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 _CRT_SECURE_NO_WARNINGS

#include <iostream>
#include <string>
#include <vector>
#include <cmath>
#include <fstream>
#include <set>
#include <utility>
#include <algorithm>
#include <queue>
#include <stack>
#include <deque>
#include <numeric>
#include <sstream>
#include <list>
#include <map>
#include <stdlib.h>
#include <time.h>

#define rep(i,p,n) for(int i=(int)p;i<(int)n;i++)
#define repp(i,p,n) for(int i=(int)p;i>=(int)n;i--)
#define Sort(x) sort(x.begin(),x.end());
#define ll long long
#define INF 2000000000

using namespace std;
vector<ll> memo(87, -1);
ll luca(int x) {
	if (x == 0)return 2;
	else if (x == 1)return 1;

	if(memo[x]==-1) return memo[x]=luca(x - 1) + luca(x - 2);
	else return memo[x];
}

int main() {
	int n;
	cin >> n;
	//n--;
	cout << luca(n) << endl;
	return 0;
}