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 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <utility>
#include <vector>

using namespace std;
using ll = long long;

constexpr ll infl = 1000000000000000007LL;
constexpr int inf = 1000000007;

int main() {
    ll n; cin >> n;
    for (ll h = 1; h <= 3500; ++h) {
        for (ll w = 1; w <= 3500; ++w) {
            ll p = n * h * w;
            ll q = 4 * h * w - n * w - n * h;
            if (q != 0 && p % q == 0 && p / q >= 1) {
                cout << h << " " << (p / q) << " " << w << endl;
                return 0;
            }
        }
    }
    assert(false);
    return 0;
}