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;
int n,a[100005],f[100004],e[100004];
int gcd(int x,int y){
	if(y==0)return x;
	return gcd(y,x%y);
}
priority_queue<int> que;
int main(){
	cin>>n;
	for(int i=0;i<n;i++)cin>>a[i];
    f[0]=a[0];
    for(int i=1;i<n;i++){
		f[i]=gcd(a[i],f[i-1]);
	}
	e[n-1]=a[n-1];
	for(int i=n-2;i>=0;i--){
		e[i]=gcd(a[i],e[i+1]);
	}
	que.push(e[1]);
	que.push(f[n-2]);
	for(int i=1;i<n-1;i++){
		que.push(gcd(f[i-1],e[i+1]));
	}
	cout<<que.top()<<endl;
}
