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 (1.15.1) (judge verdict: Accepted)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
                    .map(|e| e.parse().ok().unwrap())
                    .collect()
}

fn main() {
    let n: u32 = read::<u32>();

    let mut lucas: Vec<i64> = Vec::new();
    lucas.push(2);
    lucas.push(1);

    for i in 2..n+1 {
        // ループカウンタのiをas usizeで配列へアクセスできるようにしている
        let u = i as usize;

        let mut nw = lucas[u-2];
        nw = nw + lucas[u-1];
        lucas.push(nw);
    }

    let n = n as usize;
    println!("{}", lucas[n]);

}