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.util.*;

class Main {
   public static void main(String[] args)
   {
      Scanner scan = new Scanner(System.in);

      long[] Luca = new long[87];
      int    N    = scan.nextInt();
      Luca[0] = 2;
      Luca[1] = 1;
      for(int i = 2; i < N + 1; i++){
          Luca[i] = Luca[i - 1] + Luca[i - 2];
          System.out.println(Luca[i] = Luca[i - 1] + Luca[i - 2]);
          }
      System.out.println(Luca[N]);
   }
}