xref: /libcore/ojluni/src/main/java/java/util/Collections.java

/*
 * Copyright (C) 2014 The Android Open Source Project
 * Copyright (c) 1997, 2014, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.util;

import java.io.IOException;
import java.io.ObjectOutputStream;
import java.io.Serializable;
import java.lang.reflect.Array;
import java.util.function.BiConsumer;
import java.util.function.BiFunction;
import java.util.function.Consumer;
import java.util.function.Predicate;

/**
 * This class consists exclusively of static methods that operate on or return
 * collections.  It contains polymorphic algorithms that operate on
 * collections, "wrappers", which return a new collection backed by a
 * specified collection, and a few other odds and ends.
 *
 * <p>The methods of this class all throw a <tt>NullPointerException</tt>
 * if the collections or class objects provided to them are null.
 *
 * <p>The documentation for the polymorphic algorithms contained in this class
 * generally includes a brief description of the <i>implementation</i>.  Such
 * descriptions should be regarded as <i>implementation notes</i>, rather than
 * parts of the <i>specification</i>.  Implementors should feel free to
 * substitute other algorithms, so long as the specification itself is adhered
 * to.  (For example, the algorithm used by <tt>sort</tt> does not have to be
 * a mergesort, but it does have to be <i>stable</i>.)
 *
 * <p>The "destructive" algorithms contained in this class, that is, the
 * algorithms that modify the collection on which they operate, are specified
 * to throw <tt>UnsupportedOperationException</tt> if the collection does not
 * support the appropriate mutation primitive(s), such as the <tt>set</tt>
 * method.  These algorithms may, but are not required to, throw this
 * exception if an invocation would have no effect on the collection.  For
 * example, invoking the <tt>sort</tt> method on an unmodifiable list that is
 * already sorted may or may not throw <tt>UnsupportedOperationException</tt>.
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/../technotes/guides/collections/index.html">
 * Java Collections Framework</a>.
 *
 * @author  Josh Bloch
 * @author  Neal Gafter
 * @see     Collection
 * @see     Set
 * @see     List
 * @see     Map
 * @since   1.2
 */

public class Collections {
    // Suppresses default constructor, ensuring non-instantiability.
    private Collections() {
    }

    // Algorithms

    /*
     * Tuning parameters for algorithms - Many of the List algorithms have
     * two implementations, one of which is appropriate for RandomAccess
     * lists, the other for "sequential."  Often, the random access variant
     * yields better performance on small sequential access lists.  The
     * tuning parameters below determine the cutoff point for what constitutes
     * a "small" sequential access list for each algorithm.  The values below
     * were empirically determined to work well for LinkedList. Hopefully
     * they should be reasonable for other sequential access List
     * implementations.  Those doing performance work on this code would
     * do well to validate the values of these parameters from time to time.
     * (The first word of each tuning parameter name is the algorithm to which
     * it applies.)
     */
    private static final int BINARYSEARCH_THRESHOLD   = 5000;
    private static final int REVERSE_THRESHOLD        =   18;
    private static final int SHUFFLE_THRESHOLD        =    5;
    private static final int FILL_THRESHOLD           =   25;
    private static final int ROTATE_THRESHOLD         =  100;
    private static final int COPY_THRESHOLD           =   10;
    private static final int REPLACEALL_THRESHOLD     =   11;
    private static final int INDEXOFSUBLIST_THRESHOLD =   35;

    /**
     * Sorts the specified list into ascending order, according to the
     * {@linkplain Comparable natural ordering} of its elements.
     * All elements in the list must implement the {@link Comparable}
     * interface.  Furthermore, all elements in the list must be
     * <i>mutually comparable</i> (that is, {@code e1.compareTo(e2)}
     * must not throw a {@code ClassCastException} for any elements
     * {@code e1} and {@code e2} in the list).
     *
     * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.
     *
     * <p>The specified list must be modifiable, but need not be resizable.
     *
     * <p>Implementation note: This implementation is a stable, adaptive,
     * iterative mergesort that requires far fewer than n lg(n) comparisons
     * when the input array is partially sorted, while offering the
     * performance of a traditional mergesort when the input array is
     * randomly ordered.  If the input array is nearly sorted, the
     * implementation requires approximately n comparisons.  Temporary
     * storage requirements vary from a small constant for nearly sorted
     * input arrays to n/2 object references for randomly ordered input
     * arrays.
     *
     * <p>The implementation takes equal advantage of ascending and
     * descending order in its input array, and can take advantage of
     * ascending and descending order in different parts of the same
     * input array.  It is well-suited to merging two or more sorted arrays:
     * simply concatenate the arrays and sort the resulting array.
     *
     * <p>The implementation was adapted from Tim Peters's list sort for Python
     * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
     * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
     * Sorting and Information Theoretic Complexity", in Proceedings of the
     * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
     * January 1993.
     *
     * <p>This implementation dumps the specified list into an array, sorts
     * the array, and iterates over the list resetting each element
     * from the corresponding position in the array.  This avoids the
     * n<sup>2</sup> log(n) performance that would result from attempting
     * to sort a linked list in place.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list to be sorted.
     * @throws ClassCastException if the list contains elements that are not
     *         <i>mutually comparable</i> (for example, strings and integers).
     * @throws UnsupportedOperationException if the specified list's
     *         list-iterator does not support the {@code set} operation.
     * @throws IllegalArgumentException (optional) if the implementation
     *         detects that the natural ordering of the list elements is
     *         found to violate the {@link Comparable} contract
     */
    @SuppressWarnings("unchecked")
    public static <T extends Comparable<? super T>> void sort(List<T> list) {
        if (list.getClass() == ArrayList.class) {
            Arrays.sort(((ArrayList) list).elementData, 0, list.size());
            return;
        }

        Object[] a = list.toArray();
        Arrays.sort(a);
        ListIterator<T> i = list.listIterator();
        for (int j=0; j<a.length; j++) {
            i.next();
            i.set((T)a[j]);
        }
    }

    /**
     * Sorts the specified list according to the order induced by the
     * specified comparator.  All elements in the list must be <i>mutually
     * comparable</i> using the specified comparator (that is,
     * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
     * for any elements {@code e1} and {@code e2} in the list).
     *
     * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.
     *
     * <p>The specified list must be modifiable, but need not be resizable.
     *
     * <p>Implementation note: This implementation is a stable, adaptive,
     * iterative mergesort that requires far fewer than n lg(n) comparisons
     * when the input array is partially sorted, while offering the
     * performance of a traditional mergesort when the input array is
     * randomly ordered.  If the input array is nearly sorted, the
     * implementation requires approximately n comparisons.  Temporary
     * storage requirements vary from a small constant for nearly sorted
     * input arrays to n/2 object references for randomly ordered input
     * arrays.
     *
     * <p>The implementation takes equal advantage of ascending and
     * descending order in its input array, and can take advantage of
     * ascending and descending order in different parts of the same
     * input array.  It is well-suited to merging two or more sorted arrays:
     * simply concatenate the arrays and sort the resulting array.
     *
     * <p>The implementation was adapted from Tim Peters's list sort for Python
     * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
     * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
     * Sorting and Information Theoretic Complexity", in Proceedings of the
     * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
     * January 1993.
     *
     * <p>This implementation dumps the specified list into an array, sorts
     * the array, and iterates over the list resetting each element
     * from the corresponding position in the array.  This avoids the
     * n<sup>2</sup> log(n) performance that would result from attempting
     * to sort a linked list in place.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list to be sorted.
     * @param  c the comparator to determine the order of the list.  A
     *        {@code null} value indicates that the elements' <i>natural
     *        ordering</i> should be used.
     * @throws ClassCastException if the list contains elements that are not
     *         <i>mutually comparable</i> using the specified comparator.
     * @throws UnsupportedOperationException if the specified list's
     *         list-iterator does not support the {@code set} operation.
     * @throws IllegalArgumentException (optional) if the comparator is
     *         found to violate the {@link Comparator} contract
     */
    @SuppressWarnings({"unchecked", "rawtypes"})
    public static <T> void sort(List<T> list, Comparator<? super T> c) {
        if (list.getClass() == ArrayList.class) {
            Arrays.sort(((ArrayList) list).elementData, 0, list.size(), (Comparator) c);
            return;
        }

        Object[] a = list.toArray();
        Arrays.sort(a, (Comparator)c);
        ListIterator<T> i = list.listIterator();
        for (int j=0; j<a.length; j++) {
            i.next();
            i.set((T)a[j]);
        }
    }


    /**
     * Searches the specified list for the specified object using the binary
     * search algorithm.  The list must be sorted into ascending order
     * according to the {@linkplain Comparable natural ordering} of its
     * elements (as by the {@link #sort(List)} method) prior to making this
     * call.  If it is not sorted, the results are undefined.  If the list
     * contains multiple elements equal to the specified object, there is no
     * guarantee which one will be found.
     *
     * <p>This method runs in log(n) time for a "random access" list (which
     * provides near-constant-time positional access).  If the specified list
     * does not implement the {@link RandomAccess} interface and is large,
     * this method will do an iterator-based binary search that performs
     * O(n) link traversals and O(log n) element comparisons.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list to be searched.
     * @param  key the key to be searched for.
     * @return the index of the search key, if it is contained in the list;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the list: the index of the first
     *         element greater than the key, or <tt>list.size()</tt> if all
     *         elements in the list are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws ClassCastException if the list contains elements that are not
     *         <i>mutually comparable</i> (for example, strings and
     *         integers), or the search key is not mutually comparable
     *         with the elements of the list.
     */
    public static <T>
    int binarySearch(List<? extends Comparable<? super T>> list, T key) {
        if (list instanceof RandomAccess || list.size()<BINARYSEARCH_THRESHOLD)
            return Collections.indexedBinarySearch(list, key);
        else
            return Collections.iteratorBinarySearch(list, key);
    }

    private static <T>
    int indexedBinarySearch(List<? extends Comparable<? super T>> list, T key) {
        int low = 0;
        int high = list.size()-1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            Comparable<? super T> midVal = list.get(mid);
            int cmp = midVal.compareTo(key);

            if (cmp < 0)
                low = mid + 1;
            else if (cmp > 0)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found
    }

    private static <T>
    int iteratorBinarySearch(List<? extends Comparable<? super T>> list, T key)
    {
        int low = 0;
        int high = list.size()-1;
        ListIterator<? extends Comparable<? super T>> i = list.listIterator();

        while (low <= high) {
            int mid = (low + high) >>> 1;
            Comparable<? super T> midVal = get(i, mid);
            int cmp = midVal.compareTo(key);

            if (cmp < 0)
                low = mid + 1;
            else if (cmp > 0)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found
    }

