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: Accepted)

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

template<typename integer>
integer __lcm(integer a, integer b) {
  return (a * b) / __gcd(a, b);
}

int main() {
  int n;
  cin >> n;

  vector<long long> dp(87);
  dp[0] = 2;
  dp[1] = 1;

  rep (i, 85) {
    dp[i+2] = dp[i] + dp[i+1];
  }

  cout << dp[n] << endl;
  return 0;
}