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 Python (3.4.3) (judge verdict: Wrong Answer)

import re

def solution(N):
    if (N < 1 or N > 86):
        exit()
    
    n = lucas(3, 1, 3, N)
    # print (n)

def lucas(a, prev_a, counter, max_counter):
    if max_counter == 1:
        return 2
    if max_counter == 2:
        return 1
    if counter < max_counter:
        counter = counter + 1
        ans = a + prev_a
        lucas(ans, a, counter, max_counter)
    else:
        return (a + prev_a)



if __name__ == '__main__':
    N = input()
    if re.match('^[0-9]{1,}$', N):
        solution(int(N))