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: Accepted)

using System;
using System.Linq;

class C
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = Console.ReadLine().Split().Select(int.Parse).ToArray();

		var l = new int[n];
		var r = new int[n];
		l[0] = a[0];
		r[n - 1] = a[n - 1];
		for (int i = 1; i < n; i++)
		{
			l[i] = Gcd(l[i - 1], a[i]);
			r[n - 1 - i] = Gcd(r[n - i], a[n - 1 - i]);
		}

		var M1 = Math.Max(r[1], l[n - 2]);
		var M2 = n <= 2 ? 1 : Enumerable.Range(1, n - 2).Max(i => Gcd(l[i - 1], r[i + 1]));
		Console.WriteLine(Math.Max(M1, M2));
	}

	static int Gcd(int x, int y) { for (int r; (r = x % y) > 0; x = y, y = r) ; return y; }
}