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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;

namespace AtCoder {
	class Program {
		public static void Main() {
			int n = int.Parse(Console.ReadLine());
			for (int a = 1; a <= 3500; a++) {
				for (int b = 1; b <= 3500; b++) {
					// 4/n = 1/a + 1/b + 1/c
					// 4abc = nbc + nac + nab
					// 4abc - nbc - nac = nab
					// c (4ab - na - nb) = nab
					// c = nab / (4ab - na - nb)
					long x = n * a * b;
					long y = 4 * a * b - n * a - n * b;
					if (x > 0 && y > 0 && x % y == 0) {
						long c = x / y;
						Console.WriteLine($"{a} {b} {c}");
						return;
					}
				}
			}
		}
	}
}