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>
using namespace std;
int n,a[100009],L[100009],R[100009],M;

int gcd(int x,int y){
    if(x>y){
        int t=x;
        x=y;
        y=t;
    }
    if(x==0) return y;
    return gcd(y%x,x);
}

int main(){
    cin>>n;
    for(int i=1;i<=n;i++)cin>>a[i];
    for(int i=1;i<=n;i++){
        L[i]=gcd(L[i-1],a[i]);
    }for(int i=n;i;i--){
        R[i]=gcd(R[i+1],a[i]);
    }
    for(int i=1;i<=n;i++){
        M=max(M,gcd(L[i-1],R[i+1]));
    }
    cout<<M;
}