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 rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int gcd(int a,int b){ return b?gcd(b,a%b):a; }

int main(){
	int n,a[100000]; cin>>n;
	rep(i,n) cin>>a[i];

	int right[100001];
	right[n]=0;
	rep(i,n) right[n-i-1]=gcd(right[n-i],a[n-i-1]);

	int left=0,ans=0;
	rep(i,n){
		ans=max(ans,gcd(left,right[i+1]));
		left=gcd(left,a[i]);
	}
	cout<<ans<<endl;

	return 0;
}
