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 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 t=0;
		int max=0;
	/*	for(int i=0;i<n;i++){
			for(int j=1;j<n;j++){
				if(i==0)
					t=a[1];
				else	
					t=a[0];
				if(j!=i)
				t=gcd(t,a[j]);
			}
			if(max<t)
				max=t;
				t=0;	
		}	*/
			int[] l=new int[n+1];
			l[0]=0;
			for(int j=0;j<n;j++){
				l[j+1]=gcd(l[j],a[j]);
			}
			int[] r=new int[n+1];
			r[n]=0;
			for(int j=n-1;j>0;j--){
				r[j]=gcd(r[j+1],a[j]);
			}
			for(int i=0;i<n;i++){
				max=Math.max(max,gcd(l[i],r[i+1]));
			}
		System.out.println(max);
	}
	static int gcd(int a,int b){
		int t;
		if(a==0)
			return b;
		if(b==0)
			return a;
		if(a<b){ 
			int p=a;
			a=b;
			b=p;
		}
		while((t=a%b)!=0){
			a=b;
			b=t;
			
		}
		return b;
	}
	
}