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 OCaml (4.02.3) (judge verdict: Accepted)

(*
ocamlfind ocamlopt -package batteries -linkpkg main.ml -o a.out
*)
open Batteries

let n = Scanf.sscanf (read_line ()) "%d" ( fun n -> n)

let rec f lst n =
        match lst with
                  [] -> 0
                | first :: [] -> 0 
                | first :: second :: rest -> 
                        let luca = first + second in
                                if n = 0 then
                                        luca
                                else
                                        f (luca :: lst) (n - 1)

let () =
        (
                if n = 0 then
                        2
                else
                if n = 1 then
                        1
                else
                        f [1; 2] (n - 2)
        )
        |> Printf.printf "%d\n"