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: Wrong Answer)

import java.util.Scanner

import scala.collection.mutable

object Main {
  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)
    val N = sc.nextInt()
    val A = 1 to N map (_ => sc.nextInt)

    val ans = Math.max(scan(A(0), A.drop(1)), scan(A(1), A.take(1) ++ A.drop(2)))
    println(ans)

  }

  def scan(t: Int, A: Seq[Int]): Int = {

    val mx = Math.sqrt(t).toInt + 1
    val candidates = (1 to mx).filter(t % _ == 0).flatMap(x => Seq(x, (t/x)))

    val map: mutable.Map[Int, Int] = mutable.Map(candidates.map(_ -> 0): _*)
    map.put(1, 0)
    A.foreach { a =>
      candidates.foreach { c =>
        {
          val d = if (a % c != 0) 1 else 0
          map.put(c, map.get(c).get + d)
        }
      }
    }
    val filtered = map.filter(_._2 <= 1)
    (map.filter(_._2 <= 1).keySet).max
  }
}