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 (2.13.1) (judge verdict: Accepted)

import scala.io.StdIn._

object Main extends App {

  val n = readInt()
  val A = readLine().split(" ").map(_.toInt)

  def solve() = {
    val l = Array.fill(n)(0)
    val r = Array.fill(n)(0)
    
    for(i <- 0 until n-1) l(i+1) = gcd(l(i), A(i))
    for(i <- n-1 until 0 by-1) r(i-1) = gcd(r(i), A(i))
    
    (0 until n).foldLeft(1) { (acc, i) =>
      Math.max(acc, gcd(l(i), r(i)))
    }
  }

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

  println(solve())

}