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)

table :: [Int]
table = loop 0 []
  where
    loop i xs
      | i > 86 = xs
      | i == 0 = loop (i+1) (2:xs)
      | i == 1 = loop (i+1) (1:xs)
      | otherwise = loop (i+1) (a+b:xs)
        where
          [a,b] = take 2 xs
      
main = do
  n <- readLn :: IO Int
  print $ table !! (86 - n)