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)

/*input
4664
*/
#include "bits/stdc++.h"
using namespace std;
#define ll long long int
#define pii pair<ll,ll>
#define list vector<ll>
#define mp make_pair
#define vp vector< pair<ll,ll> >
#define in insert
#define pb push_back
#define ft first
#define sd second
#define matrix vector< vector<ll> >
#define all(x) x.begin(),x.end()
#define line string
#define rall(x) x.rbegin(),x.rend()
#define f(i,n) for(ll i=1;i<=n;i++) 
ll mod=(ll)(1e9+7);
ll total[101];
ll N;
ll solve(ll pos,ll cnt,ll foo)
{
	if(cnt==0)return foo;
	ll ans=0;
	for(ll i=1;i<=N;i++)
		if(i!=pos)
			{
					ans+=solve(i,cnt-1,foo+total[pos]);
			}
	return ans;
}
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	ll N;
	cin>>N;
	for(ll h=1;h<=3500;h++)
		for(ll n=1;n<=3500;n++)
		{
			ll num=h*N*n;
			ll deno=4*h*n-(n+h)*N;
			if(num>0&&deno>0&&num%deno==0)
			{
				cout<<h<<" "<<n<<" "<<(num/deno)<<endl;
				return 0 ;
			}
		}
	return 0 ;
}