type dir = N | E | W | S let move_with_dir (x, y) pitch = function | N -> (x, y + pitch) | W -> (x - pitch, y) | E -> (x + pitch, y) | S -> (x, y - pitch) let turn_for_x v current = let to_west = v < 0 and to_east = v > 0 in match current with | N when to_east -> Some (E, 1) | N when to_west -> Some (W, 1) | S when to_east -> Some (E, 1) | S when to_west -> Some (W, 1) | E when to_west -> Some (W, 2) | W when to_east -> Some (E, 2) | _ -> None let turn_for_y v current = let to_south = v < 0 and to_north = v > 0 in match current with | E when to_south -> Some (S, 1) | E when to_north -> Some (N, 1) | W when to_south -> Some (S, 1) | W when to_north -> Some (N, 1) | N when to_south -> Some (S, 2) | S when to_north -> Some (N, 2) | _ -> None let solve tag_x tag_y max_pitch = let move_to_x x dir = let dir, act_count = match turn_for_x tag_x dir with | None -> dir, 0 | Some v -> v in let pitch = min max_pitch (abs (tag_x - x)) in dir, act_count, pitch and move_to_y y dir = let dir, act_count = match turn_for_y tag_y dir with | None -> dir, 0 | Some v -> v in let pitch = min max_pitch (abs (tag_y - y)) in dir, act_count, pitch in let rec solve' (x, y) dir count = if (x, y) = (tag_x, tag_y) then count else if x = tag_x then let dir, act_count, pitch = move_to_y y dir in solve' (move_with_dir (x, y) pitch dir) dir (count + act_count + 1) else if y = tag_y then let dir, act_count, pitch = move_to_x x dir in solve' (move_with_dir (x, y) pitch dir) dir (count + act_count + 1) else let dir_x, act_count_x, pitch_x = move_to_x x dir and dir_y, act_count_y, pitch_y = move_to_y y dir in if act_count_x > act_count_y then solve' (move_with_dir (x, y) pitch_y dir_y) dir_y (count + act_count_y + 1) else solve' (move_with_dir (x, y) pitch_x dir_x) dir_x (count + act_count_x + 1) in solve' (0, 0) N 0 let () = let x_pos = read_line () |> int_of_string in let y_pos = read_line () |> int_of_string in let max_movable = read_line () |> int_of_string in Printf.printf "%d\n" (solve x_pos y_pos max_movable)