Problem:
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Fibonacci Number

Write a program which prints $n$-th fibonacci number for a given integer $n$. The $n$-th fibonacci number is defined by the following recursive formula:

\begin{equation*}
fib(n)= \left \{
\begin{array}{ll}
1　 & (n = 0) \\
1　 & (n = 1) \\
fib(n - 1) + fib(n - 2) & \\
\end{array}
\right.
\end{equation*}

Input

An integer $n$ is given.

output

Print the $n$-th fibonacci number in a line.

Constraints

$0 \leq n \leq 44$

Sample Input 1

3

Sample Output 1

3

Solution in Scala (judge verdict: Wrong Answer)

object Main extends App {
  val fibs: Array[Option[Int]] = Array.fill(45)(None)
  val n: Int = io.StdIn.readInt()
  fibs(0) = Some(1); fibs(1) = Some(1)
  println(fib(n))
  for(i <- 0 to 44) println(fib(i))

  def fib(n: Int): Int = fibs(n) match {
    case None =>
      val fibN: Int = fib(n-1) + fib(n-2)
      fibs(n) = Some(fibN)
      fibN
    case Some(x) => x
  }
}