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;
using ll=long long;

ll gcd(ll a ,ll b){
    return b?gcd(b,a%b):a;
}

int main()
{
   int n;cin >> n;
   vector <ll >a(n);
   vector<ll> r(n,0),l(n,0);
    for(int i=0;i<n;i++){
        cin >> a[i];
    }

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