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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

class Bmondai
{
    static void Main()
    {
        var N = Int32.Parse(Console.ReadLine());
        var A = Console.ReadLine().Split(' ').Select(x=>Int64.Parse(x)).ToArray();
        var count = 0L;
        var ans = long.MinValue;
        for (int i=0;i<N;++i)
        {
            count = i == 0 ? A[1] : A[0];
            int j = i == 0 ? 2 : 1;
            for (; j<N;++j) {
                if (j == i) continue;
                var a = count < A[j] ? A[j] : count;
                var b = a == count ? A[j] : count;
                count = GetGcd(a, b);
            }
            if (ans < count) ans = count;
        }
        Console.WriteLine(ans);
    }
    //最大公約数
    static long GetGcd(long a, long b)
    {
        while (b != 0)
        {
            var r = a % b;
            a = b;
            b = r;
        }
        return a;
    }
}