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 main() {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  let mut s: Vec<&str> = buf.split_whitespace().collect();

  let mut n: i32 = s[0].parse().unwrap();

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

  for i in 2..n+1 {
    let u = i as usize;
    let mut new = lucas[u-2];
    new = new + lucas[u-1];
    lucas.push(new);
  }
  
  let n = n as usize;
  println!("{}",lucas[n]);
}