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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<stdio.h>

long long int l[1000];
long long int Lucas(int n)
{
	long long l1, l2;
	if (n < 0)
		return 0;
	if (n == 0)
		return 2;
	if (n == 1)
		return 1;
	if (l[n] > 0)
		return l[n];
	l1 = Lucas(n - 1);
	l2 = Lucas(n - 2);
	l[n] = l1 + l2;
	return l1 + l2;
}

int main()
{
	int n;
	long long ans;

	scanf("%d", &n);
	
	if(n >= 2)
		ans = Lucas(n);

	printf("%lld", ans);

	return 0;
}