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: Runtime Error)

import scala.io.StdIn.readLine

object Main{
  def main(args: Array[String]): Unit ={
    val n : Int = readLine().toInt
    val A : Array[Int] = readLine().split(' ').map(_.toInt)
    println(new Solve(n, A).solve())
  }
}

class Solve(val n : Int, val A : Array[Int]){
  def gcd(a : Int, b : Int): Int = if(b == 0) a else gcd(b, a % b)
  val Front : Array[Int] = {
    val k : Array[Int] = Array.fill(n)(0)
    for(i <- 1 until n) k(i) = gcd(k(i-1), A(i-1))
    k
  }
  val Back : Array[Int] = {
    val k : Array[Int] = Array.fill(n)(0)
    for(i <- n-2 to 0 by -1) k(i) = gcd(A(i+1), k(i+1))
    k
  }
  def solve(idx : Int = 0, res : Int = -1) : Int = {
    if(idx == n) res
    else{
      val USA : Int = gcd(Front(idx), Back(idx))
      solve(idx + 1, if(USA > res) USA else res)
    }
  }
}