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.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    int[] numbers = new int[n];
    for (int i = 0; i < n; i++) {
      numbers[i] = Integer.parseInt(sc.next());
    }
    if (n == 1) {
      pw.println(numbers[0]);
      return;
    }
    int secondMin = getSecondMin(numbers);
    for (int i = secondMin; i >= 1; i--) {
      int numOfIndivisible = 0;
      for (int number : numbers) {
        if (number % i != 0) {
          numOfIndivisible++;
        }
        if (numOfIndivisible > 1) {
          break;
        }
      }
      if (numOfIndivisible <= 1) {
        pw.println(i);
        return;
      }
    }
    throw new RuntimeException();
  }

  static int getSecondMin(int[] numbers) {
    int min = Integer.MAX_VALUE;
    int secondMin = Integer.MAX_VALUE;
    for (int i = 0; i < numbers.length; i++) {
      if (min > numbers[i]) {
        secondMin = min;
        min = numbers[i];
      } else if (secondMin > numbers[i]) {
        secondMin = numbers[i];
      }
    }
    return secondMin;
  }
}
