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)

#define rep(i, n) for (int i=0; i < (int)(n); i++)
#include <bits/stdc++.h>
using namespace std;

int main() {
  int n;
  cin >> n;
  vector<int> l(n);
  l.at(0) = 2;
  l.at(1) = 1;
  
  if(n == 0){
    cout << l.at(0) << endl;
  }else if(n == 1){
    cout << l.at(1) << endl;
  }else{
    for(int i=3; i < n; i++){
      l.at(i) = l.at(i-1) + l.at(i-2);
    }
    cout << l.at(n) << endl;
  } 
}