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<vector>
using namespace std;

int gcd(int a,int b){
    if(b==0) return a;
    return gcd(b,a%b);
}

int main(){
    int n; cin>>n;
    vector<int> a(n);
    for(int i=0;i<n;i++) cin>>a[i];
    vector<int> l(n),r(n);
    for(int i=0;i<n-1;i++) l[i+1]=gcd(l[i],a[i]);
    for(int i=n-1;i>=1;i--) r[i-1]=gcd(r[i],a[i]);
    int ans=1;
    for(int i=0;i<n;i++) ans=max(ans,gcd(l[i],r[i]));
    cout<<ans<<endl;
}