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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
 
int lucas(int n){
  int num;
  vector<int> vec(n);
  if (n == 0) {
    vec.at(0) = 2;
    return vec.at(0);
  }
  else if (n == 1){
    vec.at(1) = 1;
    return vec.at(1);
  }
  else if (vec.at(n) == 0) vec.at(n) = lucas(n-1) + lucas(n-2);
  else return vec.at(n);
}
 
int main(){
  int N ;
  cin >> N;
  cout << lucas(N) << endl;
}