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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'
function Main(input){
  var N=input.trim()-0;
  var a=1,b=1;
  roop: while(true){
    for(b=a;b<=3500;b++){
      if(4*a*b-N*a-N*b>0&&(a*b*N)%(4*a*b-N*b-N*a)===0)
        break roop;
      }
    a++;
  }
  var c=Math.round(a*b*N/(4*a*b-N*a-N*b));
  console.log(a+' '+b+' '+c);
}

Main(require('fs').readFileSync('/dev/stdin','utf8'));