Problem:
Score : 200 points

Problem Statement

It is November 18 now in Japan. By the way, 11 and 18 are adjacent Lucas numbers.

You are given an integer N. Find the N-th Lucas number.

Here, the i-th Lucas number L_i is defined as follows:

L_0=2

L_1=1

L_i=L_{i-1}+L_{i-2} (i≥2)

Constraints

1≤N≤86

It is guaranteed that the answer is less than 10^{18}.

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the N-th Lucas number.

Sample Input 1

5

Sample Output 1

11

L_0=2

L_1=1

L_2=L_0+L_1=3

L_3=L_1+L_2=4

L_4=L_2+L_3=7

L_5=L_3+L_4=11

Thus, the 5-th Lucas number is 11.

Sample Input 2

86

Sample Output 2

939587134549734843

Solution in Scala (2.13.1) (judge verdict: Accepted)

// abc079-b
object Main extends App {
  val n = io.StdIn.readInt

  /* stackoverflow case
  def lucas(i: Int): Long = i match {
    case 0 => 2.toLong
    case 1 => 1.toLong
    case j => lucas(j-1) + lucas(j-2)
  }

  val result = lucas(n)
  println(result)
  */

  // lazy eval and memorize!
  def lucasFrom(a: Long, b: Long): Stream[Long] = a #:: lucasFrom(b, a+b)
  val lucas = lucasFrom(2, 1)
  println(lucas.take(n+1).last)
}