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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 to_bioul(tag_sequence: List[str], encoding: str = "IOB1") -> List[str]: """ Given a tag sequence encoded with IOB1 labels, recode to BIOUL. In the IOB1 scheme, I is a token inside a span, O is a token outside a span and B is the beginning of span immediately following another span of the same type. In the BIO scheme, I is a token inside a span, O is a token outside a span and B is the beginning of a span. Parameters tag_sequence : ``List[str]``, required. The tag sequence encoded in IOB1, e.g. ["I-PER", "I-PER", "O"]. encoding : `str`, optional, (default = ``IOB1``). The encoding type to convert from. Must be either "IOB1" or "BIO". Returns ------- bioul_sequence: ``List[str]`` The tag sequence encoded in IOB1, e.g. ["B-PER", "L-PER", "O"]. """


    if not encoding in {"IOB1", "BIO"}:
        raise ConfigurationError(f"Invalid encoding {encoding} passed to 'to_bioul'.")
    # pylint: disable=len-as-condition

    def replace_label(full_label, new_label):
        # example: full_label = 'I-PER', new_label = 'U', returns 'U-PER'
        parts = list(full_label.partition('-'))
        parts[0] = new_label
        return ''.join(parts)

    def pop_replace_append(in_stack, out_stack, new_label):
        # pop the last element from in_stack, replace the label, append
        # to out_stack
        tag = in_stack.pop()
        new_tag = replace_label(tag, new_label)
        out_stack.append(new_tag)

    def process_stack(stack, out_stack):
        # process a stack of labels, add them to out_stack
        if len(stack) == 1:
            # just a U token
            pop_replace_append(stack, out_stack, 'U')
        else:
            # need to code as BIL
            recoded_stack = []
            pop_replace_append(stack, recoded_stack, 'L')
            while len(stack) >= 2:
                pop_replace_append(stack, recoded_stack, 'I')
            pop_replace_append(stack, recoded_stack, 'B')
            recoded_stack.reverse()
            out_stack.extend(recoded_stack)


    # Process the tag_sequence one tag at a time, adding spans to a stack,
    # then recode them.
    bioul_sequence = []
    stack: List[str] = []

    for label in tag_sequence:
        # need to make a dict like
        # token = {'token': 'Matt', "labels": {'conll2003': "B-PER"}
        #                   'gold': 'I-PER'}
        # where 'gold' is the raw value from the CoNLL data set

        if label == 'O' and len(stack) == 0:
            bioul_sequence.append(label)
        elif label == 'O' and len(stack) > 0:
            # need to process the entries on the stack plus this one
            process_stack(stack, bioul_sequence)
            bioul_sequence.append(label)
        elif label[0] == 'I':
            # check if the previous type is the same as this one
            # if it is then append to stack
            # otherwise this start a new entity if the type
            # is different
            if len(stack) == 0:
                if encoding == "BIO":
                    raise InvalidTagSequence(tag_sequence)
                stack.append(label)
            else:
                # check if the previous type is the same as this one
                this_type = label.partition('-')[2]
                prev_type = stack[-1].partition('-')[2]
                if this_type == prev_type:
                    stack.append(label)
                else:
                    if encoding == "BIO":
                        raise InvalidTagSequence(tag_sequence)
                    # a new entity
                    process_stack(stack, bioul_sequence)
                    stack.append(label)
        elif label[0] == 'B':
            if len(stack) > 0:
                process_stack(stack, bioul_sequence)
            stack.append(label)
        else:
            raise InvalidTagSequence(tag_sequence)

    # process the stack
    if len(stack) > 0:
        process_stack(stack, bioul_sequence)

    return bioul_sequence