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 <bits/stdc++.h>
using namespace std;
const int maxn = 100010;
int gcd(int a,int b){return a == 0 ? b : gcd(b%a,a);}

int n, a[maxn], l[maxn], r[maxn];
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>=1;i--) r[i] = gcd(r[i+1], a[i]);

    int mx = 1;
    for (int i=1;i<=n;i++){
        int tmp = gcd( l[i-1], r[i+1]);
        if (tmp > mx) mx = tmp;
    }
    cout<<mx<<endl;
    return 0;
}
