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<algorithm>
using namespace std;
int n,a[100005],ans,r[100005],f[100005];
int g(int a,int b){
    return b?g(b,a%b):a;
}
int main(){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    for(int i=0;i<n;i++){
        r[i+1]=g(r[i],a[i]);
    }
    for(int i=n-1;i>0;i--){
        f[i]=g(f[i+1],a[i]);
    }
    for(int i=0;i<n;i++)ans=max(ans,g(r[i],f[i+1]));
    cout<<ans<<endl;
}