import java.io.IOException;

import java.io.InvalidObjectException;

import java.io.Serializable;

import java.util.function.BiFunction;

 * <p>As a general rule, the default load factor (.75) offers a good

 * tradeoff between time and space costs.  Higher values decrease the

 * space overhead but increase the lookup cost (reflected in most of

 * the operations of the <tt>HashMap</tt> class, including

 * <tt>get</tt> and <tt>put</tt>).  The expected number of entries in

 * the map and its load factor should be taken into account when

 * setting its initial capacity, so as to minimize the number of

 * rehash operations.  If the initial capacity is greater than the

 * maximum number of entries divided by the load factor, no rehash

 * operations will ever occur.

 * <p>If many mappings are to be stored in a <tt>HashMap</tt>

 * instance, creating it with a sufficiently large capacity will allow

 * the mappings to be stored more efficiently than letting it perform

 * automatic rehashing as needed to grow the table.  Note that using

 * many keys with the same {@code hashCode()} is a sure way to slow

 * down performance of any hash table. To ameliorate impact, when keys

 * are {@link Comparable}, this class may use comparison order among

 * keys to help break ties.

public class HashMap<K,V> extends AbstractMap<K,V>

    implements Map<K,V>, Cloneable, Serializable {

    private static final long serialVersionUID = 362498820763181265L;

    /*

     * Implementation notes.

     *

     * This map usually acts as a binned (bucketed) hash table, but

     * when bins get too large, they are transformed into bins of

     * TreeNodes, each structured similarly to those in

     * java.util.TreeMap. Most methods try to use normal bins, but

     * relay to TreeNode methods when applicable (simply by checking

     * instanceof a node).  Bins of TreeNodes may be traversed and

     * used like any others, but additionally support faster lookup

     * when overpopulated. However, since the vast majority of bins in

     * normal use are not overpopulated, checking for existence of

     * tree bins may be delayed in the course of table methods.

     *

     * Tree bins (i.e., bins whose elements are all TreeNodes) are

     * ordered primarily by hashCode, but in the case of ties, if two

     * elements are of the same "class C implements Comparable<C>",

     * type then their compareTo method is used for ordering. (We

     * conservatively check generic types via reflection to validate

     * this -- see method comparableClassFor).  The added complexity

     * of tree bins is worthwhile in providing worst-case O(log n)

     * operations when keys either have distinct hashes or are

     * orderable, Thus, performance degrades gracefully under

     * accidental or malicious usages in which hashCode() methods

     * return values that are poorly distributed, as well as those in

     * which many keys share a hashCode, so long as they are also

     * Comparable. (If neither of these apply, we may waste about a

     * factor of two in time and space compared to taking no

     * precautions. But the only known cases stem from poor user

     * programming practices that are already so slow that this makes

     * little difference.)

     *

     * Because TreeNodes are about twice the size of regular nodes, we

     * use them only when bins contain enough nodes to warrant use

     * (see TREEIFY_THRESHOLD). And when they become too small (due to

     * removal or resizing) they are converted back to plain bins.  In

     * usages with well-distributed user hashCodes, tree bins are

     * rarely used.  Ideally, under random hashCodes, the frequency of

     * nodes in bins follows a Poisson distribution

     * (http://en.wikipedia.org/wiki/Poisson_distribution) with a

     * parameter of about 0.5 on average for the default resizing

     * threshold of 0.75, although with a large variance because of

     * resizing granularity. Ignoring variance, the expected

     * occurrences of list size k are (exp(-0.5) * pow(0.5, k) /

     * factorial(k)). The first values are:

     *

     * 0:    0.60653066

     * 1:    0.30326533

     * 2:    0.07581633

     * 3:    0.01263606

     * 4:    0.00157952

     * 5:    0.00015795

     * 6:    0.00001316

     * 7:    0.00000094

     * 8:    0.00000006

     * more: less than 1 in ten million

     *

     * The root of a tree bin is normally its first node.  However,

     * sometimes (currently only upon Iterator.remove), the root might

     * be elsewhere, but can be recovered following parent links

     * (method TreeNode.root()).

     *

     * All applicable internal methods accept a hash code as an

     * argument (as normally supplied from a public method), allowing

     * them to call each other without recomputing user hashCodes.

     * Most internal methods also accept a "tab" argument, that is

     * normally the current table, but may be a new or old one when

     * resizing or converting.

     *

     * When bin lists are treeified, split, or untreeified, we keep

     * them in the same relative access/traversal order (i.e., field

     * Node.next) to better preserve locality, and to slightly

     * simplify handling of splits and traversals that invoke

     * iterator.remove. When using comparators on insertion, to keep a

     * total ordering (or as close as is required here) across

     * rebalancings, we compare classes and identityHashCodes as

     * tie-breakers.

     *

     * The use and transitions among plain vs tree modes is

     * complicated by the existence of subclass LinkedHashMap. See

     * below for hook methods defined to be invoked upon insertion,

     * removal and access that allow LinkedHashMap internals to

     * otherwise remain independent of these mechanics. (This also

     * requires that a map instance be passed to some utility methods

     * that may create new nodes.)

     *

     * The concurrent-programming-like SSA-based coding style helps

     * avoid aliasing errors amid all of the twisty pointer operations.

     */

     * The bin count threshold for using a tree rather than list for a

     * bin.  Bins are converted to trees when adding an element to a

     * bin with at least this many nodes. The value must be greater

     * than 2 and should be at least 8 to mesh with assumptions in

     * tree removal about conversion back to plain bins upon

     * shrinkage.

     */

    static final int TREEIFY_THRESHOLD = 8;

    /**

     * The bin count threshold for untreeifying a (split) bin during a

     * resize operation. Should be less than TREEIFY_THRESHOLD, and at

     * most 6 to mesh with shrinkage detection under removal.