    /**
     * Gets the ith element from the given list by repositioning the specified
     * list listIterator.
     */
    private static <T> T get(ListIterator<? extends T> i, int index) {
        T obj = null;
        int pos = i.nextIndex();
        if (pos <= index) {
            do {
                obj = i.next();
            } while (pos++ < index);
        } else {
            do {
                obj = i.previous();
            } while (--pos > index);
        }
        return obj;
    }

    /**
     * Searches the specified list for the specified object using the binary
     * search algorithm.  The list must be sorted into ascending order
     * according to the specified comparator (as by the
     * {@link #sort(List, Comparator) sort(List, Comparator)}
     * method), prior to making this call.  If it is
     * not sorted, the results are undefined.  If the list contains multiple
     * elements equal to the specified object, there is no guarantee which one
     * will be found.
     *
     * <p>This method runs in log(n) time for a "random access" list (which
     * provides near-constant-time positional access).  If the specified list
     * does not implement the {@link RandomAccess} interface and is large,
     * this method will do an iterator-based binary search that performs
     * O(n) link traversals and O(log n) element comparisons.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list to be searched.
     * @param  key the key to be searched for.
     * @param  c the comparator by which the list is ordered.
     *         A <tt>null</tt> value indicates that the elements'
     *         {@linkplain Comparable natural ordering} should be used.
     * @return the index of the search key, if it is contained in the list;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the list: the index of the first
     *         element greater than the key, or <tt>list.size()</tt> if all
     *         elements in the list are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws ClassCastException if the list contains elements that are not
     *         <i>mutually comparable</i> using the specified comparator,
     *         or the search key is not mutually comparable with the
     *         elements of the list using this comparator.
     */
    @SuppressWarnings("unchecked")
    public static <T> int binarySearch(List<? extends T> list, T key, Comparator<? super T> c) {
        if (c==null)
            return binarySearch((List<? extends Comparable<? super T>>) list, key);

        if (list instanceof RandomAccess || list.size()<BINARYSEARCH_THRESHOLD)
            return Collections.indexedBinarySearch(list, key, c);
        else
            return Collections.iteratorBinarySearch(list, key, c);
    }

    private static <T> int indexedBinarySearch(List<? extends T> l, T key, Comparator<? super T> c) {
        int low = 0;
        int high = l.size()-1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            T midVal = l.get(mid);
            int cmp = c.compare(midVal, key);

            if (cmp < 0)
                low = mid + 1;
            else if (cmp > 0)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found
    }

    private static <T> int iteratorBinarySearch(List<? extends T> l, T key, Comparator<? super T> c) {
        int low = 0;
        int high = l.size()-1;
        ListIterator<? extends T> i = l.listIterator();

        while (low <= high) {
            int mid = (low + high) >>> 1;
            T midVal = get(i, mid);
            int cmp = c.compare(midVal, key);

            if (cmp < 0)
                low = mid + 1;
            else if (cmp > 0)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found
    }

    /**
     * Reverses the order of the elements in the specified list.<p>
     *
     * This method runs in linear time.
     *
     * @param  list the list whose elements are to be reversed.
     * @throws UnsupportedOperationException if the specified list or
     *         its list-iterator does not support the <tt>set</tt> operation.
     */
    @SuppressWarnings({"rawtypes", "unchecked"})
    public static void reverse(List<?> list) {
        int size = list.size();
        if (size < REVERSE_THRESHOLD || list instanceof RandomAccess) {
            for (int i=0, mid=size>>1, j=size-1; i<mid; i++, j--)
                swap(list, i, j);
        } else {
            // instead of using a raw type here, it's possible to capture
            // the wildcard but it will require a call to a supplementary
            // private method
            ListIterator fwd = list.listIterator();
            ListIterator rev = list.listIterator(size);
            for (int i=0, mid=list.size()>>1; i<mid; i++) {
                Object tmp = fwd.next();
                fwd.set(rev.previous());
                rev.set(tmp);
            }
        }
    }

    /**
     * Randomly permutes the specified list using a default source of
     * randomness.  All permutations occur with approximately equal
     * likelihood.
     *
     * <p>The hedge "approximately" is used in the foregoing description because
     * default source of randomness is only approximately an unbiased source
     * of independently chosen bits. If it were a perfect source of randomly
     * chosen bits, then the algorithm would choose permutations with perfect
     * uniformity.
     *
     * <p>This implementation traverses the list backwards, from the last
     * element up to the second, repeatedly swapping a randomly selected element
     * into the "current position".  Elements are randomly selected from the
     * portion of the list that runs from the first element to the current
     * position, inclusive.
     *
     * <p>This method runs in linear time.  If the specified list does not
     * implement the {@link RandomAccess} interface and is large, this
     * implementation dumps the specified list into an array before shuffling
     * it, and dumps the shuffled array back into the list.  This avoids the
     * quadratic behavior that would result from shuffling a "sequential
     * access" list in place.
     *
     * @param  list the list to be shuffled.
     * @throws UnsupportedOperationException if the specified list or
     *         its list-iterator does not support the <tt>set</tt> operation.
     */
    public static void shuffle(List<?> list) {
        Random rnd = r;
        if (rnd == null)
            r = rnd = new Random(); // harmless race.
        shuffle(list, rnd);
    }

    private static Random r;

    /**
     * Randomly permute the specified list using the specified source of
     * randomness.  All permutations occur with equal likelihood
     * assuming that the source of randomness is fair.<p>
     *
     * This implementation traverses the list backwards, from the last element
     * up to the second, repeatedly swapping a randomly selected element into
     * the "current position".  Elements are randomly selected from the
     * portion of the list that runs from the first element to the current
     * position, inclusive.<p>
     *
     * This method runs in linear time.  If the specified list does not
     * implement the {@link RandomAccess} interface and is large, this
     * implementation dumps the specified list into an array before shuffling
     * it, and dumps the shuffled array back into the list.  This avoids the
     * quadratic behavior that would result from shuffling a "sequential
     * access" list in place.
     *
     * @param  list the list to be shuffled.
     * @param  rnd the source of randomness to use to shuffle the list.
     * @throws UnsupportedOperationException if the specified list or its
     *         list-iterator does not support the <tt>set</tt> operation.
     */
    @SuppressWarnings({"rawtypes", "unchecked"})
    public static void shuffle(List<?> list, Random rnd) {
        int size = list.size();
        if (size < SHUFFLE_THRESHOLD || list instanceof RandomAccess) {
            for (int i=size; i>1; i--)
                swap(list, i-1, rnd.nextInt(i));
        } else {
            Object arr[] = list.toArray();

            // Shuffle array
            for (int i=size; i>1; i--)
                swap(arr, i-1, rnd.nextInt(i));

            // Dump array back into list
            // instead of using a raw type here, it's possible to capture
            // the wildcard but it will require a call to a supplementary
            // private method
            ListIterator it = list.listIterator();
            for (int i=0; i<arr.length; i++) {
                it.next();
                it.set(arr[i]);
            }
        }
    }

    /**
     * Swaps the elements at the specified positions in the specified list.
     * (If the specified positions are equal, invoking this method leaves
     * the list unchanged.)
     *
     * @param list The list in which to swap elements.
     * @param i the index of one element to be swapped.
     * @param j the index of the other element to be swapped.
     * @throws IndexOutOfBoundsException if either <tt>i</tt> or <tt>j</tt>
     *         is out of range (i &lt; 0 || i &gt;= list.size()
     *         || j &lt; 0 || j &gt;= list.size()).
     * @since 1.4
     */
    @SuppressWarnings({"rawtypes", "unchecked"})
    public static void swap(List<?> list, int i, int j) {
        // instead of using a raw type here, it's possible to capture
        // the wildcard but it will require a call to a supplementary
        // private method
        final List l = list;
        l.set(i, l.set(j, l.get(i)));
    }

    /**
     * Swaps the two specified elements in the specified array.
     */
    private static void swap(Object[] arr, int i, int j) {
        Object tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

    /**
     * Replaces all of the elements of the specified list with the specified
     * element. <p>
     *
     * This method runs in linear time.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list to be filled with the specified element.
     * @param  obj The element with which to fill the specified list.
     * @throws UnsupportedOperationException if the specified list or its
     *         list-iterator does not support the <tt>set</tt> operation.
     */
    public static <T> void fill(List<? super T> list, T obj) {
        int size = list.size();

        if (size < FILL_THRESHOLD || list instanceof RandomAccess) {
            for (int i=0; i<size; i++)
                list.set(i, obj);
        } else {
            ListIterator<? super T> itr = list.listIterator();
            for (int i=0; i<size; i++) {
                itr.next();
                itr.set(obj);
            }
        }
    }

    /**
     * Copies all of the elements from one list into another.  After the
     * operation, the index of each copied element in the destination list
     * will be identical to its index in the source list.  The destination
     * list must be at least as long as the source list.  If it is longer, the
     * remaining elements in the destination list are unaffected. <p>
     *
     * This method runs in linear time.
     *
     * @param  <T> the class of the objects in the lists
     * @param  dest The destination list.
     * @param  src The source list.
     * @throws IndexOutOfBoundsException if the destination list is too small
     *         to contain the entire source List.
     * @throws UnsupportedOperationException if the destination list's
     *         list-iterator does not support the <tt>set</tt> operation.
     */
    public static <T> void copy(List<? super T> dest, List<? extends T> src) {
        int srcSize = src.size();
        if (srcSize > dest.size())
            throw new IndexOutOfBoundsException("Source does not fit in dest");

        if (srcSize < COPY_THRESHOLD ||
            (src instanceof RandomAccess && dest instanceof RandomAccess)) {
            for (int i=0; i<srcSize; i++)
                dest.set(i, src.get(i));
        } else {
            ListIterator<? super T> di=dest.listIterator();
            ListIterator<? extends T> si=src.listIterator();
            for (int i=0; i<srcSize; i++) {
                di.next();
                di.set(si.next());
            }
        }
    }

