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.util.*;

public class Main {
  static long[] dp;
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    dp = new long[N + 1];
    for(int i = 0; i <= N; i++) {
      dp[i] = -1;
    }
    System.out.println(searchLucas(N));
  }
  
  public static long searchLucas(int k) {
    if(k == 0) {
      dp[k] = 2;
    } else if(k == 1) {
      dp[k] = 1;
    }
    if(dp[k] != -1) {
      return dp[k];
    } else {
      return dp[k] = searchLucas(k-1) + searchLucas(k-2);
    }
  }
}