}

  <K, V> void testNavigationAgainstExpected(
      NavigableMap<K, V> expected, NavigableMap<K, V> navigableMap, Iterable<K> keysToTest) {
    for (K key : keysToTest) {
      assertEquals(expected.lowerEntry(key), navigableMap.lowerEntry(key));
      assertEquals(expected.floorEntry(key), navigableMap.floorEntry(key));
      assertEquals(expected.ceilingEntry(key), navigableMap.ceilingEntry(key));

    assertEquals(map.headMap("three", true), map.descendingMap().tailMap("three", true));
    assertThat(map.tailMap("three", false).entrySet()).contains(mapEntry("two", 3));
    assertThat(map.tailMap("three", true).lowerEntry("three")).isNull();
    assertThat(map.headMap("two", false).values()).containsExactly(3, 5).inOrder();
    assertThat(map.headMap("two", false).descendingMap().values()).containsExactly(5, 3).inOrder();

      return (NavigableMap<K, Collection<V>>) super.sortedMap();
    }

    @Override
    public @Nullable Entry<K, Collection<V>> lowerEntry(@ParametricNullness K key) {
      Entry<K, Collection<V>> entry = sortedMap().lowerEntry(key);
      return (entry == null) ? null : wrapEntry(entry);
    }

    @Override
    public @Nullable K lowerKey(@ParametricNullness K key) {

    assertEquals(map.headMap("three", true), map.descendingMap().tailMap("three", true));
    assertThat(map.tailMap("three", false).entrySet()).contains(mapEntry("two", 3));
    assertThat(map.tailMap("three", true).lowerEntry("three")).isNull();
    assertThat(map.headMap("two", false).values()).containsExactly(3, 5).inOrder();
    assertThat(map.headMap("two", false).descendingMap().values()).containsExactly(5, 3).inOrder();

    public @Nullable Entry<K, V2> lastEntry() {
      return transformEntry(fromMap().lastEntry());
    }

    @Override
    public @Nullable Entry<K, V2> lowerEntry(@ParametricNullness K key) {
      return transformEntry(fromMap().lowerEntry(key));
    }

    @Override
    public @Nullable K lowerKey(@ParametricNullness K key) {
      return fromMap().lowerKey(key);
    }

    @Override

    public @Nullable Entry<K, V2> lastEntry() {
      return transformEntry(fromMap().lastEntry());
    }

    @Override
    public @Nullable Entry<K, V2> lowerEntry(@ParametricNullness K key) {
      return transformEntry(fromMap().lowerEntry(key));
    }

    @Override
    public @Nullable K lowerKey(@ParametricNullness K key) {
      return fromMap().lowerKey(key);
    }

    @Override

        return nullableSynchronizedEntry(delegate().lastEntry(), mutex);
      }
    }

    @Override
    public Map.@Nullable Entry<K, V> lowerEntry(K key) {
      synchronized (mutex) {
        return nullableSynchronizedEntry(delegate().lowerEntry(key), mutex);
      }
    }

    @Override
    public @Nullable K lowerKey(K key) {
      synchronized (mutex) {

        return nullableSynchronizedEntry(delegate().lastEntry(), mutex);
      }
    }

    @Override
    public Map.@Nullable Entry<K, V> lowerEntry(K key) {
      synchronized (mutex) {
        return nullableSynchronizedEntry(delegate().lowerEntry(key), mutex);
      }
    }

    @Override
    public @Nullable K lowerKey(K key) {
      synchronized (mutex) {

    return getSubMap(keySet.tailIndex(checkNotNull(fromKey), inclusive), size());
  }

  @Override
  public @Nullable Entry<K, V> lowerEntry(K key) {
    return headMap(key, false).lastEntry();
  }

  @Override
  public @Nullable K lowerKey(K key) {
    return keyOrNull(lowerEntry(key));
  }

  @Override
  public @Nullable Entry<K, V> floorEntry(K key) {
    return headMap(key, true).lastEntry();