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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
 

//result = Math.pow(num1, num3)
//StringBuffer str = new StringBuffer(hoge1);
//String hoge2 = str.reverse().toString();
//map.containsKey(A)

//Map<String, Integer> map = new HashMap<String, Integer>(n);
/*for ( キーのデータ型 key : マップの名前.keySet() ) {
	データのデータ型 data = マップの名前.get( key );
	
	// keyやdataを使った処理;
}*/
//int i = Integer.parseInt(s);

//ArrayList<String> cc = new ArrayList<>(n);
//Collections.sort(list);
//Array.sort(list);
//Arrays.asList(c).contains("a")
//list.set(1,"walk");
public class Main {
	private static Scanner sc = new Scanner(System.in);
	static void p(String ans) {System.out.println(ans);};
	static void p(int ans) {System.out.println(ans);};
	static void p(long ans) {System.out.println(ans);};
	static void p(double ans) {System.out.println(ans);};
	static String s;
	public static void main(String[] args) {
		int N=sc.nextInt();
		long memo[]=new long[100];
		for(int i=0;i<=N;i++) {
			if(i==0) {
				memo[i]=2;
				continue;
			}else if(i==1) {
				memo[i]=1;
				continue;
			}
			memo[i]=memo[i-1]+memo[i-2];	
		}
		p(memo[N]);
		
		
		
	}
	
	

	
	
	
}