def _split_tree(layout):
    """Return a tuple of two layouts, one containing the left
    subtree of the root vertex, and one containing the original tree
    with the left subtree removed."""
    one_found = False
    m = None
    for i in range(len(layout)):
        if layout[i] == 1:
            if one_found:
                m = i
                break
            else:
                one_found = True
    if m is None:
        m = len(layout)
    left = [(layout[i] - 1) for i in range(1, m)]
    rest = [0] + [layout[i] for i in range(m, len(layout))]
    return left, rest
