Quellcode-Bibliothek TreeMap.java

Sprache: JAVA

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package java.util;

import java.io.Serializable;
import java.util.function.BiConsumer;
import java.util.function.BiFunction;
import java.util.function.Consumer;
import java.util.function.Function;

/**
* A Red-Black tree based {@link NavigableMap} implementation.
* The map is sorted according to the {@linkplain Comparable natural
* ordering} of its keys, or by a {@link Comparator} provided at map
* creation time, depending on which constructor is used.
*
* This implementation provides guaranteed log(n) time cost for the
* {@code containsKey}, {@code get}, {@code put} and {@code remove}
* operations. Algorithms are adaptations of those in Cormen, Leiserson, and
* Rivest's Introduction to Algorithms.
*
* Note that the ordering maintained by a tree map, like any sorted map, and
* whether or not an explicit comparator is provided, must be consistent
* with {@code equals} if this sorted map is to correctly implement the
* {@code Map} interface. (See {@code Comparable} or {@code Comparator} for a
* precise definition of consistent with equals.) This is so because
* the {@code Map} interface is defined in terms of the {@code equals}
* operation, but a sorted map performs all key comparisons using its {@code
* compareTo} (or {@code compare}) method, so two keys that are deemed equal by
* this method are, from the standpoint of the sorted map, equal. The behavior
* of a sorted map is well-defined even if its ordering is
* inconsistent with {@code equals}; it just fails to obey the general contract
* of the {@code Map} interface.
*
* Note that this implementation is not synchronized.
* If multiple threads access a map concurrently, and at least one of the
* threads modifies the map structurally, it must be synchronized
* externally. (A structural modification is any operation that adds or
* deletes one or more mappings; merely changing the value associated
* with an existing key is not a structural modification.) This is
* typically accomplished by synchronizing on some object that naturally
* encapsulates the map.
* If no such object exists, the map should be "wrapped" using the
* {@link Collections#synchronizedSortedMap Collections.synchronizedSortedMap}
* method. This is best done at creation time, to prevent accidental
* unsynchronized access to the map: <pre>
* SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));</pre>
*
* The iterators returned by the {@code iterator} method of the collections
* returned by all of this class's "collection view methods" are
* fail-fast: if the map is structurally modified at any time after
* the iterator is created, in any way except through the iterator's own
* {@code remove} method, the iterator will throw a {@link
* ConcurrentModificationException}. Thus, in the face of concurrent
* modification, the iterator fails quickly and cleanly, rather than risking
* arbitrary, non-deterministic behavior at an undetermined time in the future.
*
* Note that the fail-fast behavior of an iterator cannot be guaranteed
* as it is, generally speaking, impossible to make any hard guarantees in the
* presence of unsynchronized concurrent modification. Fail-fast iterators
* throw {@code ConcurrentModificationException} on a best-effort basis.
* Therefore, it would be wrong to write a program that depended on this
* exception for its correctness: the fail-fast behavior of iterators
* should be used only to detect bugs.
*
* All {@code Map.Entry} pairs returned by methods in this class
* and its views represent snapshots of mappings at the time they were
* produced. They do not support the {@code Entry.setValue}
* method. (Note however that it is possible to change mappings in the
* associated map using {@code put}.)
*
* This class is a member of the
* <a href="{@docRoot}/java.base/java/util/package-summary.html#CollectionsFramework">
* Java Collections Framework</a>.
*
* @param <K> the type of keys maintained by this map
* @param <V> the type of mapped values
*
* @author Josh Bloch and Doug Lea
* @see Map
* @see HashMap
* @see Hashtable
* @see Comparable
* @see Comparator
* @see Collection
* @since 1.2
*/

public class TreeMap<K,V>
 extends AbstractMap<K,V>
 implements NavigableMap<K,V>, Cloneable, java.io.Serializable
{
 /**
 * The comparator used to maintain order in this tree map, or
 * null if it uses the natural ordering of its keys.
 *
 * @serial
 */
 @SuppressWarnings("serial") // Conditionally serializable
 private final Comparator<? super K> comparator;

 private transient Entry<K,V> root;

 /**
 * The number of entries in the tree
 */
 private transient int size = 0;

 /**
 * The number of structural modifications to the tree.
 */
 private transient int modCount = 0;

 /**
 * Constructs a new, empty tree map, using the natural ordering of its
 * keys. All keys inserted into the map must implement the {@link
 * Comparable} interface. Furthermore, all such keys must be
 * mutually comparable: {@code k1.compareTo(k2)} must not throw
 * a {@code ClassCastException} for any keys {@code k1} and
 * {@code k2} in the map. If the user attempts to put a key into the
 * map that violates this constraint (for example, the user attempts to
 * put a string key into a map whose keys are integers), the
 * {@code put(Object key, Object value)} call will throw a
 * {@code ClassCastException}.
 */
 public TreeMap() {
 comparator = null;
 }

 /**
 * Constructs a new, empty tree map, ordered according to the given
 * comparator. All keys inserted into the map must be mutually
 * comparable by the given comparator: {@code comparator.compare(k1,
 * k2)} must not throw a {@code ClassCastException} for any keys
 * {@code k1} and {@code k2} in the map. If the user attempts to put
 * a key into the map that violates this constraint, the {@code put(Object
 * key, Object value)} call will throw a
 * {@code ClassCastException}.
 *
 * @param comparator the comparator that will be used to order this map.
 * If {@code null}, the {@linkplain Comparable natural
 * ordering} of the keys will be used.
 */
 public TreeMap(Comparator<? super K> comparator) {
 this.comparator = comparator;
 }

 /**
 * Constructs a new tree map containing the same mappings as the given
 * map, ordered according to the natural ordering of its keys.
 * All keys inserted into the new map must implement the {@link
 * Comparable} interface. Furthermore, all such keys must be
 * mutually comparable: {@code k1.compareTo(k2)} must not throw
 * a {@code ClassCastException} for any keys {@code k1} and
 * {@code k2} in the map. This method runs in n*log(n) time.
 *
 * @param m the map whose mappings are to be placed in this map
 * @throws ClassCastException if the keys in m are not {@link Comparable},
 * or are not mutually comparable
 * @throws NullPointerException if the specified map is null
 */
 public TreeMap(Map<? extends K, ? extends V> m) {
 comparator = null;
 putAll(m);
 }

 /**
 * Constructs a new tree map containing the same mappings and
 * using the same ordering as the specified sorted map. This
 * method runs in linear time.
 *
 * @param m the sorted map whose mappings are to be placed in this map,
 * and whose comparator is to be used to sort this map
 * @throws NullPointerException if the specified map is null
 */
 public TreeMap(SortedMap<K, ? extends V> m) {
 comparator = m.comparator();
 try {
 buildFromSorted(m.size(), m.entrySet().iterator(), null, null);
 } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 }
 }

 // Query Operations

 /**
 * Returns the number of key-value mappings in this map.
 *
 * @return the number of key-value mappings in this map
 */
 public int size() {
 return size;
 }

 /**
 * Returns {@code true} if this map contains a mapping for the specified
 * key.
 *
 * @param key key whose presence in this map is to be tested
 * @return {@code true} if this map contains a mapping for the
 * specified key
 * @throws ClassCastException if the specified key cannot be compared
 * with the keys currently in the map
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 */
 public boolean containsKey(Object key) {
 return getEntry(key) != null;
 }

 /**
 * Returns {@code true} if this map maps one or more keys to the
 * specified value. More formally, returns {@code true} if and only if
 * this map contains at least one mapping to a value {@code v} such
 * that {@code (value==null ? v==null : value.equals(v))}. This
 * operation will probably require time linear in the map size for
 * most implementations.
 *
 * @param value value whose presence in this map is to be tested
 * @return {@code true} if a mapping to {@code value} exists;
 * {@code false} otherwise
 * @since 1.2
 */
 public boolean containsValue(Object value) {
 for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e))
 if (valEquals(value, e.value))
 return true;
 return false;
 }

 /**
 * Returns the value to which the specified key is mapped,
 * or {@code null} if this map contains no mapping for the key.
 *
 * More formally, if this map contains a mapping from a key
 * {@code k} to a value {@code v} such that {@code key} compares
 * equal to {@code k} according to the map's ordering, then this
 * method returns {@code v}; otherwise it returns {@code null}.
 * (There can be at most one such mapping.)
 *
 * A return value of {@code null} does not necessarily
 * indicate that the map contains no mapping for the key; it's also
 * possible that the map explicitly maps the key to {@code null}.
 * The {@link #containsKey containsKey} operation may be used to
 * distinguish these two cases.
 *
 * @throws ClassCastException if the specified key cannot be compared
 * with the keys currently in the map
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 */
 public V get(Object key) {
 Entry<K,V> p = getEntry(key);
 return (p==null ? null : p.value);
 }

 public Comparator<? super K> comparator() {
 return comparator;
 }

 /**
 * @throws NoSuchElementException {@inheritDoc}
 */
 public K firstKey() {
 return key(getFirstEntry());
 }

 /**
 * @throws NoSuchElementException {@inheritDoc}
 */
 public K lastKey() {
 return key(getLastEntry());
 }

 /**
 * Copies all of the mappings from the specified map to this map.
 * These mappings replace any mappings that this map had for any
 * of the keys currently in the specified map.
 *
 * @param map mappings to be stored in this map
 * @throws ClassCastException if the class of a key or value in
 * the specified map prevents it from being stored in this map
 * @throws NullPointerException if the specified map is null or
 * the specified map contains a null key and this map does not
 * permit null keys
 */
 public void putAll(Map<? extends K, ? extends V> map) {
 int mapSize = map.size();
 if (size==0 && mapSize!=0 && map instanceof SortedMap) {
 if (Objects.equals(comparator, ((SortedMap<?,?>)map).comparator())) {
 ++modCount;
 try {
 buildFromSorted(mapSize, map.entrySet().iterator(),
 null, null);
 } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 }
 return;
 }
 }
 super.putAll(map);
 }

 /**
 * Returns this map's entry for the given key, or {@code null} if the map
 * does not contain an entry for the key.
 *
 * @return this map's entry for the given key, or {@code null} if the map
 * does not contain an entry for the key
 * @throws ClassCastException if the specified key cannot be compared
 * with the keys currently in the map
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 */
 final Entry<K,V> getEntry(Object key) {
 // Offload comparator-based version for sake of performance
 if (comparator != null)
 return getEntryUsingComparator(key);
 Objects.requireNonNull(key);
 @SuppressWarnings("unchecked")
 Comparable<? super K> k = (Comparable<? super K>) key;
 Entry<K,V> p = root;
 while (p != null) {
 int cmp = k.compareTo(p.key);
 if (cmp < 0)
 p = p.left;
 else if (cmp > 0)
 p = p.right;
 else
 return p;
 }
 return null;
 }

 /**
 * Version of getEntry using comparator. Split off from getEntry
 * for performance. (This is not worth doing for most methods,
 * that are less dependent on comparator performance, but is
 * worthwhile here.)
 */
 final Entry<K,V> getEntryUsingComparator(Object key) {
 @SuppressWarnings("unchecked")
 K k = (K) key;
 Comparator<? super K> cpr = comparator;
 if (cpr != null) {
 Entry<K,V> p = root;
 while (p != null) {
 int cmp = cpr.compare(k, p.key);
 if (cmp < 0)
 p = p.left;
 else if (cmp > 0)
 p = p.right;
 else
 return p;
 }
 }
 return null;
 }

