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 <stdlib.h>
#include <string.h>
#include <math.h>

int main(void){
  long int i, j, k;
  int N, f=0;
  scanf("%d",&N);

  for(i=1;i<=3500;i++){
    if(4*i<N) continue;
    for(j=i;j<=3500;j++){
      if(4*i*j<N*(i+j)) continue;
      for(k=j;k<=3500;k++){
	if(4*i*j*k==N*(i*j+j*k+k*i)){f=1;  break;}
	if(4*i*j*k==N*(i*j+j*k+k*i)) break;
      }
      if(f==1) break;
    }
    if(f==1) break;
  }
  printf("%ld %ld %ld\n",i,j,k);
  return 0;
}