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)

#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

#define CK(N, A, B) (A <= N && N < B)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define RREP(i, a, b) for (int i = (b - 1); a <= i; i--)
#define F first
#define S second
#define ll long long

const int INF = 1e9;
const long long LLINF = 1e18;

using namespace std;

int dy[] = {0,1,0,-1};
int dx[] = {1,0,-1,0};
int dy8[] = {0,1,1,1,0,-1,-1,-1};
int dx8[] = {1,1,0,-1,-1,-1,0,1};

/*==================================================*/
/*variable*/
int N;
/*==================================================*/
/*function*/

/*==================================================*/

int main() {
    cin>>N;
    long long L0 = 2;
    long long L1 = 1;

    if(N == 1){
        cout<<L1<<endl;
        return 0;
    }

    REP(i,2,N+1){
        long long newL = L0 + L1;
        L0 = L1;
        L1 = newL;
        if(i == N){
            cout<<newL<<endl;
            return 0;
        }
    }

    return 0;
}