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 java.util.Scanner
object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt
  val as = Array.fill(n)(sc.nextInt)
  def gcd(l: Int, r: Int): Int = if (r == 0) l else if (l % r == 0) r else gcd(r, l % r)
  val gcdsL = as.scanLeft(0)((z, a) => gcd(z, a))
  val gcdsR = as.scanRight(0)((a, z) => gcd(z, a))
  println(gcdsL.zip(gcdsR.tail).map(z => gcd(z._1, z._2)).max)
}