gcdr[1], gcdl[n - 2]);
        for (int i = 0; i < gcdr.length - 2; i++) {
            int ans = gcd(gcdl[i], gcdr[i + 2]);
            max = Math.max(ans, max);
        }
        System.out.println(max);

    }

    Scanner sc;

    Solver(Scanner in) {
        this.sc = in;
    }

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

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        Solver s = new Solver(sc);
        s.Solve();
        sc.close();
    }
}
