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 f(int x,int y){
    if(x<y)swap(x,y);
    if(y==0)return x;
    return f(y,x%y);
}
int s[100000],n,a[100000],b[100000],MAX;
int main(void){
    cin>>n;
    for(int i=0;i<n;i++)cin>>s[i];
    for(int i=0;i<n-1;i++){
        a[i+1]=f(a[i],s[i]);
        b[i+1]=f(b[i],s[n-i-1]);
    }
    for(int i=0;i<n;i++){
        MAX=max(MAX,f(a[i],b[n-i-1]));
    }
    cout<<MAX<<endl;
}
