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<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
int n,a[N],l[N],r[N];

int gcd(int a,int b) { return b==0 ? a : gcd(b,a%b); }

int main()
{
	cin>>n;
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	l[1]=a[1]; for (int i=2;i<=n;i++) l[i]=gcd(l[i-1],a[i]);
	r[n]=a[n]; for (int i=n-1;i;i--) r[i]=gcd(r[i+1],a[i]);
	
	int ans=l[n];
	ans=max(ans,max(r[2],l[n-1]));
	for (int i=2;i<=n-1;i++)
		ans=max(ans,gcd(l[i-1],r[i+1]));
	printf("%d\n",ans);	  
	return 0;
}