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<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
const int N=1e5+10;
int gcd(int a,int b){return !b?a:gcd(b,a%b);}
int n,a[N];
int pre[N],suf[N];
int main(){
	scanf("%d",&n);for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	pre[1]=a[1];for(int i=2;i<=n;i++)pre[i]=gcd(pre[i-1],a[i]);
	suf[n]=a[n];for(int i=n-1;i;i--)suf[i]=gcd(suf[i+1],a[i]);
	int ans=max(pre[n-1],suf[2]);
	for(int i=2;i<=n-1;i++)ans=max(ans,gcd(pre[i-1],suf[i+1]));
	cout<<ans;
}