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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int[] a = new int[n];
        for (int i = 0 ; i < n ; i++) {
            a[i] = sc.nextInt();

        }
        if (n == 2) {
            System.out.println(Math.max(a[0], a[1]));
            return;
        }

        //a0カエルケース
        int gcd1 = a[1];
        for (int i = 1 ; i < n ; i++) {
            gcd1 = gcd(gcd1, a[i]);
        }

        //a0変えないケース、a0の約数を求めたいお気持ち
        //約数の列挙エラトステネスの篩で割り切れたときの商も詰めてくとできる。
        Set<Integer> set = new HashSet<>();
        double sqrt = Math.floor(Math.sqrt(a[0]));
        for (int i = 1 ; i <=  sqrt ; i++) {
            if (a[0] % i == 0) {
                set.add(i);
                set.add(a[0] / i);
            }
        }


        int max = 1;
        //a0の約数が候補なので全探索する。a1~anの中で割り切れなかった個数が1以下のときにそいつが候補
        for (Integer i : set) {
            int count = 0;
            for (int j = 1 ; j < n ; j++) {
                if (a[j] % i != 0) {
                    count++;
                }

            }
            if (count <= 1) {
                max = Math.max(max, i);
            }
        }

        System.out.println(Math.max(gcd1, max));
    }

    private static int gcd(int m, int n) {
        if(m < n) return gcd(n, m);
        if(n == 0) return m;
        return gcd(n, m % n);
    }

}
