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: Runtime Error)

n=gets.to_i
t=1.0*4/n
a=[]
b=[0]
1.upto(3500) do |i|
  b<< 1.0/i
end
1.upto(3500) do |i|
  gg = b[i]
  i.upto(3500) do |j|
    g = t-gg - b[j]
    if g>0
      if (ggg=(1.0/g).to_i) <= 3500 && (g-(b[ggg])).abs <= 0.00000000001
        a << [i,j,ggg]
      end
    end
  end
end
if a==[]
raise
else
a.each do |e|
  if e[0]*e[1]*e[2]*4 == (e[0]*e[1]+e[0]*e[2]+e[2]*e[1])*n
    puts e.* " "
    break
  end
end
end