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;
int gcd(int a, int b){
  if(b==0) return a;
  return gcd(b, a%b);
}
int main() {
  int n;
  cin >> n;
  int a[100100];
  for(int i=0; i<n; i++) cin >> a[i];
  vector<int> L(n), R(n);
  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]);
  }
  int maxx = 1;
  for(int i=0; i<n; i++){
    maxx = max(maxx, gcd(L[i],R[i]));
  }
  cout << maxx << endl;
}