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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <limits.h>
int main(void)
{
    long int N, h, n, w;
    scanf("%ld", &N);
    
        for(h=1;h<=3500;h++){
            for(n=1;n<=3500;n++){
                if((4*h*n-N*n-N*h)!=0){
                    if((n*h*N)/(4*h*n-N*n-N*h)>0 &&
                       (n*h*N)%(4*h*n-N*n-N*h)==0){
                        w=(n*h*N/(4*h*n-N*n-N*h));
                        if(4*h*n*w==N*n*w+N*h*w+N*h*n){
                            printf("%ld %ld %ld\n", h, n, w);
                            return 0;
                        }
                    }
                }
            }
        }

        return 0;
}