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)

object Main {

  @scala.annotation.tailrec
  private def gcd(a: Int, b: Int): Int = {
    val r = a % b
    if (r == 0) b
    else gcd(b, r)
  }

  def main(args: Array[String]): Unit = {
    val n = scala.io.StdIn.readLine().toInt
    val a = scala.io.StdIn.readLine().split(" ").map(_.toInt)
    val m = Array.fill(n, n)(Int.MinValue)

    for {
      i <- 0 until n
      j <- 0 until n
      if i == j
    } m(i)(i) = a(i)

    (0 until n - 1).foreach { i =>
      ((i + 1) until n).foreach { j =>
        m(i)(j) = gcd(m(i)(j-1), a(j))
      }
    }

    val res = (0 until n).map { i =>
      if (i == 0) {
        m(1)(n-1)
      } else if (i == n - 1) {
        m(0)(n-2)
      } else {
        gcd(m(0)(i-1), m(i+1)(n-1))
      }
    }. max

    println(res)
  }

}