 /**
 * Gets the entry corresponding to the specified key; if no such entry
 * exists, returns the entry for the least key greater than the specified
 * key; if no such entry exists (i.e., the greatest key in the Tree is less
 * than the specified key), returns {@code null}.
 */
 final Entry<K,V> getCeilingEntry(K key) {
 Entry<K,V> p = root;
 while (p != null) {
 int cmp = compare(key, p.key);
 if (cmp < 0) {
 if (p.left != null)
 p = p.left;
 else
 return p;
 } else if (cmp > 0) {
 if (p.right != null) {
 p = p.right;
 } else {
 Entry<K,V> parent = p.parent;
 Entry<K,V> ch = p;
 while (parent != null && ch == parent.right) {
 ch = parent;
 parent = parent.parent;
 }
 return parent;
 }
 } else
 return p;
 }
 return null;
 }

 /**
 * Gets the entry corresponding to the specified key; if no such entry
 * exists, returns the entry for the greatest key less than the specified
 * key; if no such entry exists, returns {@code null}.
 */
 final Entry<K,V> getFloorEntry(K key) {
 Entry<K,V> p = root;
 while (p != null) {
 int cmp = compare(key, p.key);
 if (cmp > 0) {
 if (p.right != null)
 p = p.right;
 else
 return p;
 } else if (cmp < 0) {
 if (p.left != null) {
 p = p.left;
 } else {
 Entry<K,V> parent = p.parent;
 Entry<K,V> ch = p;
 while (parent != null && ch == parent.left) {
 ch = parent;
 parent = parent.parent;
 }
 return parent;
 }
 } else
 return p;

 }
 return null;
 }

 /**
 * Gets the entry for the least key greater than the specified
 * key; if no such entry exists, returns the entry for the least
 * key greater than the specified key; if no such entry exists
 * returns {@code null}.
 */
 final Entry<K,V> getHigherEntry(K key) {
 Entry<K,V> p = root;
 while (p != null) {
 int cmp = compare(key, p.key);
 if (cmp < 0) {
 if (p.left != null)
 p = p.left;
 else
 return p;
 } else {
 if (p.right != null) {
 p = p.right;
 } else {
 Entry<K,V> parent = p.parent;
 Entry<K,V> ch = p;
 while (parent != null && ch == parent.right) {
 ch = parent;
 parent = parent.parent;
 }
 return parent;
 }
 }
 }
 return null;
 }

 /**
 * Returns the entry for the greatest key less than the specified key; if
 * no such entry exists (i.e., the least key in the Tree is greater than
 * the specified key), returns {@code null}.
 */
 final Entry<K,V> getLowerEntry(K key) {
 Entry<K,V> p = root;
 while (p != null) {
 int cmp = compare(key, p.key);
 if (cmp > 0) {
 if (p.right != null)
 p = p.right;
 else
 return p;
 } else {
 if (p.left != null) {
 p = p.left;
 } else {
 Entry<K,V> parent = p.parent;
 Entry<K,V> ch = p;
 while (parent != null && ch == parent.left) {
 ch = parent;
 parent = parent.parent;
 }
 return parent;
 }
 }
 }
 return null;
 }

 /**
 * Associates the specified value with the specified key in this map.
 * If the map previously contained a mapping for the key, the old
 * value is replaced.
 *
 * @param key key with which the specified value is to be associated
 * @param value value to be associated with the specified key
 *
 * @return the previous value associated with {@code key}, or
 * {@code null} if there was no mapping for {@code key}.
 * (A {@code null} return can also indicate that the map
 * previously associated {@code null} with {@code key}.)
 * @throws ClassCastException if the specified key cannot be compared
 * with the keys currently in the map
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 */
 public V put(K key, V value) {
 return put(key, value, true);
 }

 @Override
 public V putIfAbsent(K key, V value) {
 return put(key, value, false);
 }

 /**
 * {@inheritDoc}
 *
 * This method will, on a best-effort basis, throw a
 * {@link ConcurrentModificationException} if it is detected that the
 * mapping function modifies this map during computation.
 *
 * @throws ConcurrentModificationException if it is detected that the
 * mapping function modified this map
 */
 @Override
 public V computeIfAbsent(K key, Function<? super K, ? extends V> mappingFunction) {
 Objects.requireNonNull(mappingFunction);
 V newValue;
 Entry<K,V> t = root;
 if (t == null) {
 newValue = callMappingFunctionWithCheck(key, mappingFunction);
 if (newValue != null) {
 addEntryToEmptyMap(key, newValue);
 return newValue;
 } else {
 return null;
 }
 }
 int cmp;
 Entry<K,V> parent;
 // split comparator and comparable paths
 Comparator<? super K> cpr = comparator;
 if (cpr != null) {
 do {
 parent = t;
 cmp = cpr.compare(key, t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else {
 if (t.value == null) {
 t.value = callMappingFunctionWithCheck(key, mappingFunction);
 }
 return t.value;
 }
 } while (t != null);
 } else {
 Objects.requireNonNull(key);
 @SuppressWarnings("unchecked")
 Comparable<? super K> k = (Comparable<? super K>) key;
 do {
 parent = t;
 cmp = k.compareTo(t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else {
 if (t.value == null) {
 t.value = callMappingFunctionWithCheck(key, mappingFunction);
 }
 return t.value;
 }
 } while (t != null);
 }
 newValue = callMappingFunctionWithCheck(key, mappingFunction);
 if (newValue != null) {
 addEntry(key, newValue, parent, cmp < 0);
 return newValue;
 }
 return null;
 }

 /**
 * {@inheritDoc}
 *
 * This method will, on a best-effort basis, throw a
 * {@link ConcurrentModificationException} if it is detected that the
 * remapping function modifies this map during computation.
 *
 * @throws ConcurrentModificationException if it is detected that the
 * remapping function modified this map
 */
 @Override
 public V computeIfPresent(K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 Objects.requireNonNull(remappingFunction);
 Entry<K,V> oldEntry = getEntry(key);
 if (oldEntry != null && oldEntry.value != null) {
 return remapValue(oldEntry, key, remappingFunction);
 } else {
 return null;
 }
 }

 /**
 * {@inheritDoc}
 *
 * This method will, on a best-effort basis, throw a
 * {@link ConcurrentModificationException} if it is detected that the
 * remapping function modifies this map during computation.
 *
 * @throws ConcurrentModificationException if it is detected that the
 * remapping function modified this map
 */
 @Override
 public V compute(K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 Objects.requireNonNull(remappingFunction);
 V newValue;
 Entry<K,V> t = root;
 if (t == null) {
 newValue = callRemappingFunctionWithCheck(key, null, remappingFunction);
 if (newValue != null) {
 addEntryToEmptyMap(key, newValue);
 return newValue;
 } else {
 return null;
 }
 }
 int cmp;
 Entry<K,V> parent;
 // split comparator and comparable paths
 Comparator<? super K> cpr = comparator;
 if (cpr != null) {
 do {
 parent = t;
 cmp = cpr.compare(key, t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else
 return remapValue(t, key, remappingFunction);
 } while (t != null);
 } else {
 Objects.requireNonNull(key);
 @SuppressWarnings("unchecked")
 Comparable<? super K> k = (Comparable<? super K>) key;
 do {
 parent = t;
 cmp = k.compareTo(t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else
 return remapValue(t, key, remappingFunction);
 } while (t != null);
 }
 newValue = callRemappingFunctionWithCheck(key, null, remappingFunction);
 if (newValue != null) {
 addEntry(key, newValue, parent, cmp < 0);
 return newValue;
 }
 return null;
 }

 /**
 * {@inheritDoc}
 *
 * This method will, on a best-effort basis, throw a
 * {@link ConcurrentModificationException} if it is detected that the
 * remapping function modifies this map during computation.
 *
 * @throws ConcurrentModificationException if it is detected that the
 * remapping function modified this map
 */
 @Override
 public V merge(K key, V value, BiFunction<? super V, ? super V, ? extends V> remappingFunction) {
 Objects.requireNonNull(remappingFunction);
 Objects.requireNonNull(value);
 Entry<K,V> t = root;
 if (t == null) {
 addEntryToEmptyMap(key, value);
 return value;
 }
 int cmp;
 Entry<K,V> parent;
 // split comparator and comparable paths
 Comparator<? super K> cpr = comparator;
 if (cpr != null) {
 do {
 parent = t;
 cmp = cpr.compare(key, t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else return mergeValue(t, value, remappingFunction);
 } while (t != null);
 } else {
 Objects.requireNonNull(key);
 @SuppressWarnings("unchecked")
 Comparable<? super K> k = (Comparable<? super K>) key;
 do {
 parent = t;
 cmp = k.compareTo(t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else return mergeValue(t, value, remappingFunction);
 } while (t != null);
 }
 addEntry(key, value, parent, cmp < 0);
 return value;
 }

 private V callMappingFunctionWithCheck(K key, Function<? super K, ? extends V> mappingFunction) {
 int mc = modCount;
 V newValue = mappingFunction.apply(key);
 if (mc != modCount) {
 throw new ConcurrentModificationException();
 }
 return newValue;
 }

 private V callRemappingFunctionWithCheck(K key, V oldValue, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 int mc = modCount;
 V newValue = remappingFunction.apply(key, oldValue);
 if (mc != modCount) {
 throw new ConcurrentModificationException();
 }
 return newValue;
 }

 private void addEntry(K key, V value, Entry<K, V> parent, boolean addToLeft) {
 Entry<K,V> e = new Entry<>(key, value, parent);
 if (addToLeft)
 parent.left = e;
 else
 parent.right = e;
 fixAfterInsertion(e);
 size++;
 modCount++;
 }

 private void addEntryToEmptyMap(K key, V value) {
 compare(key, key); // type (and possibly null) check
 root = new Entry<>(key, value, null);
 size = 1;
 modCount++;
 }

 private V put(K key, V value, boolean replaceOld) {
 Entry<K,V> t = root;
 if (t == null) {
 addEntryToEmptyMap(key, value);
 return null;
 }
 int cmp;
 Entry<K,V> parent;
 // split comparator and comparable paths
 Comparator<? super K> cpr = comparator;
 if (cpr != null) {
 do {
 parent = t;
 cmp = cpr.compare(key, t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else {
 V oldValue = t.value;
 if (replaceOld || oldValue == null) {
 t.value = value;
 }
 return oldValue;
 }
 } while (t != null);
 } else {
 Objects.requireNonNull(key);
 @SuppressWarnings("unchecked")
 Comparable<? super K> k = (Comparable<? super K>) key;
 do {
 parent = t;
 cmp = k.compareTo(t.key);
 if (cmp < 0)
 t = t.left;
 else if (cmp > 0)
 t = t.right;
 else {
 V oldValue = t.value;
 if (replaceOld || oldValue == null) {
 t.value = value;
 }
 return oldValue;
 }
 } while (t != null);
 }
 addEntry(key, value, parent, cmp < 0);
 return null;
 }

 private V remapValue(Entry<K,V> t, K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 V newValue = callRemappingFunctionWithCheck(key, t.value, remappingFunction);
 if (newValue == null) {
 deleteEntry(t);
 return null;
 } else {
 // replace old mapping
 t.value = newValue;
 return newValue;
 }
 }

 private V mergeValue(Entry<K,V> t, V value, BiFunction<? super V, ? super V, ? extends V> remappingFunction) {
 V oldValue = t.value;
 V newValue;
 if (t.value == null) {
 newValue = value;
 } else {
 int mc = modCount;
 newValue = remappingFunction.apply(oldValue, value);
 if (mc != modCount) {
 throw new ConcurrentModificationException();
 }
 }
 if (newValue == null) {
 deleteEntry(t);
 return null;
 } else {
 // replace old mapping
 t.value = newValue;
 return newValue;
 }
 }

