static <T> Map<S, T> keysStartingWith(String x, TreeMap<S, T> map) {
  if (empty(x)) ret map;
  S lastKey = lexicographicallyNextString(x);
  ret map.subMap(x, true, lastKey, false);
}

static <T> Map<S, T> keysStartingWith(TreeMap<S, T> map, String x) {
  ret keysStartingWith(x, map);
}