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 (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

object Main {
//  def getLucas(n: Int): Long = {
//    val l: Long = if (n == 0) {
//      2
//    } else if (n == 1) {
//      1
//    } else {
//      getLucas(n - 1) + getLucas(n - 2)
//    }
//    return l
//  }

//  def getLucas(n: Int): Long = {
//    var lucasArr: Array[Long] = Array.empty
//    lucasArr = lucasArr :+ 2.toLong
//    lucasArr = lucasArr :+ 1.toLong
//    for (i <- (2 to n)) {
//      lucasArr = lucasArr :+ (lucasArr(i - 1) + lucasArr(i - 2)).toLong
//    }
//    lucasArr(n)
//  }

  def main(args: Array[String]): Unit = {
    val input = new Scanner(System.in)
    val n: Int = input.nextInt

    var lucasArr: Array[Long] = Array.empty
    lucasArr = lucasArr :+ 2.toLong
    lucasArr = lucasArr :+ 1.toLong
    for (i <- (2 to n)) {
      lucasArr = lucasArr :+ (lucasArr(i - 1) + lucasArr(i - 2)).toLong
    }
    println(lucasArr(n))
  }
}