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.FileNotFoundException;
import java.io.FileReader;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) throws FileNotFoundException {

//    Scanner cin = new Scanner(new FileReader("input.txt"));
    Scanner cin = new Scanner(System.in);

    int n = cin.nextInt();
    int[] num = new int[n];

    for (int i = 0; i < n; i++) {
      num[i] = cin.nextInt();
    }

    int[] right = new int[n + 1];

    for (int i = n - 1; i > 0; i--) {
      right[i] = calGCD(num[i], right[i + 1]);
    }

    int res = 0;
    int left = 0;
    for (int i = 0; i < n; i++) {
      res = Math.max(calGCD(left, right[i + 1]), res);
      left = calGCD(left, num[i]);
    }
    System.out.println(res);

  }

  private static int calGCD(int a, int b) {
    if (a == 0 || b == 0) {
      return a == 0 ? b : a;
    }
    if (a >= b) {
      return calGCD(b, a % b);
    } else {
      return calGCD(a, b % a);
    }
  }


}
