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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

    private static Scanner sc;

    public Main() {
    }

    public static void main(String[] args) {
        sc = new Scanner(System.in);
        new Main().solve();
    }

    private void solve() {
        int N = sc.nextInt();
        Arrays.fill(dp, -1);
        System.out.println(luca(N));
    }
    
    long[] dp = new long[90];
    private long luca(int n) {
        if (dp[n] != -1) {
            return dp[n];
        }
        
        if (n == 0) {
            return 2;
        }
        if (n == 1) {
            return 1;
        }
        
        return dp[n] = luca(n - 2) + luca(n - 1);
    }
}