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<iostream>
#include<vector>
#include<numeric>

using namespace std;

int gcd(int a, int b)
{
	while(b) {
		int t = a % b;
		a = b;
		b = t;
	}
	
	return a;
}

int max(int *m, int n)
{

	int max = 0;
	
	for (int i = 0; i < n; i++) {
		if (m[i] > max) {
			max = m[i];
		}
	}	
	
	return max;
}


int main()
{
	int n, a;
	vector<int> A;
	
	int *L, *R, *M;
	
  	cin >> n;
  	for (int i = 0; i < n; i++) {
  		cin >> a;
  		A.push_back(a);
  	}
  	
  	 L = new int[(n+1)];
  	 R = new int[(n+1) + 1];
  	 M = new int[(n+1)]; 
  	 L[0] = R[n+1] = 0;
  	
  	for (int i = 0; i < n; i++) {
  		L[i+1] = gcd(L[i], A[i]);
  	}
  	
  	 for (int i = n; i > 0; i--) {
  		R[i] = (gcd(R[i+1], A[i]));
  	}
  	
  	 for (int i = 0; i < n; i++) {
  		M[i] = (gcd(L[i], R[i+1]));
  	}

	cout << max(M, n);

    return 0;
}