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
/*
 题意：给定n个数，每次可以替换一个数，求n个数的最大公因数。

思路：求一遍前缀后缀gcd再枚举
*/

#include<iostream>
using namespace std;

int gcd(int x,int y){
	return y==0 ? x : gcd(y,x%y);
}

int main(){
	int n,a[100005],per[100005],las[100005],ans=0;
	cin>>n;
	for(int i=1;i<=n;++i)	cin>>a[i];
	per[1]=a[1];
	las[n]=a[n];
	for(int i=2;i<=n;++i)	per[i]=gcd(per[i-1],a[i]);
	for(int i=n-1;i>=1;--i)	las[i]=gcd(las[i+1],a[i]);
	for(int i=1;i<=n;++i)
		if(ans<gcd(per[i-1],las[i+1]))
			ans=gcd(per[i-1],las[i+1]);
	cout<<ans;
}