 /**
 * Removes the mapping for this key from this TreeMap if present.
 *
 * @param key key for which mapping should be removed
 * @return the previous value associated with {@code key}, or
 * {@code null} if there was no mapping for {@code key}.
 * (A {@code null} return can also indicate that the map
 * previously associated {@code null} with {@code key}.)
 * @throws ClassCastException if the specified key cannot be compared
 * with the keys currently in the map
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 */
 public V remove(Object key) {
 Entry<K,V> p = getEntry(key);
 if (p == null)
 return null;

 V oldValue = p.value;
 deleteEntry(p);
 return oldValue;
 }

 /**
 * Removes all of the mappings from this map.
 * The map will be empty after this call returns.
 */
 public void clear() {
 modCount++;
 size = 0;
 root = null;
 }

 /**
 * Returns a shallow copy of this {@code TreeMap} instance. (The keys and
 * values themselves are not cloned.)
 *
 * @return a shallow copy of this map
 */
 public Object clone() {
 TreeMap<?,?> clone;
 try {
 clone = (TreeMap<?,?>) super.clone();
 } catch (CloneNotSupportedException e) {
 throw new InternalError(e);
 }

 // Put clone into "virgin" state (except for comparator)
 clone.root = null;
 clone.size = 0;
 clone.modCount = 0;
 clone.entrySet = null;
 clone.navigableKeySet = null;
 clone.descendingMap = null;

 // Initialize clone with our mappings
 try {
 clone.buildFromSorted(size, entrySet().iterator(), null, null);
 } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 }

 return clone;
 }

 // NavigableMap API methods

 /**
 * @since 1.6
 */
 public Map.Entry<K,V> firstEntry() {
 return exportEntry(getFirstEntry());
 }

 /**
 * @since 1.6
 */
 public Map.Entry<K,V> lastEntry() {
 return exportEntry(getLastEntry());
 }

 /**
 * @since 1.6
 */
 public Map.Entry<K,V> pollFirstEntry() {
 Entry<K,V> p = getFirstEntry();
 Map.Entry<K,V> result = exportEntry(p);
 if (p != null)
 deleteEntry(p);
 return result;
 }

 /**
 * @since 1.6
 */
 public Map.Entry<K,V> pollLastEntry() {
 Entry<K,V> p = getLastEntry();
 Map.Entry<K,V> result = exportEntry(p);
 if (p != null)
 deleteEntry(p);
 return result;
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public Map.Entry<K,V> lowerEntry(K key) {
 return exportEntry(getLowerEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public K lowerKey(K key) {
 return keyOrNull(getLowerEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public Map.Entry<K,V> floorEntry(K key) {
 return exportEntry(getFloorEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public K floorKey(K key) {
 return keyOrNull(getFloorEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public Map.Entry<K,V> ceilingEntry(K key) {
 return exportEntry(getCeilingEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public K ceilingKey(K key) {
 return keyOrNull(getCeilingEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public Map.Entry<K,V> higherEntry(K key) {
 return exportEntry(getHigherEntry(key));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if the specified key is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @since 1.6
 */
 public K higherKey(K key) {
 return keyOrNull(getHigherEntry(key));
 }

 // Views

 /**
 * Fields initialized to contain an instance of the entry set view
 * the first time this view is requested. Views are stateless, so
 * there's no reason to create more than one.
 */
 private transient EntrySet entrySet;
 private transient KeySet<K> navigableKeySet;
 private transient NavigableMap<K,V> descendingMap;

 /**
 * Returns a {@link Set} view of the keys contained in this map.
 *
 * The set's iterator returns the keys in ascending order.
 * The set's spliterator is
 * <a href="Spliterator.html#binding">late-binding</a>,
 * fail-fast, and additionally reports {@link Spliterator#SORTED}
 * and {@link Spliterator#ORDERED} with an encounter order that is ascending
 * key order. The spliterator's comparator (see
 * {@link java.util.Spliterator#getComparator()}) is {@code null} if
 * the tree map's comparator (see {@link #comparator()}) is {@code null}.
 * Otherwise, the spliterator's comparator is the same as or imposes the
 * same total ordering as the tree map's comparator.
 *
 * The set is backed by the map, so changes to the map are
 * reflected in the set, and vice-versa. If the map is modified
 * while an iteration over the set is in progress (except through
 * the iterator's own {@code remove} operation), the results of
 * the iteration are undefined. The set supports element removal,
 * which removes the corresponding mapping from the map, via the
 * {@code Iterator.remove}, {@code Set.remove},
 * {@code removeAll}, {@code retainAll}, and {@code clear}
 * operations. It does not support the {@code add} or {@code addAll}
 * operations.
 */
 public Set<K> keySet() {
 return navigableKeySet();
 }

 /**
 * @since 1.6
 */
 public NavigableSet<K> navigableKeySet() {
 KeySet<K> nks = navigableKeySet;
 return (nks != null) ? nks : (navigableKeySet = new KeySet<>(this));
 }

 /**
 * @since 1.6
 */
 public NavigableSet<K> descendingKeySet() {
 return descendingMap().navigableKeySet();
 }

 /**
 * Returns a {@link Collection} view of the values contained in this map.
 *
 * The collection's iterator returns the values in ascending order
 * of the corresponding keys. The collection's spliterator is
 * <a href="Spliterator.html#binding">late-binding</a>,
 * fail-fast, and additionally reports {@link Spliterator#ORDERED}
 * with an encounter order that is ascending order of the corresponding
 * keys.
 *
 * The collection is backed by the map, so changes to the map are
 * reflected in the collection, and vice-versa. If the map is
 * modified while an iteration over the collection is in progress
 * (except through the iterator's own {@code remove} operation),
 * the results of the iteration are undefined. The collection
 * supports element removal, which removes the corresponding
 * mapping from the map, via the {@code Iterator.remove},
 * {@code Collection.remove}, {@code removeAll},
 * {@code retainAll} and {@code clear} operations. It does not
 * support the {@code add} or {@code addAll} operations.
 */
 public Collection<V> values() {
 Collection<V> vs = values;
 if (vs == null) {
 vs = new Values();
 values = vs;
 }
 return vs;
 }

 /**
 * Returns a {@link Set} view of the mappings contained in this map.
 *
 * The set's iterator returns the entries in ascending key order. The
 * set's spliterator is
 * <a href="Spliterator.html#binding">late-binding</a>,
 * fail-fast, and additionally reports {@link Spliterator#SORTED} and
 * {@link Spliterator#ORDERED} with an encounter order that is ascending key
 * order.
 *
 * The set is backed by the map, so changes to the map are
 * reflected in the set, and vice-versa. If the map is modified
 * while an iteration over the set is in progress (except through
 * the iterator's own {@code remove} operation, or through the
 * {@code setValue} operation on a map entry returned by the
 * iterator) the results of the iteration are undefined. The set
 * supports element removal, which removes the corresponding
 * mapping from the map, via the {@code Iterator.remove},
 * {@code Set.remove}, {@code removeAll}, {@code retainAll} and
 * {@code clear} operations. It does not support the
 * {@code add} or {@code addAll} operations.
 */
 public Set<Map.Entry<K,V>> entrySet() {
 EntrySet es = entrySet;
 return (es != null) ? es : (entrySet = new EntrySet());
 }

 /**
 * @since 1.6
 */
 public NavigableMap<K, V> descendingMap() {
 NavigableMap<K, V> km = descendingMap;
 return (km != null) ? km :
 (descendingMap = new DescendingSubMap<>(this,
 true, null, true,
 true, null, true));
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if {@code fromKey} or {@code toKey} is
 * null and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @throws IllegalArgumentException {@inheritDoc}
 * @since 1.6
 */
 public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
 K toKey, boolean toInclusive) {
 return new AscendingSubMap<>(this,
 false, fromKey, fromInclusive,
 false, toKey, toInclusive);
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if {@code toKey} is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @throws IllegalArgumentException {@inheritDoc}
 * @since 1.6
 */
 public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
 return new AscendingSubMap<>(this,
 true, null, true,
 false, toKey, inclusive);
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if {@code fromKey} is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @throws IllegalArgumentException {@inheritDoc}
 * @since 1.6
 */
 public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
 return new AscendingSubMap<>(this,
 false, fromKey, inclusive,
 true, null, true);
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if {@code fromKey} or {@code toKey} is
 * null and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @throws IllegalArgumentException {@inheritDoc}
 */
 public SortedMap<K,V> subMap(K fromKey, K toKey) {
 return subMap(fromKey, true, toKey, false);
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if {@code toKey} is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @throws IllegalArgumentException {@inheritDoc}
 */
 public SortedMap<K,V> headMap(K toKey) {
 return headMap(toKey, false);
 }

 /**
 * @throws ClassCastException {@inheritDoc}
 * @throws NullPointerException if {@code fromKey} is null
 * and this map uses natural ordering, or its comparator
 * does not permit null keys
 * @throws IllegalArgumentException {@inheritDoc}
 */
 public SortedMap<K,V> tailMap(K fromKey) {
 return tailMap(fromKey, true);
 }

 @Override
 public boolean replace(K key, V oldValue, V newValue) {
 Entry<K,V> p = getEntry(key);
 if (p!=null && Objects.equals(oldValue, p.value)) {
 p.value = newValue;
 return true;
 }
 return false;
 }

 @Override
 public V replace(K key, V value) {
 Entry<K,V> p = getEntry(key);
 if (p!=null) {
 V oldValue = p.value;
 p.value = value;
 return oldValue;
 }
 return null;
 }

 @Override
 public void forEach(BiConsumer<? super K, ? super V> action) {
 Objects.requireNonNull(action);
 int expectedModCount = modCount;
 for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
 action.accept(e.key, e.value);

 if (expectedModCount != modCount) {
 throw new ConcurrentModificationException();
 }
 }
 }

 @Override
 public void replaceAll(BiFunction<? super K, ? super V, ? extends V> function) {
 Objects.requireNonNull(function);
 int expectedModCount = modCount;

 for (Entry<K, V> e = getFirstEntry(); e != null; e = successor(e)) {
 e.value = function.apply(e.key, e.value);

 if (expectedModCount != modCount) {
 throw new ConcurrentModificationException();
 }
 }
 }

 // View class support

 class Values extends AbstractCollection<V> {
 public Iterator<V> iterator() {
 return new ValueIterator(getFirstEntry());
 }

 public int size() {
 return TreeMap.this.size();
 }

 public boolean contains(Object o) {
 return TreeMap.this.containsValue(o);
 }

 public boolean remove(Object o) {
 for (Entry<K,V> e = getFirstEntry(); e != null; e = successor(e)) {
 if (valEquals(e.getValue(), o)) {
 deleteEntry(e);
 return true;
 }
 }
 return false;
 }

 public void clear() {
 TreeMap.this.clear();
 }

 public Spliterator<V> spliterator() {
 return new ValueSpliterator<>(TreeMap.this, null, null, 0, -1, 0);
 }
 }

 class EntrySet extends AbstractSet<Map.Entry<K,V>> {
 public Iterator<Map.Entry<K,V>> iterator() {
 return new EntryIterator(getFirstEntry());
 }

 public boolean contains(Object o) {
 if (!(o instanceof Map.Entry<?, ?> entry))
 return false;
 Object value = entry.getValue();
 Entry<K,V> p = getEntry(entry.getKey());
 return p != null && valEquals(p.getValue(), value);
 }

 public boolean remove(Object o) {
 if (!(o instanceof Map.Entry<?, ?> entry))
 return false;
 Object value = entry.getValue();
 Entry<K,V> p = getEntry(entry.getKey());
 if (p != null && valEquals(p.getValue(), value)) {
 deleteEntry(p);
 return true;
 }
 return false;
 }

 public int size() {
 return TreeMap.this.size();
 }

 public void clear() {
 TreeMap.this.clear();
 }

 public Spliterator<Map.Entry<K,V>> spliterator() {
 return new EntrySpliterator<>(TreeMap.this, null, null, 0, -1, 0);
 }
 }

