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>
#define df 0


int main(){
  int n;
  scanf("%d",&n);

  long int a,b,c=0;
  if(n%2==0){
    a=n;b=n;c=n/2;
  }else if(n%3==0){
    a=n/3;b=n*2;c=n*2;
  }
   else {
    for(a=3*n/4;a>0;a--){
      for(b=2*a*n/(4*a-n);b>0 && 4*a*b>n*(a+b) ;b--){
	if(n*a*b%(4*a*b-n*a-n*b)==0){
	  c=n*a*b/(4*a*b-n*a-n*b);
	  break;
	}
      }
      if(c)break;
    }
  }

  printf("%ld %ld %ld",a,b,c);
  return 0;
}


/// confirm df==0 ///