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<iostream>
#include<algorithm>
using namespace std;
int g(int a,int b){return b?g(b,a%b):a;}
int N,A[1<<17];
int L[1<<17],R[1<<17];
int main()
{
	cin>>N;
	for(int i=0;i<N;i++)cin>>A[i];
	for(int i=0;i<N;i++)L[i+1]=g(L[i],A[i]);
	for(int i=N;i--;)R[i]=g(R[i+1],A[i]);
	int ans=0;
	for(int i=0;i<N;i++)ans=max(ans,g(L[i],R[i+1]));
	cout<<ans<<endl;
}