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<bits/stdc++.h>
using namespace std;
const long long INF = (1LL << 32);
const long long MOD = 1000000007;
const long double PI = 3.1415926;
#define FOR(i,r,n) for(ll i = (ll)(r); i < (ll)(n); i++)
#define RFOR(i,r,n) for(ll i=(ll)(n-1);i>=r;i--)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(x) x.begin(),x.end()
#define RALL(x) x.rbegin(),x.rend()
typedef long long int ll;
typedef vector<ll> vi;
typedef vector<pair<ll, ll>> vp;
typedef vector<string> vs;
typedef vector<char> vc;
typedef list<ll> lst;
typedef pair<ll, ll> P;

ll n, m, k, ans = 0, sum = 0, cnt = 0;
string s;
char c;

#define Endl endl

/*--------------------template--------------------*/


int main() {
    cin >> n;
    FOR(i, 1, 3501) {
        FOR(j, 1, 3501) {
            if (4 * i * j - n * (i + j) == 0|| (n * i * j) % (4 * i * j - n * (i + j))!=0) {
                continue;
            }
            ll a = ((n * i * j) / (4 * i * j - n * (i + j)));
            if (a <= 0) {
                continue;
            }
            if (n == 4 * i*j*a / (i*j+j*a + a*i)) {
                cout << i << " " << j << " " << a << endl;
                return 0;
            }
        }
    }
}