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
#include<stdio.h>

int a[200005],c[200005],d[200005];

int _max(int x,int y){return x>y?x:y;}
int _gcd(int x,int y){return y==0?x:_gcd(y,x%y);}

int main(){
	
	/*freopen("10.in","r",stdin);
	freopen("10.out","w",stdout);*/
	int n,i,ans=0;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&a[i]);
		c[i]=_gcd(a[i],c[i-1]);
	}
	for(i=n;i>=1;i--)
		d[i]=_gcd(d[i+1],a[i]);
	for(i=1;i<=n;i++)
		ans=_max(ans,_gcd(c[i-1],d[i+1]));
	printf("%d",ans);
	return 0;
}
	
		
		
 