let select_size n =
    let rec powerset = function
      | [] -> [[]]
      | x :: xs ->
          let ps = powerset xs in
          List.concat [ps; List.map (fun ss -> x :: ss) ps]
    in
    let start =
      powerset [3; 11; 19] |> List.map (fun l -> (l, List.fold_left ( * ) 1 l))
    in

    let rec multiply_by_two (n : int) (target : int) (pow_two : int) =
      if n >= target then pow_two
      else multiply_by_two (2 * n) target (2 * pow_two)
    in

    List.map (fun (l, e) -> multiply_by_two e n 1 :: l) start
    |> List.map (fun l -> (l, List.fold_left ( * ) 1 l))
    |> fun l ->
    List.fold_left
      (fun (l, prod) ((_, acc) as a) -> if prod < acc then (l, prod) else a)
      (List.hd l)
      l