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 i;

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

int main(){
  int N;
  cin >> N;
  vector<int> A(N), L(N), R(N);
  for (i = 0; i < N; i++){
    cin >> A[i]; 
  }
  for (i = 0; i < N-1; i++){
    L[i+1] = gcd(L[i], A[i]);
  }
  for (i = N-1; i >= 1; i--){
    R[i-1] = gcd(R[i], A[i]);
  }
  int ans = 0;
  for (i = 0; i < N; i++){
    ans = max(ans, gcd(L[i], R[i]));
  }
  cout << ans << endl;
}