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;
ll n,ans,a[100005],b[100005],c[100005];
ll gcd(int x,int y){
	if(x%y==0)return y;
	return gcd(y,x%y);
}
int main(){
	cin >> n;
	for(int i=0;i<n;i++)
		cin >> a[i];
	b[0]=a[0];
	for(int i=1;i<n;i++)
		b[i]=gcd(b[i-1],a[i]);
	c[n-1]=a[n-1];
	for(int i=n-2;i>=0;i--)
		c[i]=gcd(c[i+1],a[i]);
	for(int i=0;i<n-2;i++)
		ans=max(ans,gcd(b[i],c[i+2]));
	ans=max(ans,c[1]);
	ans=max(ans,b[n-2]);
	cout << ans;
	return 0;
}