 /*
 * Unlike Values and EntrySet, the KeySet class is static,
 * delegating to a NavigableMap to allow use by SubMaps, which
 * outweighs the ugliness of needing type-tests for the following
 * Iterator methods that are defined appropriately in main versus
 * submap classes.
 */

 Iterator<K> keyIterator() {
 return new KeyIterator(getFirstEntry());
 }

 Iterator<K> descendingKeyIterator() {
 return new DescendingKeyIterator(getLastEntry());
 }

 static final class KeySet<E> extends AbstractSet<E> implements NavigableSet<E> {
 private final NavigableMap<E, ?> m;
 KeySet(NavigableMap<E,?> map) { m = map; }

 public Iterator<E> iterator() {
 if (m instanceof TreeMap)
 return ((TreeMap<E,?>)m).keyIterator();
 else
 return ((TreeMap.NavigableSubMap<E,?>)m).keyIterator();
 }

 public Iterator<E> descendingIterator() {
 if (m instanceof TreeMap)
 return ((TreeMap<E,?>)m).descendingKeyIterator();
 else
 return ((TreeMap.NavigableSubMap<E,?>)m).descendingKeyIterator();
 }

 public int size() { return m.size(); }
 public boolean isEmpty() { return m.isEmpty(); }
 public boolean contains(Object o) { return m.containsKey(o); }
 public void clear() { m.clear(); }
 public E lower(E e) { return m.lowerKey(e); }
 public E floor(E e) { return m.floorKey(e); }
 public E ceiling(E e) { return m.ceilingKey(e); }
 public E higher(E e) { return m.higherKey(e); }
 public E first() { return m.firstKey(); }
 public E last() { return m.lastKey(); }
 public Comparator<? super E> comparator() { return m.comparator(); }
 public E pollFirst() {
 Map.Entry<E,?> e = m.pollFirstEntry();
 return (e == null) ? null : e.getKey();
 }
 public E pollLast() {
 Map.Entry<E,?> e = m.pollLastEntry();
 return (e == null) ? null : e.getKey();
 }
 public boolean remove(Object o) {
 int oldSize = size();
 m.remove(o);
 return size() != oldSize;
 }
 public NavigableSet<E> subSet(E fromElement, boolean fromInclusive,
 E toElement, boolean toInclusive) {
 return new KeySet<>(m.subMap(fromElement, fromInclusive,
 toElement, toInclusive));
 }
 public NavigableSet<E> headSet(E toElement, boolean inclusive) {
 return new KeySet<>(m.headMap(toElement, inclusive));
 }
 public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
 return new KeySet<>(m.tailMap(fromElement, inclusive));
 }
 public SortedSet<E> subSet(E fromElement, E toElement) {
 return subSet(fromElement, true, toElement, false);
 }
 public SortedSet<E> headSet(E toElement) {
 return headSet(toElement, false);
 }
 public SortedSet<E> tailSet(E fromElement) {
 return tailSet(fromElement, true);
 }
 public NavigableSet<E> descendingSet() {
 return new KeySet<>(m.descendingMap());
 }

 public Spliterator<E> spliterator() {
 return keySpliteratorFor(m);
 }
 }

 /**
 * Base class for TreeMap Iterators
 */
 abstract class PrivateEntryIterator<T> implements Iterator<T> {
 Entry<K,V> next;
 Entry<K,V> lastReturned;
 int expectedModCount;

 PrivateEntryIterator(Entry<K,V> first) {
 expectedModCount = modCount;
 lastReturned = null;
 next = first;
 }

 public final boolean hasNext() {
 return next != null;
 }

 final Entry<K,V> nextEntry() {
 Entry<K,V> e = next;
 if (e == null)
 throw new NoSuchElementException();
 if (modCount != expectedModCount)
 throw new ConcurrentModificationException();
 next = successor(e);
 lastReturned = e;
 return e;
 }

 final Entry<K,V> prevEntry() {
 Entry<K,V> e = next;
 if (e == null)
 throw new NoSuchElementException();
 if (modCount != expectedModCount)
 throw new ConcurrentModificationException();
 next = predecessor(e);
 lastReturned = e;
 return e;
 }

 public void remove() {
 if (lastReturned == null)
 throw new IllegalStateException();
 if (modCount != expectedModCount)
 throw new ConcurrentModificationException();
 // deleted entries are replaced by their successors
 if (lastReturned.left != null && lastReturned.right != null)
 next = lastReturned;
 deleteEntry(lastReturned);
 expectedModCount = modCount;
 lastReturned = null;
 }
 }

 final class EntryIterator extends PrivateEntryIterator<Map.Entry<K,V>> {
 EntryIterator(Entry<K,V> first) {
 super(first);
 }
 public Map.Entry<K,V> next() {
 return nextEntry();
 }
 }

 final class ValueIterator extends PrivateEntryIterator<V> {
 ValueIterator(Entry<K,V> first) {
 super(first);
 }
 public V next() {
 return nextEntry().value;
 }
 }

 final class KeyIterator extends PrivateEntryIterator<K> {
 KeyIterator(Entry<K,V> first) {
 super(first);
 }
 public K next() {
 return nextEntry().key;
 }
 }

 final class DescendingKeyIterator extends PrivateEntryIterator<K> {
 DescendingKeyIterator(Entry<K,V> first) {
 super(first);
 }
 public K next() {
 return prevEntry().key;
 }
 public void remove() {
 if (lastReturned == null)
 throw new IllegalStateException();
 if (modCount != expectedModCount)
 throw new ConcurrentModificationException();
 deleteEntry(lastReturned);
 lastReturned = null;
 expectedModCount = modCount;
 }
 }

 // Little utilities

 /**
 * Compares two keys using the correct comparison method for this TreeMap.
 */
 @SuppressWarnings("unchecked")
 final int compare(Object k1, Object k2) {
 return comparator==null ? ((Comparable<? super K>)k1).compareTo((K)k2)
 : comparator.compare((K)k1, (K)k2);
 }

 /**
 * Test two values for equality. Differs from o1.equals(o2) only in
 * that it copes with {@code null} o1 properly.
 */
 static final boolean valEquals(Object o1, Object o2) {
 return (o1==null ? o2==null : o1.equals(o2));
 }

 /**
 * Return SimpleImmutableEntry for entry, or null if null
 */
 static <K,V> Map.Entry<K,V> exportEntry(TreeMap.Entry<K,V> e) {
 return (e == null) ? null :
 new AbstractMap.SimpleImmutableEntry<>(e);
 }

 /**
 * Return key for entry, or null if null
 */
 static <K,V> K keyOrNull(TreeMap.Entry<K,V> e) {
 return (e == null) ? null : e.key;
 }

 /**
 * Returns the key corresponding to the specified Entry.
 * @throws NoSuchElementException if the Entry is null
 */
 static <K> K key(Entry<K,?> e) {
 if (e==null)
 throw new NoSuchElementException();
 return e.key;
 }

 // SubMaps

 /**
 * Dummy value serving as unmatchable fence key for unbounded
 * SubMapIterators
 */
 private static final Object UNBOUNDED = new Object();

 /**
 * @serial include
 */
 abstract static class NavigableSubMap<K,V> extends AbstractMap<K,V>
 implements NavigableMap<K,V>, java.io.Serializable {
 @java.io.Serial
 private static final long serialVersionUID = -2102997345730753016L;
 /**
 * The backing map.
 */
 final TreeMap<K,V> m;

 /**
 * Endpoints are represented as triples (fromStart, lo,
 * loInclusive) and (toEnd, hi, hiInclusive). If fromStart is
 * true, then the low (absolute) bound is the start of the
 * backing map, and the other values are ignored. Otherwise,
 * if loInclusive is true, lo is the inclusive bound, else lo
 * is the exclusive bound. Similarly for the upper bound.
 */
 @SuppressWarnings("serial") // Conditionally serializable
 final K lo;
 @SuppressWarnings("serial") // Conditionally serializable
 final K hi;
 final boolean fromStart, toEnd;
 final boolean loInclusive, hiInclusive;

 NavigableSubMap(TreeMap<K,V> m,
 boolean fromStart, K lo, boolean loInclusive,
 boolean toEnd, K hi, boolean hiInclusive) {
 if (!fromStart && !toEnd) {
 if (m.compare(lo, hi) > 0)
 throw new IllegalArgumentException("fromKey > toKey");
 } else {
 if (!fromStart) // type check
 m.compare(lo, lo);
 if (!toEnd)
 m.compare(hi, hi);
 }

 this.m = m;
 this.fromStart = fromStart;
 this.lo = lo;
 this.loInclusive = loInclusive;
 this.toEnd = toEnd;
 this.hi = hi;
 this.hiInclusive = hiInclusive;
 }

 // internal utilities

 final boolean tooLow(Object key) {
 if (!fromStart) {
 int c = m.compare(key, lo);
 if (c < 0 || (c == 0 && !loInclusive))
 return true;
 }
 return false;
 }

 final boolean tooHigh(Object key) {
 if (!toEnd) {
 int c = m.compare(key, hi);
 if (c > 0 || (c == 0 && !hiInclusive))
 return true;
 }
 return false;
 }

 final boolean inRange(Object key) {
 return !tooLow(key) && !tooHigh(key);
 }

 final boolean inClosedRange(Object key) {
 return (fromStart || m.compare(key, lo) >= 0)
 && (toEnd || m.compare(hi, key) >= 0);
 }

 final boolean inRange(Object key, boolean inclusive) {
 return inclusive ? inRange(key) : inClosedRange(key);
 }

 /*
 * Absolute versions of relation operations.
 * Subclasses map to these using like-named "sub"
 * versions that invert senses for descending maps
 */

 final TreeMap.Entry<K,V> absLowest() {
 TreeMap.Entry<K,V> e =
 (fromStart ? m.getFirstEntry() :
 (loInclusive ? m.getCeilingEntry(lo) :
 m.getHigherEntry(lo)));
 return (e == null || tooHigh(e.key)) ? null : e;
 }

 final TreeMap.Entry<K,V> absHighest() {
 TreeMap.Entry<K,V> e =
 (toEnd ? m.getLastEntry() :
 (hiInclusive ? m.getFloorEntry(hi) :
 m.getLowerEntry(hi)));
 return (e == null || tooLow(e.key)) ? null : e;
 }

 final TreeMap.Entry<K,V> absCeiling(K key) {
 if (tooLow(key))
 return absLowest();
 TreeMap.Entry<K,V> e = m.getCeilingEntry(key);
 return (e == null || tooHigh(e.key)) ? null : e;
 }

 final TreeMap.Entry<K,V> absHigher(K key) {
 if (tooLow(key))
 return absLowest();
 TreeMap.Entry<K,V> e = m.getHigherEntry(key);
 return (e == null || tooHigh(e.key)) ? null : e;
 }

 final TreeMap.Entry<K,V> absFloor(K key) {
 if (tooHigh(key))
 return absHighest();
 TreeMap.Entry<K,V> e = m.getFloorEntry(key);
 return (e == null || tooLow(e.key)) ? null : e;
 }

 final TreeMap.Entry<K,V> absLower(K key) {
 if (tooHigh(key))
 return absHighest();
 TreeMap.Entry<K,V> e = m.getLowerEntry(key);
 return (e == null || tooLow(e.key)) ? null : e;
 }

