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 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();
    }
    int M[] = new int[N];
    for (int i=1; i<=N-1; i++) {
      M[i] = gcd(M[i-1], A[i-1]);
    }
    int U[] = new int[N];
    for (int i=1; i<=N-1; i++) {
      U[i] = gcd(U[i-1], A[N-i]);
    }
    int out = 1;
    for (int i=0; i<=N-1; i++) {
      int outtemp = gcd(M[i], U[N-i-1]);
      if(out < outtemp){
        out = outtemp;
      }
    }
    System.out.println(out);
  }

  public static int gcd(int num1, int num2) {
    if(num2 == 0) {
      return num1;
    } else {
      return gcd(num2, num1 % num2);
    }
  }
}