    /**
     * Returns the minimum element of the given collection, according to the
     * <i>natural ordering</i> of its elements.  All elements in the
     * collection must implement the <tt>Comparable</tt> interface.
     * Furthermore, all elements in the collection must be <i>mutually
     * comparable</i> (that is, <tt>e1.compareTo(e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the collection).<p>
     *
     * This method iterates over the entire collection, hence it requires
     * time proportional to the size of the collection.
     *
     * @param  <T> the class of the objects in the collection
     * @param  coll the collection whose minimum element is to be determined.
     * @return the minimum element of the given collection, according
     *         to the <i>natural ordering</i> of its elements.
     * @throws ClassCastException if the collection contains elements that are
     *         not <i>mutually comparable</i> (for example, strings and
     *         integers).
     * @throws NoSuchElementException if the collection is empty.
     * @see Comparable
     */
    public static <T extends Object & Comparable<? super T>> T min(Collection<? extends T> coll) {
        Iterator<? extends T> i = coll.iterator();
        T candidate = i.next();

        while (i.hasNext()) {
            T next = i.next();
            if (next.compareTo(candidate) < 0)
                candidate = next;
        }
        return candidate;
    }

    /**
     * Returns the minimum element of the given collection, according to the
     * order induced by the specified comparator.  All elements in the
     * collection must be <i>mutually comparable</i> by the specified
     * comparator (that is, <tt>comp.compare(e1, e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the collection).<p>
     *
     * This method iterates over the entire collection, hence it requires
     * time proportional to the size of the collection.
     *
     * @param  <T> the class of the objects in the collection
     * @param  coll the collection whose minimum element is to be determined.
     * @param  comp the comparator with which to determine the minimum element.
     *         A <tt>null</tt> value indicates that the elements' <i>natural
     *         ordering</i> should be used.
     * @return the minimum element of the given collection, according
     *         to the specified comparator.
     * @throws ClassCastException if the collection contains elements that are
     *         not <i>mutually comparable</i> using the specified comparator.
     * @throws NoSuchElementException if the collection is empty.
     * @see Comparable
     */
    @SuppressWarnings({"unchecked", "rawtypes"})
    public static <T> T min(Collection<? extends T> coll, Comparator<? super T> comp) {
        if (comp==null)
            return (T)min((Collection) coll);

        Iterator<? extends T> i = coll.iterator();
        T candidate = i.next();

        while (i.hasNext()) {
            T next = i.next();
            if (comp.compare(next, candidate) < 0)
                candidate = next;
        }
        return candidate;
    }

    /**
     * Returns the maximum element of the given collection, according to the
     * <i>natural ordering</i> of its elements.  All elements in the
     * collection must implement the <tt>Comparable</tt> interface.
     * Furthermore, all elements in the collection must be <i>mutually
     * comparable</i> (that is, <tt>e1.compareTo(e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the collection).<p>
     *
     * This method iterates over the entire collection, hence it requires
     * time proportional to the size of the collection.
     *
     * @param  <T> the class of the objects in the collection
     * @param  coll the collection whose maximum element is to be determined.
     * @return the maximum element of the given collection, according
     *         to the <i>natural ordering</i> of its elements.
     * @throws ClassCastException if the collection contains elements that are
     *         not <i>mutually comparable</i> (for example, strings and
     *         integers).
     * @throws NoSuchElementException if the collection is empty.
     * @see Comparable
     */
    public static <T extends Object & Comparable<? super T>> T max(Collection<? extends T> coll) {
        Iterator<? extends T> i = coll.iterator();
        T candidate = i.next();

        while (i.hasNext()) {
            T next = i.next();
            if (next.compareTo(candidate) > 0)
                candidate = next;
        }
        return candidate;
    }

    /**
     * Returns the maximum element of the given collection, according to the
     * order induced by the specified comparator.  All elements in the
     * collection must be <i>mutually comparable</i> by the specified
     * comparator (that is, <tt>comp.compare(e1, e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the collection).<p>
     *
     * This method iterates over the entire collection, hence it requires
     * time proportional to the size of the collection.
     *
     * @param  <T> the class of the objects in the collection
     * @param  coll the collection whose maximum element is to be determined.
     * @param  comp the comparator with which to determine the maximum element.
     *         A <tt>null</tt> value indicates that the elements' <i>natural
     *        ordering</i> should be used.
     * @return the maximum element of the given collection, according
     *         to the specified comparator.
     * @throws ClassCastException if the collection contains elements that are
     *         not <i>mutually comparable</i> using the specified comparator.
     * @throws NoSuchElementException if the collection is empty.
     * @see Comparable
     */
    @SuppressWarnings({"unchecked", "rawtypes"})
    public static <T> T max(Collection<? extends T> coll, Comparator<? super T> comp) {
        if (comp==null)
            return (T)max((Collection) coll);

        Iterator<? extends T> i = coll.iterator();
        T candidate = i.next();

        while (i.hasNext()) {
            T next = i.next();
            if (comp.compare(next, candidate) > 0)
                candidate = next;
        }
        return candidate;
    }

    /**
     * Rotates the elements in the specified list by the specified distance.
     * After calling this method, the element at index <tt>i</tt> will be
     * the element previously at index <tt>(i - distance)</tt> mod
     * <tt>list.size()</tt>, for all values of <tt>i</tt> between <tt>0</tt>
     * and <tt>list.size()-1</tt>, inclusive.  (This method has no effect on
     * the size of the list.)
     *
     * <p>For example, suppose <tt>list</tt> comprises<tt> [t, a, n, k, s]</tt>.
     * After invoking <tt>Collections.rotate(list, 1)</tt> (or
     * <tt>Collections.rotate(list, -4)</tt>), <tt>list</tt> will comprise
     * <tt>[s, t, a, n, k]</tt>.
     *
     * <p>Note that this method can usefully be applied to sublists to
     * move one or more elements within a list while preserving the
     * order of the remaining elements.  For example, the following idiom
     * moves the element at index <tt>j</tt> forward to position
     * <tt>k</tt> (which must be greater than or equal to <tt>j</tt>):
     * <pre>
     *     Collections.rotate(list.subList(j, k+1), -1);
     * </pre>
     * To make this concrete, suppose <tt>list</tt> comprises
     * <tt>[a, b, c, d, e]</tt>.  To move the element at index <tt>1</tt>
     * (<tt>b</tt>) forward two positions, perform the following invocation:
     * <pre>
     *     Collections.rotate(l.subList(1, 4), -1);
     * </pre>
     * The resulting list is <tt>[a, c, d, b, e]</tt>.
     *
     * <p>To move more than one element forward, increase the absolute value
     * of the rotation distance.  To move elements backward, use a positive
     * shift distance.
     *
     * <p>If the specified list is small or implements the {@link
     * RandomAccess} interface, this implementation exchanges the first
     * element into the location it should go, and then repeatedly exchanges
     * the displaced element into the location it should go until a displaced
     * element is swapped into the first element.  If necessary, the process
     * is repeated on the second and successive elements, until the rotation
     * is complete.  If the specified list is large and doesn't implement the
     * <tt>RandomAccess</tt> interface, this implementation breaks the
     * list into two sublist views around index <tt>-distance mod size</tt>.
     * Then the {@link #reverse(List)} method is invoked on each sublist view,
     * and finally it is invoked on the entire list.  For a more complete
     * description of both algorithms, see Section 2.3 of Jon Bentley's
     * <i>Programming Pearls</i> (Addison-Wesley, 1986).
     *
     * @param list the list to be rotated.
     * @param distance the distance to rotate the list.  There are no
     *        constraints on this value; it may be zero, negative, or
     *        greater than <tt>list.size()</tt>.
     * @throws UnsupportedOperationException if the specified list or
     *         its list-iterator does not support the <tt>set</tt> operation.
     * @since 1.4
     */
    public static void rotate(List<?> list, int distance) {
        if (list instanceof RandomAccess || list.size() < ROTATE_THRESHOLD)
            rotate1(list, distance);
        else
            rotate2(list, distance);
    }

    private static <T> void rotate1(List<T> list, int distance) {
        int size = list.size();
        if (size == 0)
            return;
        distance = distance % size;
        if (distance < 0)
            distance += size;
        if (distance == 0)
            return;

        for (int cycleStart = 0, nMoved = 0; nMoved != size; cycleStart++) {
            T displaced = list.get(cycleStart);
            int i = cycleStart;
            do {
                i += distance;
                if (i >= size)
                    i -= size;
                displaced = list.set(i, displaced);
                nMoved ++;
            } while (i != cycleStart);
        }
    }

    private static void rotate2(List<?> list, int distance) {
        int size = list.size();
        if (size == 0)
            return;
        int mid =  -distance % size;
        if (mid < 0)
            mid += size;
        if (mid == 0)
            return;

        reverse(list.subList(0, mid));
        reverse(list.subList(mid, size));
        reverse(list);
    }

    /**
     * Replaces all occurrences of one specified value in a list with another.
     * More formally, replaces with <tt>newVal</tt> each element <tt>e</tt>
     * in <tt>list</tt> such that
     * <tt>(oldVal==null ? e==null : oldVal.equals(e))</tt>.
     * (This method has no effect on the size of the list.)
     *
     * @param  <T> the class of the objects in the list
     * @param list the list in which replacement is to occur.
     * @param oldVal the old value to be replaced.
     * @param newVal the new value with which <tt>oldVal</tt> is to be
     *        replaced.
     * @return <tt>true</tt> if <tt>list</tt> contained one or more elements
     *         <tt>e</tt> such that
     *         <tt>(oldVal==null ?  e==null : oldVal.equals(e))</tt>.
     * @throws UnsupportedOperationException if the specified list or
     *         its list-iterator does not support the <tt>set</tt> operation.
     * @since  1.4
     */
    public static <T> boolean replaceAll(List<T> list, T oldVal, T newVal) {
        boolean result = false;
        int size = list.size();
        if (size < REPLACEALL_THRESHOLD || list instanceof RandomAccess) {
            if (oldVal==null) {
                for (int i=0; i<size; i++) {
                    if (list.get(i)==null) {
                        list.set(i, newVal);
                        result = true;
                    }
                }
            } else {
                for (int i=0; i<size; i++) {
                    if (oldVal.equals(list.get(i))) {
                        list.set(i, newVal);
                        result = true;
                    }
                }
            }
        } else {
            ListIterator<T> itr=list.listIterator();
            if (oldVal==null) {
                for (int i=0; i<size; i++) {
                    if (itr.next()==null) {
                        itr.set(newVal);
                        result = true;
                    }
                }
            } else {
                for (int i=0; i<size; i++) {
                    if (oldVal.equals(itr.next())) {
                        itr.set(newVal);
                        result = true;
                    }
                }
            }
        }
        return result;
    }

