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 <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>

using namespace std;

//using
using VI = vector<int>;
using VVI = vector<VI>;
using VS = vector<string>;
using PII = pair<int, int>;
using LL = long long;

//repetition
#define FOR(i,a,b) for(LL i=(a);i<(b);i++)
#define REP(i,n)  for(LL i=0;i<(n);i++)

//constant
const int INF = 1 << 29;
const double EPS = 1e-10;
const double PI = acos(-1.0);

//debug
#define dump(x)  cout << #x << " = " << (x) << endl;

int main() {
  LL N;
  cin >> N;
  // 4hnw == N(hn + nw + hw)

  FOR(i, 1, 3501) {
    FOR(j, i, 3501) {
      if (4*i*j < N*(i + j + j*i) & 4*i*j*3500 > N*(i*3500 + 3500*j + j*i)) {
        FOR(k, j, 3501) {
          if(4*i*k*j == N*(i*k + k*j + j*i)) {
            cout << i << ' ' << j << ' ' << k << endl;
            return 0;
          }
        }
      }
    }
  }
  // cout << "error";
  // cout << i << ' ' << j << ' ' << k << endl;
  return 0;
}