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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String... args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(reader.readLine());
        int[] A = new int[N];
        String[] strA = reader.readLine().split(" ");
        for (int i = 0; i < N; i++) {
            A[i] = Integer.parseInt(strA[i]);
        }
        int[] leftGcd = new int[N - 1];
        leftGcd[0] = A[0];
        for (int i = 0; i < N - 2; i++) {
            leftGcd[i + 1] = gcd(leftGcd[i], A[i + 1]);
        }
        int[] rightGcd = new int[N - 1];
        rightGcd[N - 2] = A[N - 1];
        for (int i = N - 3; 0 <= i; i--) {
            rightGcd[i] = gcd(A[i + 1], rightGcd[i + 1]);
        }
        int[] allGcd = new int[N];
        allGcd[0] = rightGcd[0];
        for (int i = 0; i < N - 2; i++) {
            allGcd[i + 1] = gcd(leftGcd[i], rightGcd[i + 1]);
        }
        allGcd[N - 1] = leftGcd[N - 2];
        int max = 0;
        for (int cur : allGcd) {
            if (max < cur) {
                max = cur;
            }
        }
        System.out.println(max);
    }

    private static int gcd(int a, int b) {
        int r = a % b;
        return (r == 0) ? b : gcd(b, r);
    }
}