    /**
     * Returns the starting position of the first occurrence of the specified
     * target list within the specified source list, or -1 if there is no
     * such occurrence.  More formally, returns the lowest index <tt>i</tt>
     * such that {@code source.subList(i, i+target.size()).equals(target)},
     * or -1 if there is no such index.  (Returns -1 if
     * {@code target.size() > source.size()})
     *
     * <p>This implementation uses the "brute force" technique of scanning
     * over the source list, looking for a match with the target at each
     * location in turn.
     *
     * @param source the list in which to search for the first occurrence
     *        of <tt>target</tt>.
     * @param target the list to search for as a subList of <tt>source</tt>.
     * @return the starting position of the first occurrence of the specified
     *         target list within the specified source list, or -1 if there
     *         is no such occurrence.
     * @since  1.4
     */
    public static int indexOfSubList(List<?> source, List<?> target) {
        int sourceSize = source.size();
        int targetSize = target.size();
        int maxCandidate = sourceSize - targetSize;

        if (sourceSize < INDEXOFSUBLIST_THRESHOLD ||
            (source instanceof RandomAccess&&target instanceof RandomAccess)) {
        nextCand:
            for (int candidate = 0; candidate <= maxCandidate; candidate++) {
                for (int i=0, j=candidate; i<targetSize; i++, j++)
                    if (!eq(target.get(i), source.get(j)))
                        continue nextCand;  // Element mismatch, try next cand
                return candidate;  // All elements of candidate matched target
            }
        } else {  // Iterator version of above algorithm
            ListIterator<?> si = source.listIterator();
        nextCand:
            for (int candidate = 0; candidate <= maxCandidate; candidate++) {
                ListIterator<?> ti = target.listIterator();
                for (int i=0; i<targetSize; i++) {
                    if (!eq(ti.next(), si.next())) {
                        // Back up source iterator to next candidate
                        for (int j=0; j<i; j++)
                            si.previous();
                        continue nextCand;
                    }
                }
                return candidate;
            }
        }
        return -1;  // No candidate matched the target
    }

    /**
     * Returns the starting position of the last occurrence of the specified
     * target list within the specified source list, or -1 if there is no such
     * occurrence.  More formally, returns the highest index <tt>i</tt>
     * such that {@code source.subList(i, i+target.size()).equals(target)},
     * or -1 if there is no such index.  (Returns -1 if
     * {@code target.size() > source.size()})
     *
     * <p>This implementation uses the "brute force" technique of iterating
     * over the source list, looking for a match with the target at each
     * location in turn.
     *
     * @param source the list in which to search for the last occurrence
     *        of <tt>target</tt>.
     * @param target the list to search for as a subList of <tt>source</tt>.
     * @return the starting position of the last occurrence of the specified
     *         target list within the specified source list, or -1 if there
     *         is no such occurrence.
     * @since  1.4
     */
    public static int lastIndexOfSubList(List<?> source, List<?> target) {
        int sourceSize = source.size();
        int targetSize = target.size();
        int maxCandidate = sourceSize - targetSize;

        if (sourceSize < INDEXOFSUBLIST_THRESHOLD ||
            source instanceof RandomAccess) {   // Index access version
        nextCand:
            for (int candidate = maxCandidate; candidate >= 0; candidate--) {
                for (int i=0, j=candidate; i<targetSize; i++, j++)
                    if (!eq(target.get(i), source.get(j)))
                        continue nextCand;  // Element mismatch, try next cand
                return candidate;  // All elements of candidate matched target
            }
        } else {  // Iterator version of above algorithm
            if (maxCandidate < 0)
                return -1;
            ListIterator<?> si = source.listIterator(maxCandidate);
        nextCand:
            for (int candidate = maxCandidate; candidate >= 0; candidate--) {
                ListIterator<?> ti = target.listIterator();
                for (int i=0; i<targetSize; i++) {
                    if (!eq(ti.next(), si.next())) {
                        if (candidate != 0) {
                            // Back up source iterator to next candidate
                            for (int j=0; j<=i+1; j++)
                                si.previous();
                        }
                        continue nextCand;
                    }
                }
                return candidate;
            }
        }
        return -1;  // No candidate matched the target
    }


    // Unmodifiable Wrappers

    /**
     * Returns an unmodifiable view of the specified collection.  This method
     * allows modules to provide users with "read-only" access to internal
     * collections.  Query operations on the returned collection "read through"
     * to the specified collection, and attempts to modify the returned
     * collection, whether direct or via its iterator, result in an
     * <tt>UnsupportedOperationException</tt>.<p>
     *
     * The returned collection does <i>not</i> pass the hashCode and equals
     * operations through to the backing collection, but relies on
     * <tt>Object</tt>'s <tt>equals</tt> and <tt>hashCode</tt> methods.  This
     * is necessary to preserve the contracts of these operations in the case
     * that the backing collection is a set or a list.<p>
     *
     * The returned collection will be serializable if the specified collection
     * is serializable.
     *
     * @param  <T> the class of the objects in the collection
     * @param  c the collection for which an unmodifiable view is to be
     *         returned.
     * @return an unmodifiable view of the specified collection.
     */
    public static <T> Collection<T> unmodifiableCollection(Collection<? extends T> c) {
        return new UnmodifiableCollection<>(c);
    }

    /**
     * @serial include
     */
    static class UnmodifiableCollection<E> implements Collection<E>, Serializable {
        private static final long serialVersionUID = 1820017752578914078L;

        final Collection<? extends E> c;

        UnmodifiableCollection(Collection<? extends E> c) {
            if (c==null)
                throw new NullPointerException();
            this.c = c;
        }

        public int size()                   {return c.size();}
        public boolean isEmpty()            {return c.isEmpty();}
        public boolean contains(Object o)   {return c.contains(o);}
        public Object[] toArray()           {return c.toArray();}
        public <T> T[] toArray(T[] a)       {return c.toArray(a);}
        public String toString()            {return c.toString();}

        public Iterator<E> iterator() {
            return new Iterator<E>() {
                private final Iterator<? extends E> i = c.iterator();

                public boolean hasNext() {return i.hasNext();}
                public E next()          {return i.next();}
                public void remove() {
                    throw new UnsupportedOperationException();
                }
                @Override
                public void forEachRemaining(Consumer<? super E> action) {
                    // Use backing collection version
                    i.forEachRemaining(action);
                }
            };
        }

        public boolean add(E e) {
            throw new UnsupportedOperationException();
        }
        public boolean remove(Object o) {
            throw new UnsupportedOperationException();
        }

        public boolean containsAll(Collection<?> coll) {
            return c.containsAll(coll);
        }
        public boolean addAll(Collection<? extends E> coll) {
            throw new UnsupportedOperationException();
        }
        public boolean removeAll(Collection<?> coll) {
            throw new UnsupportedOperationException();
        }
        public boolean retainAll(Collection<?> coll) {
            throw new UnsupportedOperationException();
        }
        public void clear() {
            throw new UnsupportedOperationException();
        }

        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> action) {
            c.forEach(action);
        }
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            throw new UnsupportedOperationException();
        }
        @SuppressWarnings("unchecked")
        @Override
        public Spliterator<E> spliterator() {
            return (Spliterator<E>)c.spliterator();
        }
    }

    /**
     * Returns an unmodifiable view of the specified set.  This method allows
     * modules to provide users with "read-only" access to internal sets.
     * Query operations on the returned set "read through" to the specified
     * set, and attempts to modify the returned set, whether direct or via its
     * iterator, result in an <tt>UnsupportedOperationException</tt>.<p>
     *
     * The returned set will be serializable if the specified set
     * is serializable.
     *
     * @param  <T> the class of the objects in the set
     * @param  s the set for which an unmodifiable view is to be returned.
     * @return an unmodifiable view of the specified set.
     */
    public static <T> Set<T> unmodifiableSet(Set<? extends T> s) {
        return new UnmodifiableSet<>(s);
    }

    /**
     * @serial include
     */
    static class UnmodifiableSet<E> extends UnmodifiableCollection<E>
                                 implements Set<E>, Serializable {
        private static final long serialVersionUID = -9215047833775013803L;

        UnmodifiableSet(Set<? extends E> s)     {super(s);}
        public boolean equals(Object o) {return o == this || c.equals(o);}
        public int hashCode()           {return c.hashCode();}
    }

    /**
     * Returns an unmodifiable view of the specified sorted set.  This method
     * allows modules to provide users with "read-only" access to internal
     * sorted sets.  Query operations on the returned sorted set "read
     * through" to the specified sorted set.  Attempts to modify the returned
     * sorted set, whether direct, via its iterator, or via its
     * <tt>subSet</tt>, <tt>headSet</tt>, or <tt>tailSet</tt> views, result in
     * an <tt>UnsupportedOperationException</tt>.<p>
     *
     * The returned sorted set will be serializable if the specified sorted set
     * is serializable.
     *
     * @param  <T> the class of the objects in the set
     * @param s the sorted set for which an unmodifiable view is to be
     *        returned.
     * @return an unmodifiable view of the specified sorted set.
     */
    public static <T> SortedSet<T> unmodifiableSortedSet(SortedSet<T> s) {
        return new UnmodifiableSortedSet<>(s);
    }

    /**
     * @serial include
     */
    static class UnmodifiableSortedSet<E>
                             extends UnmodifiableSet<E>
                             implements SortedSet<E>, Serializable {
        private static final long serialVersionUID = -4929149591599911165L;
        private final SortedSet<E> ss;

        UnmodifiableSortedSet(SortedSet<E> s) {super(s); ss = s;}

        public Comparator<? super E> comparator() {return ss.comparator();}

        public SortedSet<E> subSet(E fromElement, E toElement) {
            return new UnmodifiableSortedSet<>(ss.subSet(fromElement,toElement));
        }
        public SortedSet<E> headSet(E toElement) {
            return new UnmodifiableSortedSet<>(ss.headSet(toElement));
        }
        public SortedSet<E> tailSet(E fromElement) {
            return new UnmodifiableSortedSet<>(ss.tailSet(fromElement));
        }

        public E first()                   {return ss.first();}
        public E last()                    {return ss.last();}
    }

