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)

#![allow(unused_imports)]

use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::fmt;
use std::io::{self, BufWriter, Read, StdinLock, Write};
use std::ops::{Add, Div, Mul, Sub};
use std::str::{self, FromStr};


fn solve(n: usize) -> u64 {
    let mut v = vec![0; n + 1];
    v[0] = 2;
    v[1] = 1;
    for i in 2..n + 1 {
        v[i] = v[i - 1] + v[i - 2];
    }
    v[n]
}


fn main() {
    let stdin = io::stdin();
    let mut sc = Scanner::new(stdin.lock().bytes());
    println!("{}", solve(sc.next()));
}


struct Scanner<R: Read> {
    buf: Vec<u8>,
    bytes: io::Bytes<R>,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(bytes: io::Bytes<R>) -> Self {
        Scanner {
            buf: Vec::with_capacity(1024),
            bytes: bytes,
        }
    }

    fn next<T: FromStr>(&mut self) -> T
    where
        <T as FromStr>::Err: fmt::Debug,
    {
        let buf = &mut self.buf;
        buf.clear();
        self.bytes
            .by_ref()
            .map(Result::unwrap)
            .skip_while(|&c| c == ' ' as u8 || c == '\n' as u8)
            .take_while(|&c| !(c == ' ' as u8 || c == '\n' as u8))
            .foreach(|c| buf.push(c));
        str::from_utf8(&buf).unwrap().parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where
        <T as FromStr>::Err: fmt::Debug,
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<T1: FromStr, T2: FromStr>(&mut self, n: usize) -> Vec<(T1, T2)>
    where
        <T1 as FromStr>::Err: fmt::Debug,
        <T2 as FromStr>::Err: fmt::Debug,
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<T1: FromStr, T2: FromStr, T3: FromStr>(&mut self, n: usize) -> Vec<(T1, T2, T3)>
    where
        <T1 as FromStr>::Err: fmt::Debug,
        <T2 as FromStr>::Err: fmt::Debug,
        <T3 as FromStr>::Err: fmt::Debug,
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
    where
        <T as FromStr>::Err: fmt::Debug,
    {
        (0..m).map(|_| self.vec(n)).collect()
    }
}


trait Foreach {
    type Item;
    fn foreach<F: FnMut(Self::Item)>(self, f: F);
}

impl<T, I: Iterator<Item = T>> Foreach for I {
    type Item = T;

    fn foreach<F: FnMut(T)>(self, mut f: F) {
        self.fold((), move |(), x| f(x));
    }
}


#[allow(dead_code)]
fn print_yesno(x: bool, yes: &'static str, no: &'static str) {
    println!("{}", if x { yes } else { no });
}


#[allow(dead_code)]
fn print_foreach<T: fmt::Display, I: IntoIterator<Item = T>>(xs: I) {
    let stdout = io::stdout();
    let mut stdout = BufWriter::new(stdout.lock());
    for x in xs.into_iter() {
        writeln!(stdout, "{}", x).unwrap();
    }
    stdout.flush().unwrap();
}


#[allow(dead_code)]
fn print_or<T: fmt::Display>(x: Option<T>, or: &'static str) {
    if let Some(x) = x {
        println!("{}", x);
    } else {
        println!("{}", or);
    }
}