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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n = io.read("*n")
local f = false
for i = 1, 3500 do
  for j = 1, 3500 do
    local numer = n * i * j
    local denom = 4 * i * j - n * (i + j)
    if 0 < denom and numer % denom == 0 then
      print(i .. " " .. j .. " " .. math.floor(numer / denom))
      f = true
      break
    end
  end
  if f then break end
end