    /**
     * Returns an unmodifiable view of the specified list.  This method allows
     * modules to provide users with "read-only" access to internal
     * lists.  Query operations on the returned list "read through" to the
     * specified list, and attempts to modify the returned list, whether
     * direct or via its iterator, result in an
     * <tt>UnsupportedOperationException</tt>.<p>
     *
     * The returned list will be serializable if the specified list
     * is serializable. Similarly, the returned list will implement
     * {@link RandomAccess} if the specified list does.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list for which an unmodifiable view is to be returned.
     * @return an unmodifiable view of the specified list.
     */
    public static <T> List<T> unmodifiableList(List<? extends T> list) {
        return (list instanceof RandomAccess ?
                new UnmodifiableRandomAccessList<>(list) :
                new UnmodifiableList<>(list));
    }

    /**
     * @serial include
     */
    static class UnmodifiableList<E> extends UnmodifiableCollection<E>
                                  implements List<E> {
        private static final long serialVersionUID = -283967356065247728L;

        final List<? extends E> list;

        UnmodifiableList(List<? extends E> list) {
            super(list);
            this.list = list;
        }

        public boolean equals(Object o) {return o == this || list.equals(o);}
        public int hashCode()           {return list.hashCode();}

        public E get(int index) {return list.get(index);}
        public E set(int index, E element) {
            throw new UnsupportedOperationException();
        }
        public void add(int index, E element) {
            throw new UnsupportedOperationException();
        }
        public E remove(int index) {
            throw new UnsupportedOperationException();
        }
        public int indexOf(Object o)            {return list.indexOf(o);}
        public int lastIndexOf(Object o)        {return list.lastIndexOf(o);}
        public boolean addAll(int index, Collection<? extends E> c) {
            throw new UnsupportedOperationException();
        }
        public ListIterator<E> listIterator()   {return listIterator(0);}

        public ListIterator<E> listIterator(final int index) {
            return new ListIterator<E>() {
                private final ListIterator<? extends E> i
                    = list.listIterator(index);

                public boolean hasNext()     {return i.hasNext();}
                public E next()              {return i.next();}
                public boolean hasPrevious() {return i.hasPrevious();}
                public E previous()          {return i.previous();}
                public int nextIndex()       {return i.nextIndex();}
                public int previousIndex()   {return i.previousIndex();}

                public void remove() {
                    throw new UnsupportedOperationException();
                }
                public void set(E e) {
                    throw new UnsupportedOperationException();
                }
                public void add(E e) {
                    throw new UnsupportedOperationException();
                }

                @Override
                public void forEachRemaining(Consumer<? super E> action) {
                    i.forEachRemaining(action);
                }
            };
        }

        public List<E> subList(int fromIndex, int toIndex) {
            return new UnmodifiableList<>(list.subList(fromIndex, toIndex));
        }

        /**
         * UnmodifiableRandomAccessList instances are serialized as
         * UnmodifiableList instances to allow them to be deserialized
         * in pre-1.4 JREs (which do not have UnmodifiableRandomAccessList).
         * This method inverts the transformation.  As a beneficial
         * side-effect, it also grafts the RandomAccess marker onto
         * UnmodifiableList instances that were serialized in pre-1.4 JREs.
         *
         * Note: Unfortunately, UnmodifiableRandomAccessList instances
         * serialized in 1.4.1 and deserialized in 1.4 will become
         * UnmodifiableList instances, as this method was missing in 1.4.
         */
        private Object readResolve() {
            return (list instanceof RandomAccess
                    ? new UnmodifiableRandomAccessList<>(list)
                    : this);
        }
    }

    /**
     * @serial include
     */
    static class UnmodifiableRandomAccessList<E> extends UnmodifiableList<E>
                                              implements RandomAccess
    {
        UnmodifiableRandomAccessList(List<? extends E> list) {
            super(list);
        }

        public List<E> subList(int fromIndex, int toIndex) {
            return new UnmodifiableRandomAccessList<>(
                list.subList(fromIndex, toIndex));
        }

        private static final long serialVersionUID = -2542308836966382001L;

        /**
         * Allows instances to be deserialized in pre-1.4 JREs (which do
         * not have UnmodifiableRandomAccessList).  UnmodifiableList has
         * a readResolve method that inverts this transformation upon
         * deserialization.
         */
        private Object writeReplace() {
            return new UnmodifiableList<>(list);
        }
    }

    /**
     * Returns an unmodifiable view of the specified map.  This method
     * allows modules to provide users with "read-only" access to internal
     * maps.  Query operations on the returned map "read through"
     * to the specified map, and attempts to modify the returned
     * map, whether direct or via its collection views, result in an
     * <tt>UnsupportedOperationException</tt>.<p>
     *
     * The returned map will be serializable if the specified map
     * is serializable.
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @param  m the map for which an unmodifiable view is to be returned.
     * @return an unmodifiable view of the specified map.
     */
    public static <K,V> Map<K,V> unmodifiableMap(Map<? extends K, ? extends V> m) {
        return new UnmodifiableMap<>(m);
    }

    /**
     * @serial include
     */
    private static class UnmodifiableMap<K,V> implements Map<K,V>, Serializable {
        private static final long serialVersionUID = -1034234728574286014L;

        private final Map<? extends K, ? extends V> m;

        UnmodifiableMap(Map<? extends K, ? extends V> m) {
            if (m==null)
                throw new NullPointerException();
            this.m = m;
        }

        public int size()                        {return m.size();}
        public boolean isEmpty()                 {return m.isEmpty();}
        public boolean containsKey(Object key)   {return m.containsKey(key);}
        public boolean containsValue(Object val) {return m.containsValue(val);}
        public V get(Object key)                 {return m.get(key);}

        public V put(K key, V value) {
            throw new UnsupportedOperationException();
        }
        public V remove(Object key) {
            throw new UnsupportedOperationException();
        }
        public void putAll(Map<? extends K, ? extends V> m) {
            throw new UnsupportedOperationException();
        }
        public void clear() {
            throw new UnsupportedOperationException();
        }

        private transient Set<K> keySet = null;
        private transient Set<Map.Entry<K,V>> entrySet = null;
        private transient Collection<V> values = null;

        public Set<K> keySet() {
            if (keySet==null)
                keySet = unmodifiableSet(m.keySet());
            return keySet;
        }

        public Set<Map.Entry<K,V>> entrySet() {
            if (entrySet==null)
                entrySet = new UnmodifiableEntrySet<>(m.entrySet());
            return entrySet;
        }

        public Collection<V> values() {
            if (values==null)
                values = unmodifiableCollection(m.values());
            return values;
        }

        public boolean equals(Object o) {return o == this || m.equals(o);}
        public int hashCode()           {return m.hashCode();}
        public String toString()        {return m.toString();}

        // Override default methods in Map
        @Override
        public void forEach(BiConsumer<? super K, ? super V> action) {
            m.forEach(action);
        }

        /**
         * We need this class in addition to UnmodifiableSet as
         * Map.Entries themselves permit modification of the backing Map
         * via their setValue operation.  This class is subtle: there are
         * many possible attacks that must be thwarted.
         *
         * @serial include
         */
        static class UnmodifiableEntrySet<K,V>
            extends UnmodifiableSet<Map.Entry<K,V>> {
            private static final long serialVersionUID = 7854390611657943733L;

            @SuppressWarnings({"unchecked", "rawtypes"})
            UnmodifiableEntrySet(Set<? extends Map.Entry<? extends K, ? extends V>> s) {
                // Need to cast to raw in order to work around a limitation in the type system
                super((Set)s);
            }

            static <K, V> Consumer<Map.Entry<K, V>> entryConsumer(Consumer<? super Entry<K, V>> action) {
                return e -> action.accept(new UnmodifiableEntry<>(e));
            }

            // Override default methods in Collection
            public void forEach(Consumer<? super Entry<K, V>> action) {
                Objects.requireNonNull(action);
                c.forEach(entryConsumer(action));
            }

            static final class UnmodifiableEntrySetSpliterator<K, V>
                    implements Spliterator<Entry<K,V>> {
                final Spliterator<Map.Entry<K, V>> s;

                UnmodifiableEntrySetSpliterator(Spliterator<Entry<K, V>> s) {
                    this.s = s;
                }

                @Override
                public boolean tryAdvance(Consumer<? super Entry<K, V>> action) {
                    Objects.requireNonNull(action);
                    return s.tryAdvance(entryConsumer(action));
                }

                @Override
                public void forEachRemaining(Consumer<? super Entry<K, V>> action) {
                    Objects.requireNonNull(action);
                    s.forEachRemaining(entryConsumer(action));
                }

                @Override
                public Spliterator<Entry<K, V>> trySplit() {
                    Spliterator<Entry<K, V>> split = s.trySplit();
                    return split == null
                           ? null
                           : new UnmodifiableEntrySetSpliterator<>(split);
                }

                @Override
                public long estimateSize() {
                    return s.estimateSize();
                }

                @Override
                public long getExactSizeIfKnown() {
                    return s.getExactSizeIfKnown();
                }

                @Override
                public int characteristics() {
                    return s.characteristics();
                }

                @Override
                public boolean hasCharacteristics(int characteristics) {
                    return s.hasCharacteristics(characteristics);
                }

                @Override
                public Comparator<? super Entry<K, V>> getComparator() {
                    return s.getComparator();
                }
            }

            @SuppressWarnings("unchecked")
            public Spliterator<Entry<K,V>> spliterator() {
                return new UnmodifiableEntrySetSpliterator<>(
                        (Spliterator<Map.Entry<K, V>>) c.spliterator());
            }

            public Iterator<Map.Entry<K,V>> iterator() {
                return new Iterator<Map.Entry<K,V>>() {
                    private final Iterator<? extends Map.Entry<? extends K, ? extends V>> i = c.iterator();

                    public boolean hasNext() {
                        return i.hasNext();
                    }
                    public Map.Entry<K,V> next() {
                        return new UnmodifiableEntry<>(i.next());
                    }
                    public void remove() {
                        throw new UnsupportedOperationException();
                    }
                    // Android-note: This seems pretty inconsistent. Unlike other subclasses, we aren't
                    // delegating to the subclass iterator here. Seems like an oversight.
                };
            }

            @SuppressWarnings("unchecked")
            public Object[] toArray() {
                Object[] a = c.toArray();
                for (int i=0; i<a.length; i++)
                    a[i] = new UnmodifiableEntry<>((Map.Entry<? extends K, ? extends V>)a[i]);
                return a;
            }