 /** Returns the absolute high fence for ascending traversal */
 final TreeMap.Entry<K,V> absHighFence() {
 return (toEnd ? null : (hiInclusive ?
 m.getHigherEntry(hi) :
 m.getCeilingEntry(hi)));
 }

 /** Return the absolute low fence for descending traversal */
 final TreeMap.Entry<K,V> absLowFence() {
 return (fromStart ? null : (loInclusive ?
 m.getLowerEntry(lo) :
 m.getFloorEntry(lo)));
 }

 // Abstract methods defined in ascending vs descending classes
 // These relay to the appropriate absolute versions

 abstract TreeMap.Entry<K,V> subLowest();
 abstract TreeMap.Entry<K,V> subHighest();
 abstract TreeMap.Entry<K,V> subCeiling(K key);
 abstract TreeMap.Entry<K,V> subHigher(K key);
 abstract TreeMap.Entry<K,V> subFloor(K key);
 abstract TreeMap.Entry<K,V> subLower(K key);

 /** Returns ascending iterator from the perspective of this submap */
 abstract Iterator<K> keyIterator();

 abstract Spliterator<K> keySpliterator();

 /** Returns descending iterator from the perspective of this submap */
 abstract Iterator<K> descendingKeyIterator();

 // public methods

 public boolean isEmpty() {
 return (fromStart && toEnd) ? m.isEmpty() : entrySet().isEmpty();
 }

 public int size() {
 return (fromStart && toEnd) ? m.size() : entrySet().size();
 }

 public final boolean containsKey(Object key) {
 return inRange(key) && m.containsKey(key);
 }

 public final V put(K key, V value) {
 if (!inRange(key))
 throw new IllegalArgumentException("key out of range");
 return m.put(key, value);
 }

 public V putIfAbsent(K key, V value) {
 if (!inRange(key))
 throw new IllegalArgumentException("key out of range");
 return m.putIfAbsent(key, value);
 }

 public V merge(K key, V value, BiFunction<? super V, ? super V, ? extends V> remappingFunction) {
 if (!inRange(key))
 throw new IllegalArgumentException("key out of range");
 return m.merge(key, value, remappingFunction);
 }

 public V computeIfAbsent(K key, Function<? super K, ? extends V> mappingFunction) {
 if (!inRange(key)) {
 // Do not throw if mapping function returns null
 // to preserve compatibility with default computeIfAbsent implementation
 if (mappingFunction.apply(key) == null) return null;
 throw new IllegalArgumentException("key out of range");
 }
 return m.computeIfAbsent(key, mappingFunction);
 }

 public V compute(K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 if (!inRange(key)) {
 // Do not throw if remapping function returns null
 // to preserve compatibility with default computeIfAbsent implementation
 if (remappingFunction.apply(key, null) == null) return null;
 throw new IllegalArgumentException("key out of range");
 }
 return m.compute(key, remappingFunction);
 }

 public V computeIfPresent(K key, BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
 return !inRange(key) ? null : m.computeIfPresent(key, remappingFunction);
 }

 public final V get(Object key) {
 return !inRange(key) ? null : m.get(key);
 }

 public final V remove(Object key) {
 return !inRange(key) ? null : m.remove(key);
 }

 public final Map.Entry<K,V> ceilingEntry(K key) {
 return exportEntry(subCeiling(key));
 }

 public final K ceilingKey(K key) {
 return keyOrNull(subCeiling(key));
 }

 public final Map.Entry<K,V> higherEntry(K key) {
 return exportEntry(subHigher(key));
 }

 public final K higherKey(K key) {
 return keyOrNull(subHigher(key));
 }

 public final Map.Entry<K,V> floorEntry(K key) {
 return exportEntry(subFloor(key));
 }

 public final K floorKey(K key) {
 return keyOrNull(subFloor(key));
 }

 public final Map.Entry<K,V> lowerEntry(K key) {
 return exportEntry(subLower(key));
 }

 public final K lowerKey(K key) {
 return keyOrNull(subLower(key));
 }

 public final K firstKey() {
 return key(subLowest());
 }

 public final K lastKey() {
 return key(subHighest());
 }

 public final Map.Entry<K,V> firstEntry() {
 return exportEntry(subLowest());
 }

 public final Map.Entry<K,V> lastEntry() {
 return exportEntry(subHighest());
 }

 public final Map.Entry<K,V> pollFirstEntry() {
 TreeMap.Entry<K,V> e = subLowest();
 Map.Entry<K,V> result = exportEntry(e);
 if (e != null)
 m.deleteEntry(e);
 return result;
 }

 public final Map.Entry<K,V> pollLastEntry() {
 TreeMap.Entry<K,V> e = subHighest();
 Map.Entry<K,V> result = exportEntry(e);
 if (e != null)
 m.deleteEntry(e);
 return result;
 }

 // Views
 transient NavigableMap<K,V> descendingMapView;
 transient EntrySetView entrySetView;
 transient KeySet<K> navigableKeySetView;

 public final NavigableSet<K> navigableKeySet() {
 KeySet<K> nksv = navigableKeySetView;
 return (nksv != null) ? nksv :
 (navigableKeySetView = new TreeMap.KeySet<>(this));
 }

 public final Set<K> keySet() {
 return navigableKeySet();
 }

 public NavigableSet<K> descendingKeySet() {
 return descendingMap().navigableKeySet();
 }

 public final SortedMap<K,V> subMap(K fromKey, K toKey) {
 return subMap(fromKey, true, toKey, false);
 }

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

 public final SortedMap<K,V> tailMap(K fromKey) {
 return tailMap(fromKey, true);
 }

 // View classes

 abstract class EntrySetView extends AbstractSet<Map.Entry<K,V>> {
 private transient int size = -1, sizeModCount;

 public int size() {
 if (fromStart && toEnd)
 return m.size();
 if (size == -1 || sizeModCount != m.modCount) {
 sizeModCount = m.modCount;
 size = 0;
 Iterator<?> i = iterator();
 while (i.hasNext()) {
 size++;
 i.next();
 }
 }
 return size;
 }

 public boolean isEmpty() {
 TreeMap.Entry<K,V> n = absLowest();
 return n == null || tooHigh(n.key);
 }

 public boolean contains(Object o) {
 if (!(o instanceof Entry<?, ?> entry))
 return false;
 Object key = entry.getKey();
 if (!inRange(key))
 return false;
 TreeMap.Entry<?,?> node = m.getEntry(key);
 return node != null &&
 valEquals(node.getValue(), entry.getValue());
 }

 public boolean remove(Object o) {
 if (!(o instanceof Entry<?, ?> entry))
 return false;
 Object key = entry.getKey();
 if (!inRange(key))
 return false;
 TreeMap.Entry<K,V> node = m.getEntry(key);
 if (node!=null && valEquals(node.getValue(),
 entry.getValue())) {
 m.deleteEntry(node);
 return true;
 }
 return false;
 }
 }

 /**
 * Iterators for SubMaps
 */
 abstract class SubMapIterator<T> implements Iterator<T> {
 TreeMap.Entry<K,V> lastReturned;
 TreeMap.Entry<K,V> next;
 final Object fenceKey;
 int expectedModCount;

 SubMapIterator(TreeMap.Entry<K,V> first,
 TreeMap.Entry<K,V> fence) {
 expectedModCount = m.modCount;
 lastReturned = null;
 next = first;
 fenceKey = fence == null ? UNBOUNDED : fence.key;
 }

 public final boolean hasNext() {
 return next != null && next.key != fenceKey;
 }

 final TreeMap.Entry<K,V> nextEntry() {
 TreeMap.Entry<K,V> e = next;
 if (e == null || e.key == fenceKey)
 throw new NoSuchElementException();
 if (m.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 next = successor(e);
 lastReturned = e;
 return e;
 }

 final TreeMap.Entry<K,V> prevEntry() {
 TreeMap.Entry<K,V> e = next;
 if (e == null || e.key == fenceKey)
 throw new NoSuchElementException();
 if (m.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 next = predecessor(e);
 lastReturned = e;
 return e;
 }

 final void removeAscending() {
 if (lastReturned == null)
 throw new IllegalStateException();
 if (m.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 // deleted entries are replaced by their successors
 if (lastReturned.left != null && lastReturned.right != null)
 next = lastReturned;
 m.deleteEntry(lastReturned);
 lastReturned = null;
 expectedModCount = m.modCount;
 }

 final void removeDescending() {
 if (lastReturned == null)
 throw new IllegalStateException();
 if (m.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 m.deleteEntry(lastReturned);
 lastReturned = null;
 expectedModCount = m.modCount;
 }

 }

 final class SubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
 SubMapEntryIterator(TreeMap.Entry<K,V> first,
 TreeMap.Entry<K,V> fence) {
 super(first, fence);
 }
 public Map.Entry<K,V> next() {
 return nextEntry();
 }
 public void remove() {
 removeAscending();
 }
 }

 final class DescendingSubMapEntryIterator extends SubMapIterator<Map.Entry<K,V>> {
 DescendingSubMapEntryIterator(TreeMap.Entry<K,V> last,
 TreeMap.Entry<K,V> fence) {
 super(last, fence);
 }

 public Map.Entry<K,V> next() {
 return prevEntry();
 }
 public void remove() {
 removeDescending();
 }
 }

 // Implement minimal Spliterator as KeySpliterator backup
 final class SubMapKeyIterator extends SubMapIterator<K>
 implements Spliterator<K> {
 SubMapKeyIterator(TreeMap.Entry<K,V> first,
 TreeMap.Entry<K,V> fence) {
 super(first, fence);
 }
 public K next() {
 return nextEntry().key;
 }
 public void remove() {
 removeAscending();
 }
 public Spliterator<K> trySplit() {
 return null;
 }
 public void forEachRemaining(Consumer<? super K> action) {
 while (hasNext())
 action.accept(next());
 }
 public boolean tryAdvance(Consumer<? super K> action) {
 if (hasNext()) {
 action.accept(next());
 return true;
 }
 return false;
 }
 public long estimateSize() {
 return Long.MAX_VALUE;
 }
 public int characteristics() {
 return Spliterator.DISTINCT | Spliterator.ORDERED |
 Spliterator.SORTED;
 }
 public final Comparator<? super K> getComparator() {
 return NavigableSubMap.this.comparator();
 }
 }

 final class DescendingSubMapKeyIterator extends SubMapIterator<K>
 implements Spliterator<K> {
 DescendingSubMapKeyIterator(TreeMap.Entry<K,V> last,
 TreeMap.Entry<K,V> fence) {
 super(last, fence);
 }
 public K next() {
 return prevEntry().key;
 }
 public void remove() {
 removeDescending();
 }
 public Spliterator<K> trySplit() {
 return null;
 }
 public void forEachRemaining(Consumer<? super K> action) {
 while (hasNext())
 action.accept(next());
 }
 public boolean tryAdvance(Consumer<? super K> action) {
 if (hasNext()) {
 action.accept(next());
 return true;
 }
 return false;
 }
 public long estimateSize() {
 return Long.MAX_VALUE;
 }
 public int characteristics() {
 return Spliterator.DISTINCT | Spliterator.ORDERED;
 }
 }
 }

 /**
 * @serial include
 */
 static final class AscendingSubMap<K,V> extends NavigableSubMap<K,V> {
 @java.io.Serial
 private static final long serialVersionUID = 912986545866124060L;

