Given a path, a list of existing paths and counts for each of the
    existing paths.

def make_path_unique(path, counts, new):
    """
    Given a path, a list of existing paths and counts for each of the
    existing paths.
    """
    added = False
    while any(path == c[:i] for c in counts for i in range(1, len(c)+1)):
        count = counts[path]
        counts[path] += 1
        if (not new and len(path) > 1) or added:
            path = path[:-1]
        else:
            added = True
        path = path + (int_to_roman(count),)
    if len(path) == 1:
        path = path + (int_to_roman(counts.get(path, 1)),)
    if path not in counts:
        counts[path] = 1
    return path