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: Wrong Answer)

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

int main()
{
    int n;
    cin >> n;

    vector<int> numVec;
    int minNum = 1000000000;
    for (int i = 0; i < n; ++i)
    {
        int input;
        cin >> input;
        numVec.push_back(input);
        minNum = min(minNum, input);
    }

    int gcd = 1;
    for (int singleGcd = minNum; singleGcd > 0; --singleGcd)
    {
        int multiplesCount = 0;

        for (const int &singleNum : numVec)
        {
            if (singleNum % singleGcd == 0)
            {
                ++multiplesCount;
            }
        }

        if (multiplesCount >= n - 1)
        {
            gcd = singleGcd;
            break;
        }
    }

    cout << gcd << endl;
}