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[] L = new int[N+1];
		int[] R = new int[N+1];
		int[] ans = new int[N];
		
		for (int i=0;i<N;i++) {
			L[i+1]=gcd(L[i],A[i]);
		}
		for (int i=N;i>0;i--) {
			R[i-1]=gcd(R[i],A[i-1]);
		}
		for (int i=0;i<N;i++) {
			ans[i]=gcd(L[i],R[i+1]);
		}
		int max=0;
		for (int i=0;i<N;i++) {
			max=Math.max(max,ans[i]);
		}
		System.out.println(max);
		sc.close();
	}

	static int gcd(int m,int n) {
		if (m<n) {
			return gcd(n,m);
		}
		if (n==0) {
			return m;
		}
		return gcd(n,m%n);
	}
}
