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>
using namespace std;

int gcd(int x, int y) {if (y == 0) return x; return gcd(y,x%y);}

int main(){
  int n; cin>>n;
  int a[n]; for(int i=0;i<n;i++) cin>>a[i];
  int b[n]; b[0] = a[0];
  int c[n]; c[n-1] = a[n-1];
  for(int i=1;i<n;i++) {
    b[i] = gcd(b[i-1], a[i]);
  }
  for(int i=n-2;i>=0;i--) {
    c[i] = gcd(c[i+1], a[i]);
  }
  int an = max(c[1], b[n-2]);
  for(int i=0;i<n;i++) {
    an = max(an, gcd(b[i-1], c[i+1]));
  }
  cout<<an<<endl;
}