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>
#define I64 "%I64d"
#define RAN(v)v.begin(),v.end()
#define pb push_back
#define lb lower_bound
#define ub upper_bound
using namespace std;
typedef long long ll;
template<class T>
inline void upd1(T&a,T b){a>b?a=b:0;}
template<class T>
inline void upd2(T&a,T b){a<b?a=b:0;}
struct ano{
	operator ll(){
		ll x=0,y=0,c=getchar();
		while(c<48)
			y=c==45,c=getchar();
		while(c>47)
			x=x*10+c-48,c=getchar();
		return y?-x:x;
	}
}buf;
int main(){
	ll n=buf;
	for(int i=1;i<=3500;++i)
		for(int j=1;j<=3500;++j){
			ll a=n*i*j,b=4*i*j-n*(i+j);
			if(b>0&&a%b==0)
				return!printf("%d %d %lld\n",i,j,a/b);
		}
}