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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.Array as A
import Data.Array ((!))

main :: IO ()
main = print . (lucas !) . read =<< getLine
    
lucas :: A.Array Int Int
lucas = A.array (0, 86) [(i, lucaNum i)|i<-[0..86]]
    where 
    lucaNum 0 = 2
    lucaNum 1 = 1
    lucaNum n = lucas!(n-1) + lucas!(n-2)