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 C++14 (Clang 3.8.0) (judge verdict: Accepted)

// This file is a "Hello, world!" in C++ language by GCC for wandbox.
#include <iostream>
#include <cstdlib>

using namespace std;



int main()
{
    long long N; cin >> N;
    for (int i = 1; i <= 3500; i++){
        for (int j = 1; j <= 3500; j++){
            if (4*j*i - N*j - N*i > 0){
                if ( N*i*j % (4*j*i - N*j - N*i) == 0){
                    cout << i << " " << j << " " << N*i*j / (4*j*i - N*j - N*i) << endl;
                    return 0;
                }
            }
        }
    }

}