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;

const int MAXN=1e5+10;

int arr[MAXN],pref[MAXN],suf[MAXN],N,best;

int gcd(int a,int b)
{
	if(a<b) 
	  swap(a,b);
	if(b==0)
	  return a;
	return gcd(b,a%b);
}

int main()
{
cin>>N;
  for(int i=1;i<=N;i++)
  {
	cin>>arr[i];
	pref[i]=gcd(pref[i-1],arr[i]);
  }

  for(int i=N;i>=1;i--) 
    suf[i]=gcd(suf[i+1],arr[i]);
  for(int i=1;i<=N;i++) 
    best=max(best,gcd(pref[i-1],suf[i+1]) );
cout<<best<<endl;
return 0;
}