type 'a elem = {v : 'a; mutable next : 'a lista; mutable prev : 'a lista}
and 'a lista = 'a elem option;;

(* two_or_more dla danej niepustej listy wyciąga z niej drugi element (zwraca Some 'a) a pierwszy łączy z trzecim lub
łączy z None dla listy krótszej niż trzyelementowej, jeżeli dana lista będzie jednoelementowa to funkcja zwroci None*)
let two_or_more lst0 =
  match lst0 with
    | None -> failwith "Tak się nie stanie"
    | Some el1 ->
      match el1.next with
        | None -> (None, None)
        | Some el2 ->
          begin
            el1.next <- el2.next;
            match el2.next with
              | None -> (Some el2.v, None)
              | Some el3 ->
                begin
                  el3.prev <- Some el1;
                  (Some el2.v, Some el3)
                end
          end;;


let codrugi lst0 =
  if lst0 = None then
    None
  else
    let (new_el_v, new_curr) = two_or_more lst0 in
    if new_el_v = None then
      None
    else
      let curr = ref new_curr in
      let lst2start = {v = new_el_v; next = None; prev = None} in
      let lst2 = ref lst2start in
      while !curr != None do
        begin
          let (new_el_v, new_curr) = two_or_more !curr in
          curr := new_curr;
          let new_el = {v = new_el_v; next = None; prev = Some !lst2} in
          match Some !lst2 with
            | None -> ()
            | Some lst2s -> lst2s.next <- Some new_el
        end
      done;
      Some lst2start;;