Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

#[derive(Debug, Clone, Copy)]
struct Ratio(i64, i64);  // (numerator / denominator)
impl Ratio {
    fn new(a: i64, b: i64) -> Self {
        let x = Self::gcd(a.abs(), b.abs());
        let sign = if b > 0 { 1 } else { -1 };
        Ratio(sign * a / x, sign * b / x)
    }
    fn inv(self) -> Self { Self::new(self.1, self.0) }
    fn gcd(a: i64, b: i64) -> i64 { if b == 0 { a } else { Self::gcd(b, a % b) } }
    fn lcm(a: i64, b: i64) -> i64 { a / Self::gcd(a, b) * b }
}
impl std::ops::Neg for Ratio {
    type Output = Self;
    fn neg(self) -> Self { Ratio(-self.0, self.1) }
}
impl std::ops::Add for Ratio {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        let num = Self::lcm(self.1, other.1);
        Ratio(self.0 * num / self.1 + other.0 * num / other.1, num)
    }
}
impl std::ops::Sub for Ratio {
    type Output = Self;
    fn sub(self, other: Self) -> Self { self + (-other) }
}
impl std::ops::Mul for Ratio {
    type Output = Self;
    fn mul(self, other: Self) -> Self { Self::new(self.0 * other.0, self.1 * other.1) }
}
impl std::ops::Div for Ratio {
    type Output = Self;
    fn div(self, other: Self) -> Self { Self::new(self.0 * other.1, self.1 * other.0) }
}

fn main() {
    let mut sc = Scanner::new();
    let n: i64 = sc.cin();
    for x in 1..3501 {
        for y in 1..3501 {
            let r = Ratio(4, n) - Ratio(1, x) - Ratio(1, y);
            if r.0 == 1 && r.1 > 0 {
                put!(x, y, r.1);
                return;
            }
        }
    }
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}