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.*;

class Main { 
    public static int gcd(int a, int b){
      return b == 0 ? a:gcd(b,a%b);
    }
  
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        Integer A[] = new Integer[N];
        int ans = 0;
        for (int i=0; i<N; i++){
          A[i] = sc.nextInt();
        }
		int[] L = new int[N+1];
		int[] R = new int[N+1];
		for(int i = 0; i < N; i++)
			L[i+1] = gcd(L[i],A[i]);
		for(int i = N-1; i > 0; i--)
			R[i] = gcd(R[i+1], A[i]);
		for(int i = 0; i < N; i++)
			ans = Math.max(ans, gcd(L[i],R[i+1]));
		System.out.println(ans);  
      }
    
}