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: Runtime Error)

import java.util.Scanner

import scala.annotation.tailrec

object Main {
  def main(args: Array[String]) = {
    val sc = new Scanner(System.in)
    val N = sc.nextInt()
    val As = List.fill(N)(sc.nextInt())

    val left = As.scanLeft(0) {(pre, x) => gcd(pre, x)}
    val right = As.scanRight(0) {(pre, x) => gcd(pre, x)}

    val ret = for(i <- 0 to As.size) yield {
      gcd(left(i), right(i + 1))
    }
    println(ret)
  }

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