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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int main() {
    int N;
    scanf("%d", &N);

    long long *L = (long long *) malloc(sizeof(long long) * N);
    L[0] = 2;
    L[1] = 1;

    for (int i = 2; i <= N; i++) {
        long long tmp_sum = 0;
        for (int j = i - 2; j < i; j++) {
            tmp_sum += L[j];
        }
        L[i] = tmp_sum;
    }

    printf("%lld\n", L[N]);
    return 0;
}