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;
typedef long long ll;
const long long INF=1e18,MOD=1e9+7;
int main(){
	int n;
	ll mini=INF,p=INF;
	cin>>n;
	vector<ll>a(n);
	for(int i=0;i<n;i++){
		cin>>a[i];
		if(p>a[i]){
			mini=p;
			p=a[i];
		}
		else if(mini>a[i]){
			mini=a[i];
		}
	}
	for(;mini>0;mini--){
		int cnt=0;
		for(int i=0;i<n;i++){
			if(a[i]%mini!=0)cnt++;
			if(cnt>1)break;
		}
		if(cnt<=1){
			cout<<mini<<endl;
			break;
		}
	}
}
