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;
#define ll long long int
int main(){
    ll n;
    cin>>n;
    ll a[n];
    for(int i=0;i<n;i++)cin>>a[i];
    sort(a,a+n);
    ll count=0,ans;
    for(int i=a[1];i>0;i--){
        if(a[1]%i==0 || a[0]%i==0){
        for(int j=0;j<n;j++){
            if(a[j]%i==0)count++;
        }
        }
        if(count>n-2){
            ans=i;
            break;
        }else count=0;
    }
    cout<<ans<<endl;
}