            @SuppressWarnings("unchecked")
            public <T> T[] toArray(T[] a) {
                // We don't pass a to c.toArray, to avoid window of
                // vulnerability wherein an unscrupulous multithreaded client
                // could get his hands on raw (unwrapped) Entries from c.
                Object[] arr = c.toArray(a.length==0 ? a : Arrays.copyOf(a, 0));

                for (int i=0; i<arr.length; i++)
                    arr[i] = new UnmodifiableEntry<>((Map.Entry<? extends K, ? extends V>)arr[i]);

                if (arr.length > a.length)
                    return (T[])arr;

                System.arraycopy(arr, 0, a, 0, arr.length);
                if (a.length > arr.length)
                    a[arr.length] = null;
                return a;
            }

            /**
             * This method is overridden to protect the backing set against
             * an object with a nefarious equals function that senses
             * that the equality-candidate is Map.Entry and calls its
             * setValue method.
             */
            public boolean contains(Object o) {
                if (!(o instanceof Map.Entry))
                    return false;
                return c.contains(
                    new UnmodifiableEntry<>((Map.Entry<?,?>) o));
            }

            /**
             * The next two methods are overridden to protect against
             * an unscrupulous List whose contains(Object o) method senses
             * when o is a Map.Entry, and calls o.setValue.
             */
            public boolean containsAll(Collection<?> coll) {
                for (Object e : coll) {
                    if (!contains(e)) // Invokes safe contains() above
                        return false;
                }
                return true;
            }
            public boolean equals(Object o) {
                if (o == this)
                    return true;

                if (!(o instanceof Set))
                    return false;
                Set<?> s = (Set<?>) o;
                if (s.size() != c.size())
                    return false;
                return containsAll(s); // Invokes safe containsAll() above
            }

            /**
             * This "wrapper class" serves two purposes: it prevents
             * the client from modifying the backing Map, by short-circuiting
             * the setValue method, and it protects the backing Map against
             * an ill-behaved Map.Entry that attempts to modify another
             * Map Entry when asked to perform an equality check.
             */
            private static class UnmodifiableEntry<K,V> implements Map.Entry<K,V> {
                private Map.Entry<? extends K, ? extends V> e;

                UnmodifiableEntry(Map.Entry<? extends K, ? extends V> e)
                        {this.e = Objects.requireNonNull(e);}

                public K getKey()        {return e.getKey();}
                public V getValue()      {return e.getValue();}
                public V setValue(V value) {
                    throw new UnsupportedOperationException();
                }
                public int hashCode()    {return e.hashCode();}
                public boolean equals(Object o) {
                    if (this == o)
                        return true;
                    if (!(o instanceof Map.Entry))
                        return false;
                    Map.Entry<?,?> t = (Map.Entry<?,?>)o;
                    return eq(e.getKey(),   t.getKey()) &&
                           eq(e.getValue(), t.getValue());
                }
                public String toString() {return e.toString();}
            }
        }
    }

    /**
     * Returns an unmodifiable view of the specified sorted map.  This method
     * allows modules to provide users with "read-only" access to internal
     * sorted maps.  Query operations on the returned sorted map "read through"
     * to the specified sorted map.  Attempts to modify the returned
     * sorted map, whether direct, via its collection views, or via its
     * <tt>subMap</tt>, <tt>headMap</tt>, or <tt>tailMap</tt> views, result in
     * an <tt>UnsupportedOperationException</tt>.<p>
     *
     * The returned sorted map will be serializable if the specified sorted map
     * is serializable.
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @param m the sorted map for which an unmodifiable view is to be
     *        returned.
     * @return an unmodifiable view of the specified sorted map.
     */
    public static <K,V> SortedMap<K,V> unmodifiableSortedMap(SortedMap<K, ? extends V> m) {
        return new UnmodifiableSortedMap<>(m);
    }

    /**
     * @serial include
     */
    static class UnmodifiableSortedMap<K,V>
          extends UnmodifiableMap<K,V>
          implements SortedMap<K,V>, Serializable {
        private static final long serialVersionUID = -8806743815996713206L;

        private final SortedMap<K, ? extends V> sm;

        UnmodifiableSortedMap(SortedMap<K, ? extends V> m) {super(m); sm = m; }
        public Comparator<? super K> comparator()   { return sm.comparator(); }
        public SortedMap<K,V> subMap(K fromKey, K toKey)
             { return new UnmodifiableSortedMap<>(sm.subMap(fromKey, toKey)); }
        public SortedMap<K,V> headMap(K toKey)
                     { return new UnmodifiableSortedMap<>(sm.headMap(toKey)); }
        public SortedMap<K,V> tailMap(K fromKey)
                   { return new UnmodifiableSortedMap<>(sm.tailMap(fromKey)); }
        public K firstKey()                           { return sm.firstKey(); }
        public K lastKey()                             { return sm.lastKey(); }
    }

    // Synch Wrappers

    // TODO: Replace {@code stream} with {@link Stream} once we have them.
    /**
     * Returns a synchronized (thread-safe) collection backed by the specified
     * collection.  In order to guarantee serial access, it is critical that
     * <strong>all</strong> access to the backing collection is accomplished
     * through the returned collection.<p>
     *
     * It is imperative that the user manually synchronize on the returned
     * collection when traversing it via {@link Iterator}, {@link Spliterator}
     * or {@code Stream}:
     * <pre>
     *  Collection c = Collections.synchronizedCollection(myCollection);
     *     ...
     *  synchronized (c) {
     *      Iterator i = c.iterator(); // Must be in the synchronized block
     *      while (i.hasNext())
     *         foo(i.next());
     *  }
     * </pre>
     * Failure to follow this advice may result in non-deterministic behavior.
     *
     * <p>The returned collection does <i>not</i> pass the {@code hashCode}
     * and {@code equals} operations through to the backing collection, but
     * relies on {@code Object}'s equals and hashCode methods.  This is
     * necessary to preserve the contracts of these operations in the case
     * that the backing collection is a set or a list.<p>
     *
     * The returned collection will be serializable if the specified collection
     * is serializable.
     *
     * @param  <T> the class of the objects in the collection
     * @param  c the collection to be "wrapped" in a synchronized collection.
     * @return a synchronized view of the specified collection.
     */
    public static <T> Collection<T> synchronizedCollection(Collection<T> c) {
        return new SynchronizedCollection<>(c);
    }

    static <T> Collection<T> synchronizedCollection(Collection<T> c, Object mutex) {
        return new SynchronizedCollection<>(c, mutex);
    }

    /**
     * @serial include
     */
    static class SynchronizedCollection<E> implements Collection<E>, Serializable {
        private static final long serialVersionUID = 3053995032091335093L;

        final Collection<E> c;  // Backing Collection
        final Object mutex;     // Object on which to synchronize

        SynchronizedCollection(Collection<E> c) {
            this.c = Objects.requireNonNull(c);
            mutex = this;
        }

        SynchronizedCollection(Collection<E> c, Object mutex) {
            this.c = Objects.requireNonNull(c);
            this.mutex = Objects.requireNonNull(mutex);
        }

        public int size() {
            synchronized (mutex) {return c.size();}
        }
        public boolean isEmpty() {
            synchronized (mutex) {return c.isEmpty();}
        }
        public boolean contains(Object o) {
            synchronized (mutex) {return c.contains(o);}
        }
        public Object[] toArray() {
            synchronized (mutex) {return c.toArray();}
        }
        public <T> T[] toArray(T[] a) {
            synchronized (mutex) {return c.toArray(a);}
        }

        public Iterator<E> iterator() {
            return c.iterator(); // Must be manually synched by user!
        }

        public boolean add(E e) {
            synchronized (mutex) {return c.add(e);}
        }
        public boolean remove(Object o) {
            synchronized (mutex) {return c.remove(o);}
        }

        public boolean containsAll(Collection<?> coll) {
            synchronized (mutex) {return c.containsAll(coll);}
        }
        public boolean addAll(Collection<? extends E> coll) {
            synchronized (mutex) {return c.addAll(coll);}
        }
        public boolean removeAll(Collection<?> coll) {
            synchronized (mutex) {return c.removeAll(coll);}
        }
        public boolean retainAll(Collection<?> coll) {
            synchronized (mutex) {return c.retainAll(coll);}
        }
        public void clear() {
            synchronized (mutex) {c.clear();}
        }
        public String toString() {
            synchronized (mutex) {return c.toString();}
        }
        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> consumer) {
            synchronized (mutex) {c.forEach(consumer);}
        }
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            synchronized (mutex) {return c.removeIf(filter);}
        }
        @Override
        public Spliterator<E> spliterator() {
            return c.spliterator(); // Must be manually synched by user!
        }

        private void writeObject(ObjectOutputStream s) throws IOException {
            synchronized (mutex) {s.defaultWriteObject();}
        }
    }

    /**
     * Returns a synchronized (thread-safe) set backed by the specified
     * set.  In order to guarantee serial access, it is critical that
     * <strong>all</strong> access to the backing set is accomplished
     * through the returned set.<p>
     *
     * It is imperative that the user manually synchronize on the returned
     * set when iterating over it:
     * <pre>
     *  Set s = Collections.synchronizedSet(new HashSet());
     *      ...
     *  synchronized (s) {
     *      Iterator i = s.iterator(); // Must be in the synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * Failure to follow this advice may result in non-deterministic behavior.
     *
     * <p>The returned set will be serializable if the specified set is
     * serializable.
     *
     * @param  <T> the class of the objects in the set
     * @param  s the set to be "wrapped" in a synchronized set.
     * @return a synchronized view of the specified set.
     */
    public static <T> Set<T> synchronizedSet(Set<T> s) {
        return new SynchronizedSet<>(s);
    }

    static <T> Set<T> synchronizedSet(Set<T> s, Object mutex) {
        return new SynchronizedSet<>(s, mutex);
    }

    /**
     * @serial include
     */
    static class SynchronizedSet<E>
          extends SynchronizedCollection<E>
          implements Set<E> {
        private static final long serialVersionUID = 487447009682186044L;

        SynchronizedSet(Set<E> s) {
            super(s);
        }
        SynchronizedSet(Set<E> s, Object mutex) {
            super(s, mutex);
        }

        public boolean equals(Object o) {
            if (this == o)
                return true;
            synchronized (mutex) {return c.equals(o);}
        }
        public int hashCode() {
            synchronized (mutex) {return c.hashCode();}
        }
    }

