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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 _expand_pattern_lists(pattern, **mappings):
    '''
    Expands the pattern for any list-valued mappings, such that for any list of
    length N in the mappings present in the pattern, N copies of the pattern are
    returned, each with an element of the list substituted.

    pattern:
        A pattern to expand, for example ``by-role/{grains[roles]}``

    mappings:
        A dictionary of variables that can be expanded into the pattern.

    Example: Given the pattern `` by-role/{grains[roles]}`` and the below grains

    .. code-block:: yaml

        grains:
            roles:
                - web
                - database

    This function will expand into two patterns,
    ``[by-role/web, by-role/database]``.

    Note that this method does not expand any non-list patterns.
    '''
    expanded_patterns = []
    f = string.Formatter()
    '''
    This function uses a string.Formatter to get all the formatting tokens from
    the pattern, then recursively replaces tokens whose expanded value is a
    list. For a list with N items, it will create N new pattern strings and
    then continue with the next token. In practice this is expected to not be
    very expensive, since patterns will typically involve a handful of lists at
    most.
    '''  # pylint: disable=W0105
    for (_, field_name, _, _) in f.parse(pattern):
        if field_name is None:
            continue
        (value, _) = f.get_field(field_name, None, mappings)
        if isinstance(value, list):
            token = '{{{0}}}'.format(field_name)
            expanded = [pattern.replace(token, six.text_type(elem)) for elem in value]
            for expanded_item in expanded:
                result = _expand_pattern_lists(expanded_item, **mappings)
                expanded_patterns += result
            return expanded_patterns
    return [pattern]