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;
typedef long long int ll;
#define rep(i,n) for(ll i=0;i<(n);i++)
ll GCD(ll a,ll b) { return b ? GCD(b, a%b) : a; }
int main(){
  ll n;cin>>n;
  vector<ll> v(n);
  rep(i,n) cin>>v[i];
  vector<ll> left(n+1,0),right(n+1,0);
  rep(i,n) left[i+1]=GCD(left[i],v[i]);
  for(ll i=n-1;i>=0;i--) right[i]=GCD(right[i+1],v[i]);
  ll ans=0;
  rep(i,n) ans=max(ans,GCD(left[i],right[i+1]));
  cout<<ans<<endl;
}
