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)

#!/usr/bin/ruby 
#encoding: utf-8

LucasAry = Array.new(100,-1)

def lucas(n)
  if n == 0
    LucasAry[0] = 2
    return LucasAry[0]
  elsif n == 1
    LucasAry[1] = 1
  else
    if LucasAry[n] == -1 then
      LucasAry[n] = lucas(n-1) + lucas(n-2)
      return LucasAry[n]
    else
      return LucasAry[n]
    end
  end
end

n = gets.to_i
puts lucas(n)