<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _get_parent_timestamp(dirname, mtime):
 """ Get the timestamps up the directory tree. All the way to root. Because they affect every subdirectory. """

    parent_pathname = os.path.dirname(dirname)

    # max between the parent timestamp the one passed in
    mtime = _max_timestamps(parent_pathname, False, mtime)

    if dirname != os.path.dirname(parent_pathname):
        # this is only called if we're not at the root
        mtime = _get_parent_timestamp(parent_pathname, mtime)

    return mtime