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.Scanner;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		long N = scan.nextLong();
		if(N < 1 || N > 86){
			return;
		}
		if(N == 0){
			System.out.println(2);
			return;
		}
		
		if(N == 1){
			System.out.println(1);
			return;
		}
		if(N == 2){
			System.out.println(3);
			return;
		}
		
		if(N >= 3){
			long i = 0;
			long sum = 0;
			long current = 3;
			long before = 1;
			
			while(i < N-2){
				sum = before + current;
				before = current;
				current = sum;
				i++;
			}
			
			System.out.println(sum);
			return;
		}	
		
	}

}