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 Ruby (2.3.3) (judge verdict: Accepted)

#! ruby -Ku

class Fibonatchi
	@@memo = []

	def initialize()
		@@memo[87] = nil
	end

	def fib(n)
		return @@memo[n] if @@memo[n] != nil
		return 2 if n == 0
		return 1 if n == 1
		return @@memo[n] = fib(n-1) + fib(n-2)
	end
end

num = gets.to_i

cls = Fibonatchi.new()
puts cls.fib(num)