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)

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).toSeq

    if (values.min == values.max) {
      values.max.toString
    } else {
      var result = 0L
      for (i <- values.indices) {
        val vs =
          if (i == 0) {
            values.slice(1, values.size)
          } else if (i == values.size - 1) {
            values.slice(0, values.size - 1)
          } else {
            values.slice(0, i) ++: values.slice(i + 1, values.size)
          }
        for (j <- 1 until vs.size) {
          val g = gcd(vs(j), vs(j - 1))
          if (g > result) result = g
        }
      }
      result.toString
    }
  }

  def gcd(a: Long, b: Long): Long = {
    if (b == 0) a else gcd(b, a % b)
  }
}