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;
#define N 100005
#define rep1(i,n) for((i)=1;(i)<=(n);(i)++)

int n,ans;
int a[N];
int l[N],r[N];
int gcd(int x,int y)
{
	if(y==0) return x;
	return gcd(y,x%y);
}

int main()
{
	
	int i;
	cin>>n;
	rep1(i,n) cin>>a[i];
	rep1(i,n) l[i]=gcd(a[i],l[i-1]);
	for(i=n;i>=1;i--) r[i]=gcd(a[i],r[i+1]);
	rep1(i,n) ans=max(ans,gcd(l[i-1],r[i+1]));
	cout<<ans<<'\n';
	
	return 0;
}