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)


n = gets.to_i

val = Rational(4, n)

x = 1
cnt = 0
ans = []
loop do
  r = Rational(1, x)
  if (val - r).to_f >= 0 then
    val -= r
    ans.push(x)
    cnt += 1
    next
  end
  break if val.to_f < 0 or cnt == 2
  x += 1
end

if (val.numerator) == 1 and cnt == 2 then
  ans.push(val.denominator)
end

if ans.length == 1 then
  ans = [ans[0]*3, ans[0]*3, ans[0]*3]
elsif ans.length == 2 then
  ans = [ans[0], ans[1]*2, ans[1]*2]
end

puts "#{ans[0]} #{ans[1]} #{ans[2]}"