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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

//package reedeka;
import java.util.*;
import java.math.*;
public class Main {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n;
		n = sc.nextInt();
		//System.close();
		long t1 = 2, t2 = 1;
		int i;
		long s = t2;
		if(n==0) {
			s = t1;
		}
		else {
		for(i=2; i<=n; i++) {
			s = t1 + t2;
			t1 = t2;
			t2 = s;
		}
		}
		System.out.println(s);
	}
}