*
   * <p><b>Warning:</b> the result takes <i>O(n log n)</i> space, so use cautiously.
   *
   * <p>This uses an efficient binary recursive algorithm to compute the factorial with balanced
   * multiplies. It also removes all the 2s from the intermediate products (shifting them back in at
   * the end).
   *
   * @throws IllegalArgumentException if {@code n < 0}
   */
  public static BigInteger factorial(int n) {

                    "msg": "Input should be a valid integer, unable to parse string as an integer",
                    "input": "foo",
                }
            ]
        }
    ) | IsDict(
        # TODO: remove when deprecating Pydantic v1
        {
            "detail": [
                {
                    "loc": ["body", "__key__"],
                    "msg": "value is not a valid integer",

                paramMap.put(HcHttpClient.PROXY_CREDENTIALS_PROPERTY, new UsernamePasswordCredentials(
                        paramMap.remove(Param.Client.PROXY_USERNAME).toString(), paramMap.remove(Param.Client.PROXY_PASSWORD).toString()));
            }
        } else {
            initializeDefaultHttpProxy(paramMap);
        }

        crawlerClientFactory = factory;

    return collection != null && collection.contains(value);
  }

  @CanIgnoreReturnValue
  @Override
  public boolean remove(@CheckForNull Object key, @CheckForNull Object value) {
    Collection<V> collection = asMap().get(key);
    return collection != null && collection.remove(value);
  }

  @CanIgnoreReturnValue
  @Override
  public boolean put(@ParametricNullness K key, @ParametricNullness V value) {

    /**
     * Get the filename of this metadata on the local repository.
     *
     * @param repository the remote repository it came from
     * @return the filename
     */
    String getLocalFilename(ArtifactRepository repository);

    /**
     * Get the filename of this metadata on the remote repository.
     *
     * @return the filename
     */
    String getRemoteFilename();

    /**

   * assume that using setCount() to increase the count is permitted iff add()
   * is permitted and similarly for decrease/remove(). We assume that a
   * setCount() no-op is permitted if either add() or remove() is permitted,
   * though we also allow it to "succeed" if neither is permitted.
   */

  private void assertSetCount(E element, int count) {

                    "input": "XL",
                }
            ],
            "body": {"title": "towel", "size": "XL"},
        }
    ) | IsDict(
        # TODO: remove when deprecating Pydantic v1
        {
            "detail": [
                {
                    "loc": ["body", "size"],
                    "msg": "value is not a valid integer",

                    "msg": "Input should be a valid integer, unable to parse string as an integer",
                    "input": "foo",
                }
            ]
        }
    ) | IsDict(
        # TODO: remove when deprecating Pydantic v1
        {
            "detail": [
                {
                    "loc": ["path", "item_id"],
                    "msg": "value is not a valid integer",

                                    ],
                                }
                            )
                            | IsDict(
                                # TODO: remove when deprecating Pydantic v1
                                {
                                    "title": "X-Token",
                                    "type": "array",

    async def connect(self, websocket: WebSocket):
        await websocket.accept()
        self.active_connections.append(websocket)

    def disconnect(self, websocket: WebSocket):
        self.active_connections.remove(websocket)

    async def send_personal_message(self, message: str, websocket: WebSocket):
        await websocket.send_text(message)

    async def broadcast(self, message: str):