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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		Arrays.fill(memo, -1);
		Main main = new Main();
		System.out.println(main.searchRucasNum(N));

	}
	static long[] memo= new long[87];
	public long searchRucasNum(int n) {
		long ans;
		if (memo[n] != -1) {
			ans = memo[n];
		}else {
			if (n == 0) {
				ans =  2;
			}else if (n == 1) {
				ans =  1;
			}else {
				ans =  searchRucasNum(n-1)+searchRucasNum(n-2);
			}
		}
		if (memo[n] == -1) {memo[n] = ans;}
		return ans;
	}

}