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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        String line = buffer.readLine();
        int x = Integer.parseInt(line);

        System.out.println(lucas(x));
    }

    public static long lucas(int x) {
      long l0 = 2;
      long l1 = 1;
      long lx = 0;

      if (x == 0){
        return l0;
      } else if (x == 1){
        return l1;
      } else {
        for (int i = 2; i <= x; i++){
          lx = l0 + l1;
          l0 = l1;
          l1 = lx;
        }

        return lx;
      }
    }

}