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: Accepted)

import scala.io.StdIn


object Main extends App {
  val n  = StdIn.readLine().toInt
  val a  = StdIn.readLine().split(" ").map(_.toInt)

  def solve(a: Array[Int]): Int = {

    val b = a.scanLeft(0) {(acc, x) => gcd(acc, x)}
    val c = a.scanRight(0) {(acc, x) => gcd(acc, x)}

    val d = for (x <- 0 to a.length -1) yield {
      gcd(b(x), c(x + 1))
    }
    d.max
  }

  def gcd(x: Int, y: Int) :Int = {
    if (y == 0 ) x
    else gcd(y, (x % y))
  }

  println(solve(a))

}