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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
int lucas(int, int[]);

int main(){
  int input;
  int lu[86];
  for(int i = 0; i < 86; i++) lu[i] = 0;
  scanf("%d", &input);
  printf("%d", lucas(input, lu));
  return 0;
}

int lucas(int input, int lu[]){

  if(lu[input] != 0)return lu[input];
	if(input == 0)return 2;
	if(input == 1)return 1;
  lu[input] = lucas(input - 2, lu) + lucas(input - 1, lu);
  return lu[input];
}