public void testHigher() {
    resetWithHole();
    assertEquals(c, navigableMap.higherEntry(a.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(a.getKey()));
    assertEquals(c, navigableMap.higherEntry(b.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(b.getKey()));
    assertEquals(null, navigableMap.higherEntry(c.getKey()));
    assertEquals(null, navigableMap.higherKey(c.getKey()));
  }

  public void testHigher() {
    resetWithHole();
    assertEquals(c, navigableMap.higherEntry(a.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(a.getKey()));
    assertEquals(c, navigableMap.higherEntry(b.getKey()));
    assertEquals(c.getKey(), navigableMap.higherKey(b.getKey()));
    assertEquals(null, navigableMap.higherEntry(c.getKey()));
    assertEquals(null, navigableMap.higherKey(c.getKey()));
  }

  public NavigableMap<K, V> headMap(K toKey, boolean inclusive) {
    return new SafeTreeMap<>(delegate.headMap(checkValid(toKey), inclusive));
  }

  @Override
  public @Nullable Entry<K, V> higherEntry(K key) {
    return delegate.higherEntry(checkValid(key));
  }

  @Override
  public @Nullable K higherKey(K key) {
    return delegate.higherKey(checkValid(key));
  }

  @Override
  public boolean isEmpty() {

  public NavigableMap<K, V> headMap(K toKey, boolean inclusive) {
    return new SafeTreeMap<>(delegate.headMap(checkValid(toKey), inclusive));
  }

  @Override
  public @Nullable Entry<K, V> higherEntry(K key) {
    return delegate.higherEntry(checkValid(key));
  }

  @Override
  public @Nullable K higherKey(K key) {
    return delegate.higherKey(checkValid(key));
  }

  @Override
  public boolean isEmpty() {

    coalescedRange = coalesce(coalescedRange, value, lowerEntry);

    Entry<Cut<K>, RangeMapEntry<K, V>> higherEntry =
        entriesByLowerBound.floorEntry(range.upperBound);
    coalescedRange = coalesce(coalescedRange, value, higherEntry);

    return coalescedRange;
  }

  /** Returns the range that spans the given range and entry, if the entry can be coalesced. */

    public SortedMap<K, V> headMap(K toKey) {
      return headMap(toKey, false);
    }

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

    @Override
    @CheckForNull
    public K higherKey(K key) {
      synchronized (mutex) {

      return transformEntries(fromMap().headMap(toKey, inclusive), transformer);
    }

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

    @Override
    @CheckForNull
    public K higherKey(@ParametricNullness K key) {
      return fromMap().higherKey(key);
    }

    return keyOrNull(ceilingEntry(key));
  }

  @Override
  @CheckForNull
  public Entry<K, V> higherEntry(K key) {
    return tailMap(key, false).firstEntry();
  }

  @Override
  @CheckForNull
  public K higherKey(K key) {
    return keyOrNull(higherEntry(key));
  }

  @Override
  @CheckForNull
  public Entry<K, V> firstEntry() {

    return keyOrNull(ceilingEntry(key));
  }

  @Override
  @CheckForNull
  public Entry<K, V> higherEntry(K key) {
    return tailMap(key, false).firstEntry();
  }

  @Override
  @CheckForNull
  public K higherKey(K key) {
    return keyOrNull(higherEntry(key));
  }

  @Override
  @CheckForNull
  public Entry<K, V> firstEntry() {

    assertEquals("three", map.higherKey("r"));
    assertEquals("three", map.ceilingKey("r"));
    assertEquals("one", map.ceilingKey("one"));
    assertEquals(mapEntry("three", 5), map.higherEntry("one"));
    assertEquals(mapEntry("one", 3), map.ceilingEntry("one"));
    assertEquals("one", map.lowerKey("three"));
    assertEquals("one", map.lowerKey("r"));
    assertEquals("one", map.floorKey("r"));