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 scala.util.control.Breaks

object Main {
  def main(args: Array[String]): Unit = {
    val lines = io.Source.stdin.getLines().toSeq
    println(solve(lines))
  }

  def solve(lines: Seq[String]): String = {
    val n = lines.head.toInt
    val values = lines(1).split(" ").take(n).map(_.toLong)

    if (values.min == values.max) {
      values.max.toString
    } else {
      var divisersList = Vector[Vector[Long]]()
      for (i <- values.indices) {
        val d = divisors(values(i))
        divisersList = d +: divisersList
      }
      val reversed = divisersList.flatten.distinct.sorted.reverse
      var result = 0L
      val b = new Breaks
      b.breakable {
        reversed.foreach { v =>
          if (divisersList.count(_.contains(v)) >= n - 1) {
            result = v
            b.break()
          }
        }
      }
      result.toString
    }
  }

  def divisors(n: Long): Vector[Long] =
    (for (i <- 1L to n if n % i == 0) yield i).toVector
}