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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]

// language: Rust(1.42.0)
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"
// My Library Repositry is at "https://github.com/Loptall/prcn_lib"

/*
    青perfほしいよ〜！
*/

// from std...
use std::cmp::{
    max, min, Ordering,
    Ordering::{Equal, Greater, Less},
    Reverse,
};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::convert::TryInto;
use std::fmt;
use std::mem::swap;
use std::num::{NonZeroU32, ParseIntError};
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Index, IndexMut, Mul, MulAssign, Neg, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
    SubAssign,
};
use std::process::exit;
use std::{f32, f64, i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

// Dep' crates are...
use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_complex::Complex;
use num_integer::{binomial, gcd, lcm, multinomial, Integer};
use num_rational::Rational;
use num_traits::{
    clamp, one, pow, zero, Num, NumAssignOps, NumOps, One, Pow, Signed, Unsigned, Zero,
};
use permutohedron::Heap;
use proconio::{
    derive_readable, fastout, input, is_stdin_empty,
    marker::{Bytes, Chars, Isize1, Usize1},
};
use rand::random;

pub trait Visualize {
    fn visualize(&self, split: &str);
    fn continuous(&self) {
        self.visualize("");
    }
    fn spaces(&self) {
        self.visualize(" ");
    }
    fn lines(&self) {
        self.visualize("\n");
    }
}
macro_rules ! impl_vis_for_sized {($ ($ t : ty ) ,+ ) => {$ (impl Visualize for $ t {fn visualize (& self , _split : & str ) {print ! ("{}" , self ) ; } } ) + } ; }
impl_vis_for_sized! {usize , u8 , u16 , u32 , u64 , u128 , isize , i8 , i16 , i32 , i64 , i128 , String , & str }
impl<T: fmt::Display> Visualize for [T] {
    fn visualize(&self, split: &str) {
        print!("{}", self.iter().join(split));
    }
}
/// macro to output answer improved to println
///
/// this macro will print '\n' at the last.
///
/// # Patterns
///
/// `,`, it means one space, it formats the elements, which is before, space-split.
/// And insert a space after the prefix, unless it is at last.
///
/// `=>`, it means empty string, it formats the element, witch is before, without any split.
/// And insert nothing between two element.
///
/// `;`, it means newline(\n), it formats the element, witch is before, newline-split.
/// And insert a newline after the prefix, unless it is at last.
///
/// # Eample
///
/// ```
/// #[test]
/// fn vis_test() {
///     let a = 1;
///     let b = 2;
///     let c = 3;
///
///     let v = vec!['a', 'b', 'c'];
///
///     // single element test ...
///
///     vis!(a); // 1\n
///     vis!(a,); // 1\n
///     vis!(a =>); // 1\n
///     vis!(a;); // 1\n
///
///     println!();
///
///     vis!(a + b); // 3\n
///
///     println!();
///
///     vis!(v); // a b c\n
///     vis!(v,); // a b c\n
///     vis!(v =>); // abc\n
///     vis!(v;); // a\nb\nc\n
///
///     println!();
///
///     // multi elements connected by common operater test ...
///
///     println!();
///
///     vis!(a, b); // 1 2\n
///     vis!(a, b, c); // 1 2 3\n
///     vis!(a, b, c;); // 1 2 3\n
///
///     println!();
///
///     vis!(a => b); // 12\n
///     vis!(a => b => c); // 123\n
///     vis!(a => b => c ,); // 123\n
///
///     println!();
///
///     vis!(a; b); // 1\n2\n
///     vis!(a; b; c); // 1\n2\n3\n
///     vis!(a; b; c =>); // 1\n2\n3\n
///
///     println!();
///
///     // multi elements connected by different operater test ...
///
///     vis!(a, b; c); // 1 2\n3\n
///     vis!(a; b, c); // 1\n2 3\n
///     vis!(a => b, c); // 12 3\n
///     vis!(a; b => c); // 1\n23\n
///
///     println!();
///
///     vis!(a, v); // 1 a b c\n;
///     vis!(a, v;); // 1 a\nb\nc\n;
///     vis!(a => v =>); // 1abc\n;
///
///     println!("\d");
///     // panic!()
/// }
/// ```
#[macro_export]
macro_rules ! vis {() => {println ! () ; } ; ($ last : expr ; ) => {$ last . lines () ; vis ! () } ; ($ last : expr => ) => {$ last . continuous () ; vis ! () ; } ; ($ last : expr $ (, ) ? ) => {$ last . spaces () ; vis ! () ; } ; ($ first : expr ; $ ($ rest : tt ) * ) => {$ first . lines () ; println ! () ; vis ! ($ ($ rest ) * ) ; } ; ($ first : expr => $ ($ rest : tt ) * ) => {$ first . continuous () ; vis ! ($ ($ rest ) * ) ; } ; ($ first : expr , $ ($ rest : tt ) * ) => {$ first . spaces () ; print ! (" " ) ; vis ! ($ ($ rest ) * ) ; } ; }

pub const MOD10E9_7: usize = 1000000007;
pub const MOD99_: usize = 998244353;
pub const MAX: usize = std::usize::MAX;
pub const PI: f64 = f64::consts::PI;
pub const ASCII_A: u8 = 65;
pub const ASCII_0: u8 = 48;

// code...
// #[fastout]
fn main() {
    input! {
        n: i64
    }

    for h in 1..=3500 {
        for w in 1..=3500 {
            if 4 * h * w - n * w - n * h != 0
                && n * h * w % (4 * h * w - n * w - n * h) == 0
                && n * h * w / (4 * h * w - n * w - n * h) > 0
            {
                vis!(h, n * h * w / (4 * h * w - n * w - n * h), w);
                return;
            }
        }
    }
}