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)

#include <bits/stdc++.h>
typedef long long lint;

#define PI acos(-1)
#define INF64 1LL << 60
#define INF32 1 << 29
#define all(a) (a).begin(), (a).end()
#define INV ((long long int)1000000007)

using namespace std;

void execute()
{
	int N;
	cin >> N;

	lint ans = 0;
	lint a = 2;
	lint b = 1;
	for (int i = 0; i < N - 1; i++)
	{
		ans = a + b;
		a = b;
		b = ans;
	}

	cout << ans << endl;
	return;
}

int main()
{
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
	execute();

	int stop;
	cin >> stop;

	return 0;
}