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.*;

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

    int N = scn.nextInt();

    int[] A = new int[N];
    for (int i = 0; i < N; i++) {
      A[i] = scn.nextInt();
    }

    int[] L = new int[N + 1];
    L[0] = 0;
    L[1] = A[0];
    int[] R = new int[N];
    R[N - 1] = 0;
    R[N - 2] = A[N - 1];
    for (int i = 2; i < N; i++) {
      L[i] = gcd(L[i - 1], A[i - 1]);
    }
    for (int i = N - 3; i >= 0; i--) {
      R[i] = gcd(R[i + 1], A[i + 1]);
    }

    int max = 1;
    for (int i = 0; i < N; i++) {
      max = Math.max(gcd(L[i], R[i]), max);

    }
    System.out.println(max);

  }

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

}