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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.util.Scanner

object Main extends App  {
  val sc = new Scanner(System.in)

  val n = sc.nextInt


  val al = List.fill(n)(sc.nextInt)

  val res =
    (0 until n).foldLeft(1){(max, i) =>
      val t2 = al.zipWithIndex.filter(_._2 != i).map(_._1)

      val temp = t2.tail.foldLeft(t2.head)(gcd(_,_))

      Math.max(max, temp)
    }
  println(res)

  def gcd(a: Int, b: Int): Int ={
    (a,b) match{
      case (x,y) if y == 0 => x
      case (x,y) if x < y  => gcd(y, x)
      case (x,y)           => gcd(y, x % y)
    }
  }

}