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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func solve() {
	var N int
	fmt.Scan(&N)

	fmt.Println(luca(N))
}

func luca(N int) int {
	ans := 0
	pre := 1
	prepre := 2
	if N == 0 {
		return 2
	}
	if N == 1 {
		return 1
	}
	for i := 2; i <= N; i++ {
		ans = pre + prepre
		prepre = pre
		pre = ans
	}
	return ans
}

func main() {
	solve()
}