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;
#define rep(i,n) for(int i=0;i<n;i++)
int n,a[111111];
map<int,int>mp;
int main(){
	cin>>n;
	rep(i,n){
		cin>>a[i];
		if(i<=1){
			for(int j=1;j<=sqrt(a[i]);j++){
				if(a[i]%j==0){
					if(j*j==a[i])mp[j]++;
					else mp[j]++,mp[a[i]/j]++;
				}
			}
		}
	}
	int ans=1;
	for(auto p:mp){
		int ok=2;
		rep(i,n)if(a[i]%p.first)ok--;
		if(ok>0)ans=max(ans,p.first);
		
	}
	cout<<ans<<endl;
	return 0;
}