    /**
     * Returns a synchronized (thread-safe) sorted set backed by the specified
     * sorted set.  In order to guarantee serial access, it is critical that
     * <strong>all</strong> access to the backing sorted set is accomplished
     * through the returned sorted set (or its views).<p>
     *
     * It is imperative that the user manually synchronize on the returned
     * sorted set when iterating over it or any of its <tt>subSet</tt>,
     * <tt>headSet</tt>, or <tt>tailSet</tt> views.
     * <pre>
     *  SortedSet s = Collections.synchronizedSortedSet(new TreeSet());
     *      ...
     *  synchronized (s) {
     *      Iterator i = s.iterator(); // Must be in the synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * or:
     * <pre>
     *  SortedSet s = Collections.synchronizedSortedSet(new TreeSet());
     *  SortedSet s2 = s.headSet(foo);
     *      ...
     *  synchronized (s) {  // Note: s, not s2!!!
     *      Iterator i = s2.iterator(); // Must be in the synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * Failure to follow this advice may result in non-deterministic behavior.
     *
     * <p>The returned sorted set will be serializable if the specified
     * sorted set is serializable.
     *
     * @param  <T> the class of the objects in the set
     * @param  s the sorted set to be "wrapped" in a synchronized sorted set.
     * @return a synchronized view of the specified sorted set.
     */
    public static <T> SortedSet<T> synchronizedSortedSet(SortedSet<T> s) {
        return new SynchronizedSortedSet<>(s);
    }

    /**
     * @serial include
     */
    static class SynchronizedSortedSet<E>
        extends SynchronizedSet<E>
        implements SortedSet<E>
    {
        private static final long serialVersionUID = 8695801310862127406L;

        private final SortedSet<E> ss;

        SynchronizedSortedSet(SortedSet<E> s) {
            super(s);
            ss = s;
        }
        SynchronizedSortedSet(SortedSet<E> s, Object mutex) {
            super(s, mutex);
            ss = s;
        }

        public Comparator<? super E> comparator() {
            synchronized (mutex) {return ss.comparator();}
        }

        public SortedSet<E> subSet(E fromElement, E toElement) {
            synchronized (mutex) {
                return new SynchronizedSortedSet<>(
                    ss.subSet(fromElement, toElement), mutex);
            }
        }
        public SortedSet<E> headSet(E toElement) {
            synchronized (mutex) {
                return new SynchronizedSortedSet<>(ss.headSet(toElement), mutex);
            }
        }
        public SortedSet<E> tailSet(E fromElement) {
            synchronized (mutex) {
               return new SynchronizedSortedSet<>(ss.tailSet(fromElement),mutex);
            }
        }

        public E first() {
            synchronized (mutex) {return ss.first();}
        }
        public E last() {
            synchronized (mutex) {return ss.last();}
        }
    }

    /**
     * Returns a synchronized (thread-safe) list backed by the specified
     * list.  In order to guarantee serial access, it is critical that
     * <strong>all</strong> access to the backing list is accomplished
     * through the returned list.<p>
     *
     * It is imperative that the user manually synchronize on the returned
     * list when iterating over it:
     * <pre>
     *  List list = Collections.synchronizedList(new ArrayList());
     *      ...
     *  synchronized (list) {
     *      Iterator i = list.iterator(); // Must be in synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * Failure to follow this advice may result in non-deterministic behavior.
     *
     * <p>The returned list will be serializable if the specified list is
     * serializable.
     *
     * @param  <T> the class of the objects in the list
     * @param  list the list to be "wrapped" in a synchronized list.
     * @return a synchronized view of the specified list.
     */
    public static <T> List<T> synchronizedList(List<T> list) {
        return (list instanceof RandomAccess ?
                new SynchronizedRandomAccessList<>(list) :
                new SynchronizedList<>(list));
    }

    static <T> List<T> synchronizedList(List<T> list, Object mutex) {
        return (list instanceof RandomAccess ?
                new SynchronizedRandomAccessList<>(list, mutex) :
                new SynchronizedList<>(list, mutex));
    }

    /**
     * @serial include
     */
    static class SynchronizedList<E>
        extends SynchronizedCollection<E>
        implements List<E> {
        private static final long serialVersionUID = -7754090372962971524L;

        final List<E> list;

        SynchronizedList(List<E> list) {
            super(list);
            this.list = list;
        }
        SynchronizedList(List<E> list, Object mutex) {
            super(list, mutex);
            this.list = list;
        }

        public boolean equals(Object o) {
            if (this == o)
                return true;
            synchronized (mutex) {return list.equals(o);}
        }
        public int hashCode() {
            synchronized (mutex) {return list.hashCode();}
        }

        public E get(int index) {
            synchronized (mutex) {return list.get(index);}
        }
        public E set(int index, E element) {
            synchronized (mutex) {return list.set(index, element);}
        }
        public void add(int index, E element) {
            synchronized (mutex) {list.add(index, element);}
        }
        public E remove(int index) {
            synchronized (mutex) {return list.remove(index);}
        }

        public int indexOf(Object o) {
            synchronized (mutex) {return list.indexOf(o);}
        }
        public int lastIndexOf(Object o) {
            synchronized (mutex) {return list.lastIndexOf(o);}
        }

        public boolean addAll(int index, Collection<? extends E> c) {
            synchronized (mutex) {return list.addAll(index, c);}
        }

        public ListIterator<E> listIterator() {
            return list.listIterator(); // Must be manually synched by user
        }

        public ListIterator<E> listIterator(int index) {
            return list.listIterator(index); // Must be manually synched by user
        }

        public List<E> subList(int fromIndex, int toIndex) {
            synchronized (mutex) {
                return new SynchronizedList<>(list.subList(fromIndex, toIndex),
                                            mutex);
            }
        }

        /**
         * SynchronizedRandomAccessList instances are serialized as
         * SynchronizedList instances to allow them to be deserialized
         * in pre-1.4 JREs (which do not have SynchronizedRandomAccessList).
         * This method inverts the transformation.  As a beneficial
         * side-effect, it also grafts the RandomAccess marker onto
         * SynchronizedList instances that were serialized in pre-1.4 JREs.
         *
         * Note: Unfortunately, SynchronizedRandomAccessList instances
         * serialized in 1.4.1 and deserialized in 1.4 will become
         * SynchronizedList instances, as this method was missing in 1.4.
         */
        private Object readResolve() {
            return (list instanceof RandomAccess
                    ? new SynchronizedRandomAccessList<>(list)
                    : this);
        }
    }

    /**
     * @serial include
     */
    static class SynchronizedRandomAccessList<E>
        extends SynchronizedList<E>
        implements RandomAccess {

        SynchronizedRandomAccessList(List<E> list) {
            super(list);
        }

        SynchronizedRandomAccessList(List<E> list, Object mutex) {
            super(list, mutex);
        }

        public List<E> subList(int fromIndex, int toIndex) {
            synchronized (mutex) {
                return new SynchronizedRandomAccessList<>(
                    list.subList(fromIndex, toIndex), mutex);
            }
        }

        private static final long serialVersionUID = 1530674583602358482L;

        /**
         * Allows instances to be deserialized in pre-1.4 JREs (which do
         * not have SynchronizedRandomAccessList).  SynchronizedList has
         * a readResolve method that inverts this transformation upon
         * deserialization.
         */
        private Object writeReplace() {
            return new SynchronizedList<>(list);
        }
    }

    /**
     * Returns a synchronized (thread-safe) map backed by the specified
     * map.  In order to guarantee serial access, it is critical that
     * <strong>all</strong> access to the backing map is accomplished
     * through the returned map.<p>
     *
     * It is imperative that the user manually synchronize on the returned
     * map when iterating over any of its collection views:
     * <pre>
     *  Map m = Collections.synchronizedMap(new HashMap());
     *      ...
     *  Set s = m.keySet();  // Needn't be in synchronized block
     *      ...
     *  synchronized (m) {  // Synchronizing on m, not s!
     *      Iterator i = s.iterator(); // Must be in synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * Failure to follow this advice may result in non-deterministic behavior.
     *
     * <p>The returned map will be serializable if the specified map is
     * serializable.
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @param  m the map to be "wrapped" in a synchronized map.
     * @return a synchronized view of the specified map.
     */
    public static <K,V> Map<K,V> synchronizedMap(Map<K,V> m) {
        return new SynchronizedMap<>(m);
    }

    /**
     * @serial include
     */
    private static class SynchronizedMap<K,V>
        implements Map<K,V>, Serializable {
        private static final long serialVersionUID = 1978198479659022715L;

        private final Map<K,V> m;     // Backing Map
        final Object      mutex;        // Object on which to synchronize

        SynchronizedMap(Map<K,V> m) {
            this.m = Objects.requireNonNull(m);
            mutex = this;
        }

        SynchronizedMap(Map<K,V> m, Object mutex) {
            this.m = m;
            this.mutex = mutex;
        }

        public int size() {
            synchronized (mutex) {return m.size();}
        }
        public boolean isEmpty() {
            synchronized (mutex) {return m.isEmpty();}
        }
        public boolean containsKey(Object key) {
            synchronized (mutex) {return m.containsKey(key);}
        }
        public boolean containsValue(Object value) {
            synchronized (mutex) {return m.containsValue(value);}
        }
        public V get(Object key) {
            synchronized (mutex) {return m.get(key);}
        }

        public V put(K key, V value) {
            synchronized (mutex) {return m.put(key, value);}
        }
        public V remove(Object key) {
            synchronized (mutex) {return m.remove(key);}
        }
        public void putAll(Map<? extends K, ? extends V> map) {
            synchronized (mutex) {m.putAll(map);}
        }
        public void clear() {
            synchronized (mutex) {m.clear();}
        }

        private transient Set<K> keySet = null;
        private transient Set<Map.Entry<K,V>> entrySet = null;
        private transient Collection<V> values = null;

        public Set<K> keySet() {
            synchronized (mutex) {
                if (keySet==null)
                    keySet = new SynchronizedSet<>(m.keySet(), mutex);
                return keySet;
            }
        }

        public Set<Map.Entry<K,V>> entrySet() {
            synchronized (mutex) {
                if (entrySet==null)
                    entrySet = new SynchronizedSet<>(m.entrySet(), mutex);
                return entrySet;
            }
        }

        public Collection<V> values() {
            synchronized (mutex) {
                if (values==null)
                    values = new SynchronizedCollection<>(m.values(), mutex);
                return values;
            }
        }

        public boolean equals(Object o) {
            if (this == o)
                return true;
            synchronized (mutex) {return m.equals(o);}
        }
        public int hashCode() {
            synchronized (mutex) {return m.hashCode();}
        }
        public String toString() {
            synchronized (mutex) {return m.toString();}
        }
        // Override default methods in Map
        @Override
        public void forEach(BiConsumer<? super K, ? super V> action) {
            synchronized (mutex) {m.forEach(action);}
        }

        private void writeObject(ObjectOutputStream s) throws IOException {
            synchronized (mutex) {s.defaultWriteObject();}
        }
    }

