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 Ruby (2.3.3) (judge verdict: Wrong Answer)

input =gets.to_i
def func(b,nu, de)
  ans =[b]
  if nu == 1
    ans.push(de*2).push(de*2)
  elsif nu == 3
    b = de/3 +1
    cal = Rational(3, de) - Rational(1, b)
    c = cal.denominator
    d = cal.numerator
    ans.push(b).push(c*d)
  end
end


if input%2 == 0
  a = input/2
  if a%2 == 0
  ans = [input*3/4,input*3/4,input*3/4]
  else
    b = input/2
    c = b*2
    ans=[b,c,c]
  end
else
  b = input/4 + 1
  cal = Rational(4, input) - Rational(1, b)
  ans = func(b,cal.numerator, cal.denominator)
end

print ans[0].to_s+' '+ans[1].to_s+' '+ans[2].to_s