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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import Control.Monad
import Data.List
import Data.Maybe
main = do
  n <- readLn
  let ans =
        [ [a, b, c] | a <- [1 .. 3500 :: Int], b <- [1 .. 3500 :: Int], let ue = n * a * b, let sita = if 4 * a * b - n * (a + b) == 0 then 9999 else 4 * a * b - n * (a + b), let c = div ue sita, mod ue sita == 0 && c > 0
        ]

  mapM print $ head ans