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;
typedef long long ll;
const int maxn=1e5+5;
int a[maxn];
int l[maxn];
int r[maxn];
int n;
int ans;
inline int gcd(int a,int b){
	return b?gcd(b,a%b):a; 
}
int main(){
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i];
	l[1]=a[1]; r[n]=a[n];
	for(int i=2;i<=n;i++) l[i]=gcd(l[i-1],a[i]);
	for(int i=n-1;i>=1;i--) r[i]=gcd(r[i+1],a[i]);
	ans=max(r[2],l[n-1]);
	for(int i=2;i<=n-1;i++)
		ans=max(ans,gcd(l[i-1],r[i+1]));
	cout<<ans<<endl;
	return 0;
}