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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def universal_transformer_layer(x, hparams, ffn_unit, attention_unit, pad_remover=None):
 """Core function applying the universal transformer layer. Args: x: input hparams: model hyper-parameters ffn_unit: feed-forward unit attention_unit: multi-head attention unit pad_remover: to mask out padding in convolutional layers (efficiency). Returns: the output tensor, extra output (can be memory, ponder time, etc.) Raises: ValueError: Unknown recurrence type """


  def add_vanilla_transformer_layer(x, num_layers, name):
    """Passes the input through num_layers of vanilla transformer layers.

    Args:
     x: input
     num_layers: number of layers
     name: string, prefix of layer names

    Returns:
       output of vanilla_transformer_layer
    """
    if hparams.add_position_timing_signal:
      # In case of add_position_timing_signal=true, we set  hparams.pos=None
      # and add position timing signal at the beginning of each step, so for
      # the vanilla transformer, we need to add timing signal here.
      x = common_attention.add_timing_signal_1d(x)
    for layer in range(num_layers):
      with tf.variable_scope(name + "layer_%d" % layer):
        x = ffn_unit(attention_unit(x))
    return x

  with tf.variable_scope("universal_transformer_%s" % hparams.recurrence_type):
    if (hparams.mix_with_transformer and
        "before_ut" in hparams.mix_with_transformer):
      x = add_vanilla_transformer_layer(x, hparams.num_mixedin_layers,
                                        "before_ut_")

    if hparams.recurrence_type == "act":
      output, extra_output = universal_transformer_act(
          x, hparams, ffn_unit, attention_unit)

    else:  # for all the other recurrency types with fixed number of steps

      ut_function, initializer = get_ut_layer(x, hparams, ffn_unit,
                                              attention_unit, pad_remover)

      output, _, extra_output = tf.foldl(
          ut_function, tf.range(hparams.num_rec_steps),
          initializer=initializer)

      # Right now, this is only possible when the transition function is an lstm
      if (hparams.recurrence_type == "lstm" and
          hparams.get("use_memory_as_final_state", False)):
        output = extra_output

    if (hparams.mix_with_transformer and
        "after_ut" in hparams.mix_with_transformer):
      output = add_vanilla_transformer_layer(output, hparams.num_mixedin_layers,
                                             "after_ut_")

    return output, extra_output