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)

import java.util.*;
import java.math.BigInteger;
// warm-up
public class Main {

	static void solve() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt()-1;
		BigInteger[] c = {new BigInteger("2"), BigInteger.ONE};
		while (N-->0) {
			BigInteger t = c[0].add(c[1]);
			c[0] = c[1];
			c[1] = t;
		}
		System.out.println(c[1]);
		sc.close();		
	}

	public static void main(String args[]) {
		solve();
	}

}