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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n = io.read("*n")
for i = 1, 3500 do
  for j = i, 3500 do
    --[[
    4ijk = Njk + Nik + Nij
    k(4ij - Nj - Ni) = Nij
    ]]
    local a = n * i * j
    local b = 4 * i * j - n * (i + j)
    if 0 < b and a % b == 0 then
      local k = a // b
      print(i .." " .. j .. " " .. k)
      os.exit()
    end
  end
end