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 {
  def main(args: Array[String]): Unit = {
    val n = StdIn.readLine.toInt
    val as = StdIn.readLine.split(" ").map(_.toInt)

    //(0 +: as :+ 0).foreach {println}  // 別にこれいらないか

    val l = Array.fill(n + 2)(0)
    val r = Array.fill(n + 2)(0)

    for (i <- 1 to n) {
      l(i) = gcd(l(i - 1), as(i - 1))
    }

    for (i <- n to 1 by -1) {
      r(i) = gcd(r(i + 1), as(i - 1))
    }

    println((1 to n).toList.map(i => gcd(l(i - 1), r(i + 1))).max)
  }

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