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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var N = int.Parse(ReadLine());
        var A = ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();

        if(N == 2)
        {
            WriteLine(Math.Max(A[0], A[1]));
            return;
        }

        var gcd1 = new int[N];
        var gcd2 = new int[N];
        for (int i = 0; i < N; i++)
        {
            gcd1[i] = (int)GcdLcm.Gcd(A[0], A[i]);
            gcd2[i] = (int)GcdLcm.Gcd(A[1], A[i]);
        }

        gcd1[0] = int.MaxValue;
        gcd2[1] = int.MaxValue;

        var sortedGcd1 = gcd1.Select((v, i) => (v, i)).OrderBy(x => x.v).ToArray();
        var sortedGcd2 = gcd2.Select((v, i) => (v, i)).OrderBy(x => x.v).ToArray();

        var minGcd1 = sortedGcd1[0];
        var minGcd2 = sortedGcd2[0];
        var secondMinGcd1 = sortedGcd1[1];
        var secondMinGcd2 = sortedGcd2[1];

        if (secondMinGcd1.v < secondMinGcd2.v)
            A[minGcd2.i] = secondMinGcd2.v;
        else
            A[minGcd1.i] = secondMinGcd1.v;

        var ans = int.MaxValue;

        for (int i = 1; i < N; i++)
            ans = Math.Min(ans, (int)GcdLcm.Gcd(A[0], A[i]));

        WriteLine(ans);
    }
}
static class GcdLcm
{
    public static long Gcd(long a, long b) => (b != 0) ? Gcd(b, a % b) : a;
    public static long Lcm(long a, long b) => a / Gcd(a, b) * b;
}