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: Wrong Answer)

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>

#define FOR(i, a, b) for (int i = (a); i < int(b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= int(a); --i)
#define REP(i, n) FOR(i, 0, n)
#define REP1(i, n) FOR(i, 1, int(n) + 1)
#define RREP(i, n) RFOR(i, 0, n)
#define RREP1(i, n) RFOR(i, 1, int(n) + 1)
#define ALL(c) begin(c), end(c)

int _ = (
#ifndef LOCAL
    std::cin.tie(nullptr), std::ios::sync_with_stdio(false),
#endif
    std::cout.precision(10), std::cout.setf(std::ios::fixed));

using ll = long long;
using ld = long double;
// constexpr auto mod = 1000000007;
using namespace std;

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

  vector<ll> L(N + 1);
  if (N <= 1) {
    cout << 2 << endl;
  }
  else {
    L[0] = 2;
    L[1] = 1;
    FOR(i, 2, N + 1) {
      L[i] = L[i - 1] + L[i - 2];
    }
    cout << L[N] << endl;
  }
  return 0;
}