 AscendingSubMap(TreeMap<K,V> m,
 boolean fromStart, K lo, boolean loInclusive,
 boolean toEnd, K hi, boolean hiInclusive) {
 super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
 }

 public Comparator<? super K> comparator() {
 return m.comparator();
 }

 public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
 K toKey, boolean toInclusive) {
 if (!inRange(fromKey, fromInclusive))
 throw new IllegalArgumentException("fromKey out of range");
 if (!inRange(toKey, toInclusive))
 throw new IllegalArgumentException("toKey out of range");
 return new AscendingSubMap<>(m,
 false, fromKey, fromInclusive,
 false, toKey, toInclusive);
 }

 public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
 if (!inRange(toKey, inclusive))
 throw new IllegalArgumentException("toKey out of range");
 return new AscendingSubMap<>(m,
 fromStart, lo, loInclusive,
 false, toKey, inclusive);
 }

 public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
 if (!inRange(fromKey, inclusive))
 throw new IllegalArgumentException("fromKey out of range");
 return new AscendingSubMap<>(m,
 false, fromKey, inclusive,
 toEnd, hi, hiInclusive);
 }

 public NavigableMap<K,V> descendingMap() {
 NavigableMap<K,V> mv = descendingMapView;
 return (mv != null) ? mv :
 (descendingMapView =
 new DescendingSubMap<>(m,
 fromStart, lo, loInclusive,
 toEnd, hi, hiInclusive));
 }

 Iterator<K> keyIterator() {
 return new SubMapKeyIterator(absLowest(), absHighFence());
 }

 Spliterator<K> keySpliterator() {
 return new SubMapKeyIterator(absLowest(), absHighFence());
 }

 Iterator<K> descendingKeyIterator() {
 return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
 }

 final class AscendingEntrySetView extends EntrySetView {
 public Iterator<Map.Entry<K,V>> iterator() {
 return new SubMapEntryIterator(absLowest(), absHighFence());
 }
 }

 public Set<Map.Entry<K,V>> entrySet() {
 EntrySetView es = entrySetView;
 return (es != null) ? es : (entrySetView = new AscendingEntrySetView());
 }

 TreeMap.Entry<K,V> subLowest() { return absLowest(); }
 TreeMap.Entry<K,V> subHighest() { return absHighest(); }
 TreeMap.Entry<K,V> subCeiling(K key) { return absCeiling(key); }
 TreeMap.Entry<K,V> subHigher(K key) { return absHigher(key); }
 TreeMap.Entry<K,V> subFloor(K key) { return absFloor(key); }
 TreeMap.Entry<K,V> subLower(K key) { return absLower(key); }
 }

 /**
 * @serial include
 */
 static final class DescendingSubMap<K,V> extends NavigableSubMap<K,V> {
 @java.io.Serial
 private static final long serialVersionUID = 912986545866120460L;
 DescendingSubMap(TreeMap<K,V> m,
 boolean fromStart, K lo, boolean loInclusive,
 boolean toEnd, K hi, boolean hiInclusive) {
 super(m, fromStart, lo, loInclusive, toEnd, hi, hiInclusive);
 }

 @SuppressWarnings("serial") // Conditionally serializable
 private final Comparator<? super K> reverseComparator =
 Collections.reverseOrder(m.comparator);

 public Comparator<? super K> comparator() {
 return reverseComparator;
 }

 public NavigableMap<K,V> subMap(K fromKey, boolean fromInclusive,
 K toKey, boolean toInclusive) {
 if (!inRange(fromKey, fromInclusive))
 throw new IllegalArgumentException("fromKey out of range");
 if (!inRange(toKey, toInclusive))
 throw new IllegalArgumentException("toKey out of range");
 return new DescendingSubMap<>(m,
 false, toKey, toInclusive,
 false, fromKey, fromInclusive);
 }

 public NavigableMap<K,V> headMap(K toKey, boolean inclusive) {
 if (!inRange(toKey, inclusive))
 throw new IllegalArgumentException("toKey out of range");
 return new DescendingSubMap<>(m,
 false, toKey, inclusive,
 toEnd, hi, hiInclusive);
 }

 public NavigableMap<K,V> tailMap(K fromKey, boolean inclusive) {
 if (!inRange(fromKey, inclusive))
 throw new IllegalArgumentException("fromKey out of range");
 return new DescendingSubMap<>(m,
 fromStart, lo, loInclusive,
 false, fromKey, inclusive);
 }

 public NavigableMap<K,V> descendingMap() {
 NavigableMap<K,V> mv = descendingMapView;
 return (mv != null) ? mv :
 (descendingMapView =
 new AscendingSubMap<>(m,
 fromStart, lo, loInclusive,
 toEnd, hi, hiInclusive));
 }

 Iterator<K> keyIterator() {
 return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
 }

 Spliterator<K> keySpliterator() {
 return new DescendingSubMapKeyIterator(absHighest(), absLowFence());
 }

 Iterator<K> descendingKeyIterator() {
 return new SubMapKeyIterator(absLowest(), absHighFence());
 }

 final class DescendingEntrySetView extends EntrySetView {
 public Iterator<Map.Entry<K,V>> iterator() {
 return new DescendingSubMapEntryIterator(absHighest(), absLowFence());
 }
 }

 public Set<Map.Entry<K,V>> entrySet() {
 EntrySetView es = entrySetView;
 return (es != null) ? es : (entrySetView = new DescendingEntrySetView());
 }

 TreeMap.Entry<K,V> subLowest() { return absHighest(); }
 TreeMap.Entry<K,V> subHighest() { return absLowest(); }
 TreeMap.Entry<K,V> subCeiling(K key) { return absFloor(key); }
 TreeMap.Entry<K,V> subHigher(K key) { return absLower(key); }
 TreeMap.Entry<K,V> subFloor(K key) { return absCeiling(key); }
 TreeMap.Entry<K,V> subLower(K key) { return absHigher(key); }
 }

 /**
 * This class exists solely for the sake of serialization
 * compatibility with previous releases of TreeMap that did not
 * support NavigableMap. It translates an old-version SubMap into
 * a new-version AscendingSubMap. This class is never otherwise
 * used.
 *
 * @serial include
 */
 private class SubMap extends AbstractMap<K,V>
 implements SortedMap<K,V>, java.io.Serializable {
 @java.io.Serial
 private static final long serialVersionUID = -6520786458950516097L;
 private boolean fromStart = false, toEnd = false;
 @SuppressWarnings("serial") // Conditionally serializable
 private K fromKey;
 @SuppressWarnings("serial") // Conditionally serializable
 private K toKey;
 @java.io.Serial
 private Object readResolve() {
 return new AscendingSubMap<>(TreeMap.this,
 fromStart, fromKey, true,
 toEnd, toKey, false);
 }
 public Set<Map.Entry<K,V>> entrySet() { throw new InternalError(); }
 public K lastKey() { throw new InternalError(); }
 public K firstKey() { throw new InternalError(); }
 public SortedMap<K,V> subMap(K fromKey, K toKey) { throw new InternalError(); }
 public SortedMap<K,V> headMap(K toKey) { throw new InternalError(); }
 public SortedMap<K,V> tailMap(K fromKey) { throw new InternalError(); }
 public Comparator<? super K> comparator() { throw new InternalError(); }
 }

 // Red-black mechanics

 private static final boolean RED = false;
 private static final boolean BLACK = true;

 /**
 * Node in the Tree. Doubles as a means to pass key-value pairs back to
 * user (see Map.Entry).
 */

 static final class Entry<K,V> implements Map.Entry<K,V> {
 K key;
 V value;
 Entry<K,V> left;
 Entry<K,V> right;
 Entry<K,V> parent;
 boolean color = BLACK;

 /**
 * Make a new cell with given key, value, and parent, and with
 * {@code null} child links, and BLACK color.
 */
 Entry(K key, V value, Entry<K,V> parent) {
 this.key = key;
 this.value = value;
 this.parent = parent;
 }

 /**
 * Returns the key.
 *
 * @return the key
 */
 public K getKey() {
 return key;
 }

 /**
 * Returns the value associated with the key.
 *
 * @return the value associated with the key
 */
 public V getValue() {
 return value;
 }

 /**
 * Replaces the value currently associated with the key with the given
 * value.
 *
 * @return the value associated with the key before this method was
 * called
 */
 public V setValue(V value) {
 V oldValue = this.value;
 this.value = value;
 return oldValue;
 }

 public boolean equals(Object o) {
 return o instanceof Map.Entry<?, ?> e
 && valEquals(key,e.getKey())
 && valEquals(value,e.getValue());
 }

 public int hashCode() {
 int keyHash = (key==null ? 0 : key.hashCode());
 int valueHash = (value==null ? 0 : value.hashCode());
 return keyHash ^ valueHash;
 }

 public String toString() {
 return key + "=" + value;
 }
 }

 /**
 * Returns the first Entry in the TreeMap (according to the TreeMap's
 * key-sort function). Returns null if the TreeMap is empty.
 */
 final Entry<K,V> getFirstEntry() {
 Entry<K,V> p = root;
 if (p != null)
 while (p.left != null)
 p = p.left;
 return p;
 }

 /**
 * Returns the last Entry in the TreeMap (according to the TreeMap's
 * key-sort function). Returns null if the TreeMap is empty.
 */
 final Entry<K,V> getLastEntry() {
 Entry<K,V> p = root;
 if (p != null)
 while (p.right != null)
 p = p.right;
 return p;
 }

 /**
 * Returns the successor of the specified Entry, or null if no such.
 */
 static <K,V> TreeMap.Entry<K,V> successor(Entry<K,V> t) {
 if (t == null)
 return null;
 else if (t.right != null) {
 Entry<K,V> p = t.right;
 while (p.left != null)
 p = p.left;
 return p;
 } else {
 Entry<K,V> p = t.parent;
 Entry<K,V> ch = t;
 while (p != null && ch == p.right) {
 ch = p;
 p = p.parent;
 }
 return p;
 }
 }

 /**
 * Returns the predecessor of the specified Entry, or null if no such.
 */
 static <K,V> Entry<K,V> predecessor(Entry<K,V> t) {
 if (t == null)
 return null;
 else if (t.left != null) {
 Entry<K,V> p = t.left;
 while (p.right != null)
 p = p.right;
 return p;
 } else {
 Entry<K,V> p = t.parent;
 Entry<K,V> ch = t;
 while (p != null && ch == p.left) {
 ch = p;
 p = p.parent;
 }
 return p;
 }
 }

 /**
 * Balancing operations.
 *
 * Implementations of rebalancings during insertion and deletion are
 * slightly different than the CLR version. Rather than using dummy
 * nilnodes, we use a set of accessors that deal properly with null. They
 * are used to avoid messiness surrounding nullness checks in the main
 * algorithms.
 */

 private static <K,V> boolean colorOf(Entry<K,V> p) {
 return (p == null ? BLACK : p.color);
 }

 private static <K,V> Entry<K,V> parentOf(Entry<K,V> p) {
 return (p == null ? null: p.parent);
 }

 private static <K,V> void setColor(Entry<K,V> p, boolean c) {
 if (p != null)
 p.color = c;
 }

 private static <K,V> Entry<K,V> leftOf(Entry<K,V> p) {
 return (p == null) ? null: p.left;
 }

 private static <K,V> Entry<K,V> rightOf(Entry<K,V> p) {
 return (p == null) ? null: p.right;
 }

 /** From CLR */
 private void rotateLeft(Entry<K,V> p) {
 if (p != null) {
 Entry<K,V> r = p.right;
 p.right = r.left;
 if (r.left != null)
 r.left.parent = p;
 r.parent = p.parent;
 if (p.parent == null)
 root = r;
 else if (p.parent.left == p)
 p.parent.left = r;
 else
 p.parent.right = r;
 r.left = p;
 p.parent = r;
 }
 }

