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 main(){
    int n,ans=0,r;
    cin >> n;
    int a[n],b[n],maxa;
    for (int i = 0; i < n; i++) cin >> a[i];
    sort(a,a +n);

    for(int i = a[1]; i > 0; i--){
        int tmp =0;
        for(int j = 0; j < n; j++){
            if(a[j] % i !=0)
                tmp++;
        }
        if(tmp < 2){
            ans = i;
            break;
        }
    }
    cout << ans << endl;    
    
}