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>
#include<algorithm>
#include<cstdio>
using namespace std;
int gcd(int a,int b)
{
	return b==0?a:gcd(b,a%b);
}
int g[100010],a[100010],n;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		g[i]=gcd(g[i-1],a[i]);
	}
	int ans=0;
	for(int i=n;i>=1;i--)
	{
		ans=max(ans,gcd(g[i-1],g[i+1]));
		g[i]=gcd(g[i+1],a[i]);
	}
	printf("%d\n",ans);
	return 0;
}