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 Rust (1.42.0) (judge verdict: Accepted)

use whiteread::parse_line;

fn calc(n: usize, lucas: &mut Vec<usize>) -> usize {
    if lucas[n] == 0 {
        lucas[n] = calc(n - 1, lucas) + calc(n - 2, lucas)
    }
    lucas[n]
}

fn main() {
    let n: usize = parse_line().unwrap();
    let mut lucas = vec![0; n + 1];
    lucas[0] = 2;
    lucas[1] = 1;

    println!("{}", calc(n, &mut lucas));
}