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 Go (1.6) (judge verdict: Accepted)

package main
import "fmt"

func main() {

  var result uint64
  var n int
  fmt.Scan(&n)
  
  result = lucas(n)
  fmt.Print(result)
}

func lucas(n int) uint64 {
  var prev uint64 = 2
  var thiv uint64 = 1
  var result uint64 = 0
  if n == 0 {
    return 2
  } else if n == 1 {
    return 1
  }
  for  i  := 2 ; i<= n ; i++ {
    result = thiv + prev
    prev = thiv
    thiv = result
  }
  return result
}