 /** From CLR */
 private void rotateRight(Entry<K,V> p) {
 if (p != null) {
 Entry<K,V> l = p.left;
 p.left = l.right;
 if (l.right != null) l.right.parent = p;
 l.parent = p.parent;
 if (p.parent == null)
 root = l;
 else if (p.parent.right == p)
 p.parent.right = l;
 else p.parent.left = l;
 l.right = p;
 p.parent = l;
 }
 }

 /** From CLR */
 private void fixAfterInsertion(Entry<K,V> x) {
 x.color = RED;

 while (x != null && x != root && x.parent.color == RED) {
 if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
 Entry<K,V> y = rightOf(parentOf(parentOf(x)));
 if (colorOf(y) == RED) {
 setColor(parentOf(x), BLACK);
 setColor(y, BLACK);
 setColor(parentOf(parentOf(x)), RED);
 x = parentOf(parentOf(x));
 } else {
 if (x == rightOf(parentOf(x))) {
 x = parentOf(x);
 rotateLeft(x);
 }
 setColor(parentOf(x), BLACK);
 setColor(parentOf(parentOf(x)), RED);
 rotateRight(parentOf(parentOf(x)));
 }
 } else {
 Entry<K,V> y = leftOf(parentOf(parentOf(x)));
 if (colorOf(y) == RED) {
 setColor(parentOf(x), BLACK);
 setColor(y, BLACK);
 setColor(parentOf(parentOf(x)), RED);
 x = parentOf(parentOf(x));
 } else {
 if (x == leftOf(parentOf(x))) {
 x = parentOf(x);
 rotateRight(x);
 }
 setColor(parentOf(x), BLACK);
 setColor(parentOf(parentOf(x)), RED);
 rotateLeft(parentOf(parentOf(x)));
 }
 }
 }
 root.color = BLACK;
 }

 /**
 * Delete node p, and then rebalance the tree.
 */
 private void deleteEntry(Entry<K,V> p) {
 modCount++;
 size--;

 // If strictly internal, copy successor's element to p and then make p
 // point to successor.
 if (p.left != null && p.right != null) {
 Entry<K,V> s = successor(p);
 p.key = s.key;
 p.value = s.value;
 p = s;
 } // p has 2 children

 // Start fixup at replacement node, if it exists.
 Entry<K,V> replacement = (p.left != null ? p.left : p.right);

 if (replacement != null) {
 // Link replacement to parent
 replacement.parent = p.parent;
 if (p.parent == null)
 root = replacement;
 else if (p == p.parent.left)
 p.parent.left = replacement;
 else
 p.parent.right = replacement;

 // Null out links so they are OK to use by fixAfterDeletion.
 p.left = p.right = p.parent = null;

 // Fix replacement
 if (p.color == BLACK)
 fixAfterDeletion(replacement);
 } else if (p.parent == null) { // return if we are the only node.
 root = null;
 } else { // No children. Use self as phantom replacement and unlink.
 if (p.color == BLACK)
 fixAfterDeletion(p);

 if (p.parent != null) {
 if (p == p.parent.left)
 p.parent.left = null;
 else if (p == p.parent.right)
 p.parent.right = null;
 p.parent = null;
 }
 }
 }

 /** From CLR */
 private void fixAfterDeletion(Entry<K,V> x) {
 while (x != root && colorOf(x) == BLACK) {
 if (x == leftOf(parentOf(x))) {
 Entry<K,V> sib = rightOf(parentOf(x));

 if (colorOf(sib) == RED) {
 setColor(sib, BLACK);
 setColor(parentOf(x), RED);
 rotateLeft(parentOf(x));
 sib = rightOf(parentOf(x));
 }

 if (colorOf(leftOf(sib)) == BLACK &&
 colorOf(rightOf(sib)) == BLACK) {
 setColor(sib, RED);
 x = parentOf(x);
 } else {
 if (colorOf(rightOf(sib)) == BLACK) {
 setColor(leftOf(sib), BLACK);
 setColor(sib, RED);
 rotateRight(sib);
 sib = rightOf(parentOf(x));
 }
 setColor(sib, colorOf(parentOf(x)));
 setColor(parentOf(x), BLACK);
 setColor(rightOf(sib), BLACK);
 rotateLeft(parentOf(x));
 x = root;
 }
 } else { // symmetric
 Entry<K,V> sib = leftOf(parentOf(x));

 if (colorOf(sib) == RED) {
 setColor(sib, BLACK);
 setColor(parentOf(x), RED);
 rotateRight(parentOf(x));
 sib = leftOf(parentOf(x));
 }

 if (colorOf(rightOf(sib)) == BLACK &&
 colorOf(leftOf(sib)) == BLACK) {
 setColor(sib, RED);
 x = parentOf(x);
 } else {
 if (colorOf(leftOf(sib)) == BLACK) {
 setColor(rightOf(sib), BLACK);
 setColor(sib, RED);
 rotateLeft(sib);
 sib = leftOf(parentOf(x));
 }
 setColor(sib, colorOf(parentOf(x)));
 setColor(parentOf(x), BLACK);
 setColor(leftOf(sib), BLACK);
 rotateRight(parentOf(x));
 x = root;
 }
 }
 }

 setColor(x, BLACK);
 }

 @java.io.Serial
 private static final long serialVersionUID = 919286545866124006L;

 /**
 * Save the state of the {@code TreeMap} instance to a stream (i.e.,
 * serialize it).
 *
 * @serialData The size of the TreeMap (the number of key-value
 * mappings) is emitted (int), followed by the key (Object)
 * and value (Object) for each key-value mapping represented
 * by the TreeMap. The key-value mappings are emitted in
 * key-order (as determined by the TreeMap's Comparator,
 * or by the keys' natural ordering if the TreeMap has no
 * Comparator).
 */
 @java.io.Serial
 private void writeObject(java.io.ObjectOutputStream s)
 throws java.io.IOException {
 // Write out the Comparator and any hidden stuff
 s.defaultWriteObject();

 // Write out size (number of Mappings)
 s.writeInt(size);

 // Write out keys and values (alternating)
 for (Map.Entry<K, V> e : entrySet()) {
 s.writeObject(e.getKey());
 s.writeObject(e.getValue());
 }
 }

 /**
 * Reconstitute the {@code TreeMap} instance from a stream (i.e.,
 * deserialize it).
 */
 @java.io.Serial
 private void readObject(final java.io.ObjectInputStream s)
 throws java.io.IOException, ClassNotFoundException {
 // Read in the Comparator and any hidden stuff
 s.defaultReadObject();

 // Read in size
 int size = s.readInt();

 buildFromSorted(size, null, s, null);
 }

 /** Intended to be called only from TreeSet.readObject */
 void readTreeSet(int size, java.io.ObjectInputStream s, V defaultVal)
 throws java.io.IOException, ClassNotFoundException {
 buildFromSorted(size, null, s, defaultVal);
 }

 /** Intended to be called only from TreeSet.addAll */
 void addAllForTreeSet(SortedSet<? extends K> set, V defaultVal) {
 try {
 buildFromSorted(set.size(), set.iterator(), null, defaultVal);
 } catch (java.io.IOException | ClassNotFoundException cannotHappen) {
 }
 }

 /**
 * Linear time tree building algorithm from sorted data. Can accept keys
 * and/or values from iterator or stream. This leads to too many
 * parameters, but seems better than alternatives. The four formats
 * that this method accepts are:
 *
 * 1) An iterator of Map.Entries. (it != null, defaultVal == null).
 * 2) An iterator of keys. (it != null, defaultVal != null).
 * 3) A stream of alternating serialized keys and values.
 * (it == null, defaultVal == null).
 * 4) A stream of serialized keys. (it == null, defaultVal != null).
 *
 * It is assumed that the comparator of the TreeMap is already set prior
 * to calling this method.
 *
 * @param size the number of keys (or key-value pairs) to be read from
 * the iterator or stream
 * @param it If non-null, new entries are created from entries
 * or keys read from this iterator.
 * @param str If non-null, new entries are created from keys and
 * possibly values read from this stream in serialized form.
 * Exactly one of it and str should be non-null.
 * @param defaultVal if non-null, this default value is used for
 * each value in the map. If null, each value is read from
 * iterator or stream, as described above.
 * @throws java.io.IOException propagated from stream reads. This cannot
 * occur if str is null.
 * @throws ClassNotFoundException propagated from readObject.
 * This cannot occur if str is null.
 */
 private void buildFromSorted(int size, Iterator<?> it,
 java.io.ObjectInputStream str,
 V defaultVal)
 throws java.io.IOException, ClassNotFoundException {
 this.size = size;
 root = buildFromSorted(0, 0, size-1, computeRedLevel(size),
 it, str, defaultVal);
 }

 /**
 * Recursive "helper method" that does the real work of the
 * previous method. Identically named parameters have
 * identical definitions. Additional parameters are documented below.
 * It is assumed that the comparator and size fields of the TreeMap are
 * already set prior to calling this method. (It ignores both fields.)
 *
 * @param level the current level of tree. Initial call should be 0.
 * @param lo the first element index of this subtree. Initial should be 0.
 * @param hi the last element index of this subtree. Initial should be
 * size-1.
 * @param redLevel the level at which nodes should be red.
 * Must be equal to computeRedLevel for tree of this size.
 */
 @SuppressWarnings("unchecked")
 private final Entry<K,V> buildFromSorted(int level, int lo, int hi,
 int redLevel,
 Iterator<?> it,
 java.io.ObjectInputStream str,
 V defaultVal)
 throws java.io.IOException, ClassNotFoundException {
 /*
 * Strategy: The root is the middlemost element. To get to it, we
 * have to first recursively construct the entire left subtree,
 * so as to grab all of its elements. We can then proceed with right
 * subtree.
 *
 * The lo and hi arguments are the minimum and maximum
 * indices to pull out of the iterator or stream for current subtree.
 * They are not actually indexed, we just proceed sequentially,
 * ensuring that items are extracted in corresponding order.
 */

 if (hi < lo) return null;

 int mid = (lo + hi) >>> 1;

 Entry<K,V> left = null;
 if (lo < mid)
 left = buildFromSorted(level+1, lo, mid - 1, redLevel,
 it, str, defaultVal);

 // extract key and/or value from iterator or stream
 K key;
 V value;
 if (it != null) {
 if (defaultVal==null) {
 Map.Entry<?,?> entry = (Map.Entry<?,?>)it.next();
 key = (K)entry.getKey();
 value = (V)entry.getValue();
 } else {
 key = (K)it.next();
 value = defaultVal;
 }
 } else { // use stream
 key = (K) str.readObject();
 value = (defaultVal != null ? defaultVal : (V) str.readObject());
 }

 Entry<K,V> middle = new Entry<>(key, value, null);

 // color nodes in non-full bottommost level red
 if (level == redLevel)
 middle.color = RED;

 if (left != null) {
 middle.left = left;
 left.parent = middle;
 }

 if (mid < hi) {
 Entry<K,V> right = buildFromSorted(level+1, mid+1, hi, redLevel,
 it, str, defaultVal);
 middle.right = right;
 right.parent = middle;
 }

 return middle;
 }

 /**
 * Finds the level down to which to assign all nodes BLACK. This is the
 * last `full' level of the complete binary tree produced by buildTree.
 * The remaining nodes are colored RED. (This makes a `nice' set of
 * color assignments wrt future insertions.) This level number is
 * computed by finding the number of splits needed to reach the zeroeth
 * node.
 *
 * @param size the (non-negative) number of keys in the tree to be built
 */
 private static int computeRedLevel(int size) {
 return 31 - Integer.numberOfLeadingZeros(size + 1);
 }

