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: Wrong Answer)


import java.math.BigInteger;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		no2();
	}

	static void no2() {
		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();

			BigInteger f0 = new BigInteger("2");
			BigInteger f1 = new BigInteger("1");
			BigInteger f2 = null;

			if (n == 1) {
				System.out.println(f0);
				return;
			}
			if (n == 2) {
				System.out.println(f1);
				return;
			}

			for (int i = 3; i <= n; i++) {
				f2 = f0.add(f1);
				f0 = f1;
				f1 = f2;
			}

			System.out.println(f2);
		}
	}
}