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: Runtime Error)

package atcoder;

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();

        //リュカ数を求める
        long L[] = new long[N+1];
        for (int i = 0; i <= N; i++) {
            if (i == 0) {
                L[i] = 2;
            } else if (i == 1) {
                L[i] = 1;
            } else {
                L[i] = L[i-1] + L[i-2];
            }
            //System.out.println("L[" + i + "]：" + L[i]);
        }

        //System.out.println(N + "番目のリュカ数：" + L[N]);
        System.out.println(L[N]);
    }

}