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<iostream>
#include <bits/stdc++.h>
#include <string>
#include <vector>
#include <algorithm>
#include <set>
using namespace std;

long long ryuka(int n){

    long long array[n] ;
    array[0] = 2 ;
    array[1] = 1 ;

    for(int i=2;i<=n;++i){
        array[i] = array[i-1] + array[i-2] ;
    }

    return array[n] ;
}


int main() {

    int n ;
    cin >>n  ;

    cout << ryuka(n) << endl  ;

 return 0 ;
}