Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int gcd(int a, int b){
  if(b > a) return gcd(b, a);
  if(b == 0) return a;
  return gcd(b, a % b);
}

int main() {
  int n; cin >> n;
  
  int ans = 0;
  
  vector<int> a(n);
  for(int i = 0; i < n; i++){
    int temp; cin >> temp;
      a.at(i) = temp;
  }
  
  vector<int> l(n + 2, 0), r(n + 2, 0);
  
  for(int i = 1; i <= n; i++){
    l.at(i) = gcd(a.at(i - 1), l.at(i - 1));
  }
  for(int i = n; i > 0; i--){
    r.at(i) = gcd(a.at(i - 1), r.at(i + 1));
  }
  
  for(int i = 0; i < n; i++){
    ans = max(ans, gcd(l.at(i), r.at(i + 2)));
  }
  
  cout << ans << endl;
  
}