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;
typedef long long ll;
typedef pair<ll, ll> P;
#define rep(i,n) for (ll i = 0; i < (n); ++i)
#define vcout(v) rep(i,v.size()) cout << v[i] << " "; cout << endl
#define mcout(m) rep(j,m.size()){vcout(m[j]);}
const ll MOD = 1e9 + 7;

int mainsolve(){


	ll n; cin >> n;


	for(ll a = 1; a <= 3500; a++){
		for(ll b = a; b <= 3500; b++){
			ll d = 4*a*b - n*b - n*a;

			if(d==0 && n*a*b == 0){
				printf("%lld %lld %lld\n",a,b,1);
				return 0;
			}
			
			if(d>0 && n*a*b % d == 0 && n*a*b / d > 0){
				printf("%lld %lld %lld\n",a,b,n*a*b / d);
				return 0;				
			}
			
		}
	}


	assert(false);
}

int main(){

	return mainsolve();
}