For example, suppose the path is "/foo/bar/baz".
   * No matter baz is a file or a directory,
   * the parent path is "/foo/bar".
   * If bar exists, then the ancestor path is also "/foo/bar".
   * If bar does not exist and foo exists,
   * then the ancestor path is "/foo".
   * Further, if both foo and bar do not exist,
   * then the ancestor path is "/".
For example, suppose the path is "/foo/bar/baz".
   * No matter baz is a file or a directory,
   * the parent path is "/foo/bar".
   * If bar exists, then the ancestor path is also "/foo/bar".
   * If bar does not exist and foo exists,
   * then the ancestor path is "/foo".
   * Further, if both foo and bar do not exist,
   * then the ancestor path is "/". | FSPermissionChecker.java