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 (LuaJIT 2.1.0) (judge verdict: Accepted)

local n=io.read("n")
for i=1,3500 do
    for j=1,3500 do
        local a=n*i*j
        local b=(4*i*j-n*j-n*i)
        if b>0 and a%b==0 then
            local k=math.floor(a/b)
            print(i.." "..j.." "..k)
            os.exit()
        end
    end
end