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 gcd(int m,int n){if(!n)return m;return gcd(n,m%n);}
int main()
{
	int ans,i,n,a[114514],g[114514],h[114514];
	cin>>n;for(i=0;i<n;i++)cin>>a[i];
	g[0]=a[0];for(i=1;i<n;i++)g[i]=gcd(g[i-1],a[i]);
	h[n-1]=a[n-1];for(i=n-2;i>=0;i--)h[i]=gcd(h[i+1],a[i]);
	ans=max(h[1],g[n-2]);for(i=0;i<n-2;i++)ans=max(ans,gcd(g[i],h[i+2]));
	cout<<ans<<endl;
}