 /**
 * Currently, we support Spliterator-based versions only for the
 * full map, in either plain of descending form, otherwise relying
 * on defaults because size estimation for submaps would dominate
 * costs. The type tests needed to check these for key views are
 * not very nice but avoid disrupting existing class
 * structures. Callers must use plain default spliterators if this
 * returns null.
 */
 static <K> Spliterator<K> keySpliteratorFor(NavigableMap<K,?> m) {
 if (m instanceof TreeMap) {
 @SuppressWarnings("unchecked") TreeMap<K,Object> t =
 (TreeMap<K,Object>) m;
 return t.keySpliterator();
 }
 if (m instanceof DescendingSubMap) {
 @SuppressWarnings("unchecked") DescendingSubMap<K,?> dm =
 (DescendingSubMap<K,?>) m;
 TreeMap<K,?> tm = dm.m;
 if (dm == tm.descendingMap) {
 @SuppressWarnings("unchecked") TreeMap<K,Object> t =
 (TreeMap<K,Object>) tm;
 return t.descendingKeySpliterator();
 }
 }
 @SuppressWarnings("unchecked") NavigableSubMap<K,?> sm =
 (NavigableSubMap<K,?>) m;
 return sm.keySpliterator();
 }

 final Spliterator<K> keySpliterator() {
 return new KeySpliterator<>(this, null, null, 0, -1, 0);
 }

 final Spliterator<K> descendingKeySpliterator() {
 return new DescendingKeySpliterator<>(this, null, null, 0, -2, 0);
 }

 /**
 * Base class for spliterators. Iteration starts at a given
 * origin and continues up to but not including a given fence (or
 * null for end). At top-level, for ascending cases, the first
 * split uses the root as left-fence/right-origin. From there,
 * right-hand splits replace the current fence with its left
 * child, also serving as origin for the split-off spliterator.
 * Left-hands are symmetric. Descending versions place the origin
 * at the end and invert ascending split rules. This base class
 * is non-committal about directionality, or whether the top-level
 * spliterator covers the whole tree. This means that the actual
 * split mechanics are located in subclasses. Some of the subclass
 * trySplit methods are identical (except for return types), but
 * not nicely factorable.
 *
 * Currently, subclass versions exist only for the full map
 * (including descending keys via its descendingMap). Others are
 * possible but currently not worthwhile because submaps require
 * O(n) computations to determine size, which substantially limits
 * potential speed-ups of using custom Spliterators versus default
 * mechanics.
 *
 * To bootstrap initialization, external constructors use
 * negative size estimates: -1 for ascend, -2 for descend.
 */
 static class TreeMapSpliterator<K,V> {
 final TreeMap<K,V> tree;
 TreeMap.Entry<K,V> current; // traverser; initially first node in range
 TreeMap.Entry<K,V> fence; // one past last, or null
 int side; // 0: top, -1: is a left split, +1: right
 int est; // size estimate (exact only for top-level)
 int expectedModCount; // for CME checks

 TreeMapSpliterator(TreeMap<K,V> tree,
 TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
 int side, int est, int expectedModCount) {
 this.tree = tree;
 this.current = origin;
 this.fence = fence;
 this.side = side;
 this.est = est;
 this.expectedModCount = expectedModCount;
 }

 final int getEstimate() { // force initialization
 int s; TreeMap<K,V> t;
 if ((s = est) < 0) {
 if ((t = tree) != null) {
 current = (s == -1) ? t.getFirstEntry() : t.getLastEntry();
 s = est = t.size;
 expectedModCount = t.modCount;
 }
 else
 s = est = 0;
 }
 return s;
 }

 public final long estimateSize() {
 return (long)getEstimate();
 }
 }

 static final class KeySpliterator<K,V>
 extends TreeMapSpliterator<K,V>
 implements Spliterator<K> {
 KeySpliterator(TreeMap<K,V> tree,
 TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
 int side, int est, int expectedModCount) {
 super(tree, origin, fence, side, est, expectedModCount);
 }

 public KeySpliterator<K,V> trySplit() {
 if (est < 0)
 getEstimate(); // force initialization
 int d = side;
 TreeMap.Entry<K,V> e = current, f = fence,
 s = ((e == null || e == f) ? null : // empty
 (d == 0) ? tree.root : // was top
 (d > 0) ? e.right : // was right
 (d < 0 && f != null) ? f.left : // was left
 null);
 if (s != null && s != e && s != f &&
 tree.compare(e.key, s.key) < 0) { // e not already past s
 side = 1;
 return new KeySpliterator<>
 (tree, e, current = s, -1, est >>>= 1, expectedModCount);
 }
 return null;
 }

 public void forEachRemaining(Consumer<? super K> action) {
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 TreeMap.Entry<K,V> f = fence, e, p, pl;
 if ((e = current) != null && e != f) {
 current = f; // exhaust
 do {
 action.accept(e.key);
 if ((p = e.right) != null) {
 while ((pl = p.left) != null)
 p = pl;
 }
 else {
 while ((p = e.parent) != null && e == p.right)
 e = p;
 }
 } while ((e = p) != null && e != f);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 }
 }

 public boolean tryAdvance(Consumer<? super K> action) {
 TreeMap.Entry<K,V> e;
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 if ((e = current) == null || e == fence)
 return false;
 current = successor(e);
 action.accept(e.key);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 return true;
 }

 public int characteristics() {
 return (side == 0 ? Spliterator.SIZED : 0) |
 Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.ORDERED;
 }

 public final Comparator<? super K> getComparator() {
 return tree.comparator;
 }

 }

 static final class DescendingKeySpliterator<K,V>
 extends TreeMapSpliterator<K,V>
 implements Spliterator<K> {
 DescendingKeySpliterator(TreeMap<K,V> tree,
 TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
 int side, int est, int expectedModCount) {
 super(tree, origin, fence, side, est, expectedModCount);
 }

 public DescendingKeySpliterator<K,V> trySplit() {
 if (est < 0)
 getEstimate(); // force initialization
 int d = side;
 TreeMap.Entry<K,V> e = current, f = fence,
 s = ((e == null || e == f) ? null : // empty
 (d == 0) ? tree.root : // was top
 (d < 0) ? e.left : // was left
 (d > 0 && f != null) ? f.right : // was right
 null);
 if (s != null && s != e && s != f &&
 tree.compare(e.key, s.key) > 0) { // e not already past s
 side = 1;
 return new DescendingKeySpliterator<>
 (tree, e, current = s, -1, est >>>= 1, expectedModCount);
 }
 return null;
 }

 public void forEachRemaining(Consumer<? super K> action) {
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 TreeMap.Entry<K,V> f = fence, e, p, pr;
 if ((e = current) != null && e != f) {
 current = f; // exhaust
 do {
 action.accept(e.key);
 if ((p = e.left) != null) {
 while ((pr = p.right) != null)
 p = pr;
 }
 else {
 while ((p = e.parent) != null && e == p.left)
 e = p;
 }
 } while ((e = p) != null && e != f);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 }
 }

 public boolean tryAdvance(Consumer<? super K> action) {
 TreeMap.Entry<K,V> e;
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 if ((e = current) == null || e == fence)
 return false;
 current = predecessor(e);
 action.accept(e.key);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 return true;
 }

 public int characteristics() {
 return (side == 0 ? Spliterator.SIZED : 0) |
 Spliterator.DISTINCT | Spliterator.ORDERED;
 }
 }

 static final class ValueSpliterator<K,V>
 extends TreeMapSpliterator<K,V>
 implements Spliterator<V> {
 ValueSpliterator(TreeMap<K,V> tree,
 TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
 int side, int est, int expectedModCount) {
 super(tree, origin, fence, side, est, expectedModCount);
 }

 public ValueSpliterator<K,V> trySplit() {
 if (est < 0)
 getEstimate(); // force initialization
 int d = side;
 TreeMap.Entry<K,V> e = current, f = fence,
 s = ((e == null || e == f) ? null : // empty
 (d == 0) ? tree.root : // was top
 (d > 0) ? e.right : // was right
 (d < 0 && f != null) ? f.left : // was left
 null);
 if (s != null && s != e && s != f &&
 tree.compare(e.key, s.key) < 0) { // e not already past s
 side = 1;
 return new ValueSpliterator<>
 (tree, e, current = s, -1, est >>>= 1, expectedModCount);
 }
 return null;
 }

 public void forEachRemaining(Consumer<? super V> action) {
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 TreeMap.Entry<K,V> f = fence, e, p, pl;
 if ((e = current) != null && e != f) {
 current = f; // exhaust
 do {
 action.accept(e.value);
 if ((p = e.right) != null) {
 while ((pl = p.left) != null)
 p = pl;
 }
 else {
 while ((p = e.parent) != null && e == p.right)
 e = p;
 }
 } while ((e = p) != null && e != f);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 }
 }

 public boolean tryAdvance(Consumer<? super V> action) {
 TreeMap.Entry<K,V> e;
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 if ((e = current) == null || e == fence)
 return false;
 current = successor(e);
 action.accept(e.value);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 return true;
 }

 public int characteristics() {
 return (side == 0 ? Spliterator.SIZED : 0) | Spliterator.ORDERED;
 }
 }

 static final class EntrySpliterator<K,V>
 extends TreeMapSpliterator<K,V>
 implements Spliterator<Map.Entry<K,V>> {
 EntrySpliterator(TreeMap<K,V> tree,
 TreeMap.Entry<K,V> origin, TreeMap.Entry<K,V> fence,
 int side, int est, int expectedModCount) {
 super(tree, origin, fence, side, est, expectedModCount);
 }

 public EntrySpliterator<K,V> trySplit() {
 if (est < 0)
 getEstimate(); // force initialization
 int d = side;
 TreeMap.Entry<K,V> e = current, f = fence,
 s = ((e == null || e == f) ? null : // empty
 (d == 0) ? tree.root : // was top
 (d > 0) ? e.right : // was right
 (d < 0 && f != null) ? f.left : // was left
 null);
 if (s != null && s != e && s != f &&
 tree.compare(e.key, s.key) < 0) { // e not already past s
 side = 1;
 return new EntrySpliterator<>
 (tree, e, current = s, -1, est >>>= 1, expectedModCount);
 }
 return null;
 }

 public void forEachRemaining(Consumer<? super Map.Entry<K, V>> action) {
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 TreeMap.Entry<K,V> f = fence, e, p, pl;
 if ((e = current) != null && e != f) {
 current = f; // exhaust
 do {
 action.accept(e);
 if ((p = e.right) != null) {
 while ((pl = p.left) != null)
 p = pl;
 }
 else {
 while ((p = e.parent) != null && e == p.right)
 e = p;
 }
 } while ((e = p) != null && e != f);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 }
 }

 public boolean tryAdvance(Consumer<? super Map.Entry<K,V>> action) {
 TreeMap.Entry<K,V> e;
 if (action == null)
 throw new NullPointerException();
 if (est < 0)
 getEstimate(); // force initialization
 if ((e = current) == null || e == fence)
 return false;
 current = successor(e);
 action.accept(e);
 if (tree.modCount != expectedModCount)
 throw new ConcurrentModificationException();
 return true;
 }

 public int characteristics() {
 return (side == 0 ? Spliterator.SIZED : 0) |
 Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.ORDERED;
 }

 @Override
 public Comparator<Map.Entry<K, V>> getComparator() {
 // Adapt or create a key-based comparator
 if (tree.comparator != null) {
 return Map.Entry.comparingByKey(tree.comparator);
 }
 else {
 return (Comparator<Map.Entry<K, V>> & Serializable) (e1, e2) -> {
 @SuppressWarnings("unchecked")
 Comparable<? super K> k1 = (Comparable<? super K>) e1.getKey();
 return k1.compareTo(e2.getKey());
 };
 }
 }
 }
}

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