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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define repr(i, n) for (int i = n-1; i >= 0; i--)
#define ALL(x) x.begin(), x.end()
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
const int mod = 1e9+7;
const int INF = 1e9;
const int MAX = 1e6;

int main() {
    int n;
    cin >> n;
    vector<ll> l(n+1);
    rep(i, n+1) {
        if (i == 0) l[i]= 2;
        else if (i == 1) l[i] = 1;
        else l[i] = l[i-1] + l[i-2];
    }
    cout << l[n] << endl;
}