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 x, int y){
  int r;
  while((r=x%y)!=0){x=y; y=r;}
  return y;
}

int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  for(int i=0;i<N;i++)cin >> A[i];
  sort(A.begin(),A.end());
  for(int i=A[1];i>=1;i--){
    int cnt=0; bool q=true;
    for(int j=0;j<N;j++){
      if(A[j]%i!=0){cnt++;}
      if(cnt>=2){q=false; break;}
    }
    if(q){cout << i << endl; return 0;}
  }
}