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;
int gcd(int a,int b)
{
	if(a%b==0)return b;
	else return gcd(b,a%b);
}
set<int>a;
int n,x,k;
int main()
{
	cin>>n;
	while(n--)
	{
		set<int>b;
		b.clear();
		swap(a,b);
		cin>>x;
		for(set<int>::iterator it=b.begin();it!=b.end();it++)
			a.insert(gcd(*it,x));
		a.insert(k);
		k=gcd(k,x);
	}
	int ans=1;
	for(set<int>::iterator it=a.begin();it!=a.end();it++)
	{
		ans=max(ans,*it);
	}
	cout<<ans<<endl;
}