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 <stdio.h>
#include <iostream>
#include <sstream>
#include <vector>
#include <queue>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <set>
#include <algorithm>
#include <math.h>
using namespace std;
using i64 = int64_t;
#define rep(i, n) for(int i=0;i<n;++i)
#define rep2(i, x, n) for(int i=x;i<n;++i)

int main()
{   
    int n;
    cin >> n;
    vector<i64> l(n+1);
    l[0] = 2;
    l[1] = 1;
    rep2(i,2,n+1) l[i] = l[i-1]+l[i-2]; 

    cout << l[n] << endl;
    return 0;
}