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>
#define maxn 100005
using namespace std;

int n,a[maxn],fr[maxn],bk[maxn],ans=1;

int gcd(int x,int y)
{
	if(!y) return x;
	return gcd(y,x%y);
}

int main()
{
	cin>>n;
	for(int i=1;i<=n;++i) scanf("%d",&a[i]);
	fr[1]=a[1],bk[n]=a[n];
	for(int i=2;i<=n;++i) fr[i]=gcd(fr[i-1],a[i]);
	for(int i=n-1;i>=1;--i) bk[i]=gcd(bk[i+1],a[i]);
	ans=max(fr[n-1],bk[2]);
	for(int i=2;i<n;++i)
	{
		ans=max(ans,gcd(fr[i-1],bk[i+1]));
	}
	cout<<ans;
	return 0;
}