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 REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()
#define LL long long
#define pii pair<int,int>
#define pll pair<LL,LL>

using namespace std;

int main(){

    LL N;cin>>N;

    for(int h=1;h<=3500;h++){
        for(int n=1;n<=3500;n++){
            if((4*n*h-N*n-N*h)>0&&(N*h*n)%(4*n*h-N*n-N*h)==0){
                cout<<h<<" "<<n<<" "<<(N*h*n)/(4*n*h-N*n-N*h)<<endl;
                return 0;
            }
        }
    }

    return 0;
}