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.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;


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

            int[] f = new int[N];
            int[] b = new int[N];
            int gcd = A[N - 1];
            for (int i = N - 1; i >= 0; i--) {
                gcd = gcd(gcd, A[i]);
                b[i] = gcd;
            }
            gcd = A[0];
            for (int i = 0; i < N; i++) {
                gcd = gcd(gcd, A[i]);
                f[i] = gcd;
            }

            int max = 0;
            for (int i = 0; i < N; i++) {
                int a = i - 1 >= 0 ? f[i - 1] : 0;
                int c = i + 1 < N ? b[i + 1] : 0;
                max = Math.max(max, gcd(a > 0 ? a : c, c > 0 ? c : a));
            }

            System.out.println(max);
        }
    }

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

    public static final ArrayList<Integer> divisor(int n) {
        ArrayList<Integer> res = new ArrayList<>();
        for (int i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                res.add(i);
                if (n / i != i) {
                    res.add(n / i);
                }
            }
        }
        return res;
    }
}
