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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<string>
#include<algorithm>
#include<cstring>
#include<iostream>

using namespace std;
long long L(int n);
int main()
{
	int n;
	long long result;
	scanf("%d",&n);
	result=L(n);
	printf("%d\n",result);
	return 0;
}
long long L(int n)
{
	if(n==0)
		return 2;
	else if(n==1)
		return 1;
	else
		return(L(n-1)+L(n-2));
}