     */

    static final int UNTREEIFY_THRESHOLD = 6;

    /**

     * The smallest table capacity for which bins may be treeified.

     * (Otherwise the table is resized if too many nodes in a bin.)

     * Should be at least 4 * TREEIFY_THRESHOLD to avoid conflicts

     * between resizing and treeification thresholds.

     */

    static final int MIN_TREEIFY_CAPACITY = 64;

    /**

     * Basic hash bin node, used for most entries.  (See below for

     * TreeNode subclass, and in LinkedHashMap for its Entry subclass.)

    static class Node<K,V> implements Map.Entry<K,V> {

        final int hash;

        final K key;

        V value;

        Node<K,V> next;

        Node(int hash, K key, V value, Node<K,V> next) {

            this.hash = hash;

            this.key = key;

            this.value = value;

            this.next = next;

        }

        public final K getKey()        { return key; }

        public final V getValue()      { return value; }

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

        public final int hashCode() {

            return Objects.hashCode(key) ^ Objects.hashCode(value);

        }

        public final V setValue(V newValue) {

            V oldValue = value;

            value = newValue;

            return oldValue;

        }

        public final boolean equals(Object o) {

            if (o == this)

                return true;

            if (o instanceof Map.Entry) {

                Map.Entry<?,?> e = (Map.Entry<?,?>)o;

                if (Objects.equals(key, e.getKey()) &&

                    Objects.equals(value, e.getValue()))

                    return true;

            }

            return false;

        }

    }

    /* ---------------- Static utilities -------------- */

     * Computes key.hashCode() and spreads (XORs) higher bits of hash

     * to lower.  Because the table uses power-of-two masking, sets of

     * hashes that vary only in bits above the current mask will

     * always collide. (Among known examples are sets of Float keys

     * holding consecutive whole numbers in small tables.)  So we

     * apply a transform that spreads the impact of higher bits

     * downward. There is a tradeoff between speed, utility, and

     * quality of bit-spreading. Because many common sets of hashes

     * are already reasonably distributed (so don't benefit from

     * spreading), and because we use trees to handle large sets of

     * collisions in bins, we just XOR some shifted bits in the

     * cheapest possible way to reduce systematic lossage, as well as

     * to incorporate impact of the highest bits that would otherwise

     * never be used in index calculations because of table bounds.

     */

    static final int hash(Object key) {

        int h;

        return (key == null) ? 0 : (h = key.hashCode()) ^ (h >>> 16);

    }

    /**

     * Returns x's Class if it is of the form "class C implements

     * Comparable<C>", else null.

    static Class<?> comparableClassFor(Object x) {

        if (x instanceof Comparable) {

            Class<?> c; Type[] ts, as; Type t; ParameterizedType p;

            if ((c = x.getClass()) == String.class) // bypass checks

                return c;

            if ((ts = c.getGenericInterfaces()) != null) {

                for (int i = 0; i < ts.length; ++i) {

                    if (((t = ts[i]) instanceof ParameterizedType) &&

                        ((p = (ParameterizedType)t).getRawType() ==

                         Comparable.class) &&

                        (as = p.getActualTypeArguments()) != null &&

                        as.length == 1 && as[0] == c) // type arg is c

                        return c;

                }

            }

        }

        return null;

    }

    /**

     * Returns k.compareTo(x) if x matches kc (k's screened comparable

     * class), else 0.

     */

    @SuppressWarnings({"rawtypes","unchecked"}) // for cast to Comparable

    static int compareComparables(Class<?> kc, Object k, Object x) {

        return (x == null || x.getClass() != kc ? 0 :

                ((Comparable)k).compareTo(x));

    }

    /**

     * Returns a power of two size for the given target capacity.

     */

    static final int tableSizeFor(int cap) {

        int n = cap - 1;

        n |= n >>> 1;

        n |= n >>> 2;

        n |= n >>> 4;

        n |= n >>> 8;

        n |= n >>> 16;

        return (n < 0) ? 1 : (n >= MAXIMUM_CAPACITY) ? MAXIMUM_CAPACITY : n + 1;

    }

    /* ---------------- Fields -------------- */

    /**

     * The table, initialized on first use, and resized as

     * necessary. When allocated, length is always a power of two.

     * (We also tolerate length zero in some operations to allow

     * bootstrapping mechanics that are currently not needed.)

     */

    transient Node<K,V>[] table;

    /**

     * Holds cached entrySet(). Note that AbstractMap fields are used

     * for keySet() and values().

     */

    transient Set<Map.Entry<K,V>> entrySet;

     * The next size value at which to resize (capacity * load factor).

     *

     * @serial

    // (The javadoc description is true upon serialization.

    // Additionally, if the table array has not been allocated, this

    // field holds the initial array capacity, or zero signifying

    // DEFAULT_INITIAL_CAPACITY.)

    int threshold;

     * The load factor for the hash table.

     * @serial

    final float loadFactor;

    /* ---------------- Public operations -------------- */

        this.threshold = tableSizeFor(initialCapacity);

        this.loadFactor = DEFAULT_LOAD_FACTOR; // all other fields defaulted

        this.loadFactor = DEFAULT_LOAD_FACTOR;

        putMapEntries(m, false);

     * Implements Map.putAll and Map constructor

     *

     * @param m the map

     * @param evict false when initially constructing this map, else

     * true (relayed to method afterNodeInsertion).

    final void putMapEntries(Map<? extends K, ? extends V> m, boolean evict) {

        int s = m.size();

        if (s > 0) {

            if (table == null) { // pre-size

                float ft = ((float)s / loadFactor) + 1.0F;