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<iostream>
using namespace std;
int a[100005],b[100005],c[100005];
int gcd(int a,int b){
	if(a<b) swap(a,b);
	if(b==0)
		return a;
	else
		return gcd(b,a%b);
}
int main()
{
	int n,i;
	cin>>n;
	for(i=1;i<=n;i++)
		cin>>a[i];
	
	b[1]=a[1];
	for(i=2;i<=n;i++)
		b[i]=gcd(b[i-1],a[i]);
	
	c[n]=a[n];
	for(i=n-1;i>=1;i--)
		c[i]=gcd(c[i+1],a[i]);
	
	int maxv=0;
	for(i=1;i<=n;i++)
		maxv=max(maxv,gcd(b[i-1],c[i+1]));
	cout<<maxv;
	return 0;
}