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