    /**
     * Returns a synchronized (thread-safe) sorted map backed by the specified
     * sorted map.  In order to guarantee serial access, it is critical that
     * <strong>all</strong> access to the backing sorted map is accomplished
     * through the returned sorted map (or its views).<p>
     *
     * It is imperative that the user manually synchronize on the returned
     * sorted map when iterating over any of its collection views, or the
     * collections views of any of its <tt>subMap</tt>, <tt>headMap</tt> or
     * <tt>tailMap</tt> views.
     * <pre>
     *  SortedMap m = Collections.synchronizedSortedMap(new TreeMap());
     *      ...
     *  Set s = m.keySet();  // Needn't be in synchronized block
     *      ...
     *  synchronized (m) {  // Synchronizing on m, not s!
     *      Iterator i = s.iterator(); // Must be in synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * or:
     * <pre>
     *  SortedMap m = Collections.synchronizedSortedMap(new TreeMap());
     *  SortedMap m2 = m.subMap(foo, bar);
     *      ...
     *  Set s2 = m2.keySet();  // Needn't be in synchronized block
     *      ...
     *  synchronized (m) {  // Synchronizing on m, not m2 or s2!
     *      Iterator i = s.iterator(); // Must be in synchronized block
     *      while (i.hasNext())
     *          foo(i.next());
     *  }
     * </pre>
     * Failure to follow this advice may result in non-deterministic behavior.
     *
     * <p>The returned sorted map will be serializable if the specified
     * sorted map is serializable.
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @param  m the sorted map to be "wrapped" in a synchronized sorted map.
     * @return a synchronized view of the specified sorted map.
     */
    public static <K,V> SortedMap<K,V> synchronizedSortedMap(SortedMap<K,V> m) {
        return new SynchronizedSortedMap<>(m);
    }

    /**
     * @serial include
     */
    static class SynchronizedSortedMap<K,V>
        extends SynchronizedMap<K,V>
        implements SortedMap<K,V>
    {
        private static final long serialVersionUID = -8798146769416483793L;

        private final SortedMap<K,V> sm;

        SynchronizedSortedMap(SortedMap<K,V> m) {
            super(m);
            sm = m;
        }
        SynchronizedSortedMap(SortedMap<K,V> m, Object mutex) {
            super(m, mutex);
            sm = m;
        }

        public Comparator<? super K> comparator() {
            synchronized (mutex) {return sm.comparator();}
        }

        public SortedMap<K,V> subMap(K fromKey, K toKey) {
            synchronized (mutex) {
                return new SynchronizedSortedMap<>(
                    sm.subMap(fromKey, toKey), mutex);
            }
        }
        public SortedMap<K,V> headMap(K toKey) {
            synchronized (mutex) {
                return new SynchronizedSortedMap<>(sm.headMap(toKey), mutex);
            }
        }
        public SortedMap<K,V> tailMap(K fromKey) {
            synchronized (mutex) {
               return new SynchronizedSortedMap<>(sm.tailMap(fromKey),mutex);
            }
        }

        public K firstKey() {
            synchronized (mutex) {return sm.firstKey();}
        }
        public K lastKey() {
            synchronized (mutex) {return sm.lastKey();}
        }
    }

    // Dynamically typesafe collection wrappers

    /**
     * Returns a dynamically typesafe view of the specified collection.
     * Any attempt to insert an element of the wrong type will result in an
     * immediate {@link ClassCastException}.  Assuming a collection
     * contains no incorrectly typed elements prior to the time a
     * dynamically typesafe view is generated, and that all subsequent
     * access to the collection takes place through the view, it is
     * <i>guaranteed</i> that the collection cannot contain an incorrectly
     * typed element.
     *
     * <p>The generics mechanism in the language provides compile-time
     * (static) type checking, but it is possible to defeat this mechanism
     * with unchecked casts.  Usually this is not a problem, as the compiler
     * issues warnings on all such unchecked operations.  There are, however,
     * times when static type checking alone is not sufficient.  For example,
     * suppose a collection is passed to a third-party library and it is
     * imperative that the library code not corrupt the collection by
     * inserting an element of the wrong type.
     *
     * <p>Another use of dynamically typesafe views is debugging.  Suppose a
     * program fails with a {@code ClassCastException}, indicating that an
     * incorrectly typed element was put into a parameterized collection.
     * Unfortunately, the exception can occur at any time after the erroneous
     * element is inserted, so it typically provides little or no information
     * as to the real source of the problem.  If the problem is reproducible,
     * one can quickly determine its source by temporarily modifying the
     * program to wrap the collection with a dynamically typesafe view.
     * For example, this declaration:
     *  <pre> {@code
     *     Collection<String> c = new HashSet<>();
     * }</pre>
     * may be replaced temporarily by this one:
     *  <pre> {@code
     *     Collection<String> c = Collections.checkedCollection(
     *         new HashSet<>(), String.class);
     * }</pre>
     * Running the program again will cause it to fail at the point where
     * an incorrectly typed element is inserted into the collection, clearly
     * identifying the source of the problem.  Once the problem is fixed, the
     * modified declaration may be reverted back to the original.
     *
     * <p>The returned collection does <i>not</i> pass the hashCode and equals
     * operations through to the backing collection, but relies on
     * {@code Object}'s {@code equals} and {@code hashCode} methods.  This
     * is necessary to preserve the contracts of these operations in the case
     * that the backing collection is a set or a list.
     *
     * <p>The returned collection will be serializable if the specified
     * collection is serializable.
     *
     * <p>Since {@code null} is considered to be a value of any reference
     * type, the returned collection permits insertion of null elements
     * whenever the backing collection does.
     *
     * @param <E> the class of the objects in the collection
     * @param c the collection for which a dynamically typesafe view is to be
     *          returned
     * @param type the type of element that {@code c} is permitted to hold
     * @return a dynamically typesafe view of the specified collection
     * @since 1.5
     */
    public static <E> Collection<E> checkedCollection(Collection<E> c,
                                                      Class<E> type) {
        return new CheckedCollection<>(c, type);
    }

    @SuppressWarnings("unchecked")
    static <T> T[] zeroLengthArray(Class<T> type) {
        return (T[]) Array.newInstance(type, 0);
    }

    /**
     * @serial include
     */
    static class CheckedCollection<E> implements Collection<E>, Serializable {
        private static final long serialVersionUID = 1578914078182001775L;

        final Collection<E> c;
        final Class<E> type;

        void typeCheck(Object o) {
            if (o != null && !type.isInstance(o))
                throw new ClassCastException(badElementMsg(o));
        }

        private String badElementMsg(Object o) {
            return "Attempt to insert " + o.getClass() +
                " element into collection with element type " + type;
        }

        CheckedCollection(Collection<E> c, Class<E> type) {
            if (c==null || type == null)
                throw new NullPointerException();
            this.c = c;
            this.type = type;
        }

        public int size()                 { return c.size(); }
        public boolean isEmpty()          { return c.isEmpty(); }
        public boolean contains(Object o) { return c.contains(o); }
        public Object[] toArray()         { return c.toArray(); }
        public <T> T[] toArray(T[] a)     { return c.toArray(a); }
        public String toString()          { return c.toString(); }
        public boolean remove(Object o)   { return c.remove(o); }
        public void clear()               {        c.clear(); }

        public boolean containsAll(Collection<?> coll) {
            return c.containsAll(coll);
        }
        public boolean removeAll(Collection<?> coll) {
            return c.removeAll(coll);
        }
        public boolean retainAll(Collection<?> coll) {
            return c.retainAll(coll);
        }

        public Iterator<E> iterator() {
            // JDK-6363904 - unwrapped iterator could be typecast to
            // ListIterator with unsafe set()
            final Iterator<E> it = c.iterator();
            return new Iterator<E>() {
                public boolean hasNext() { return it.hasNext(); }
                public E next()          { return it.next(); }
                public void remove()     {        it.remove(); }};
            // Android-note: Should we delegate to it for forEachRemaining ?
        }

        public boolean add(E e) {
            typeCheck(e);
            return c.add(e);
        }

        private E[] zeroLengthElementArray = null; // Lazily initialized

        private E[] zeroLengthElementArray() {
            return zeroLengthElementArray != null ? zeroLengthElementArray :
                (zeroLengthElementArray = zeroLengthArray(type));
        }

        @SuppressWarnings("unchecked")
        Collection<E> checkedCopyOf(Collection<? extends E> coll) {
            Object[] a = null;
            try {
                E[] z = zeroLengthElementArray();
                a = coll.toArray(z);
                // Defend against coll violating the toArray contract
                if (a.getClass() != z.getClass())
                    a = Arrays.copyOf(a, a.length, z.getClass());
            } catch (ArrayStoreException ignore) {
                // To get better and consistent diagnostics,
                // we call typeCheck explicitly on each element.
                // We call clone() to defend against coll retaining a
                // reference to the returned array and storing a bad
                // element into it after it has been type checked.
                a = coll.toArray().clone();
                for (Object o : a)
                    typeCheck(o);
            }
            // A slight abuse of the type system, but safe here.
            return (Collection<E>) Arrays.asList(a);
        }

        public boolean addAll(Collection<? extends E> coll) {
            // Doing things this way insulates us from concurrent changes
            // in the contents of coll and provides all-or-nothing
            // semantics (which we wouldn't get if we type-checked each
            // element as we added it)
            return c.addAll(checkedCopyOf(coll));
        }

        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> action) {c.forEach(action);}
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            return c.removeIf(filter);
        }
        @Override
        public Spliterator<E> spliterator() {return c.spliterator();}
    }

    /**
     * Returns a dynamically typesafe view of the specified set.
     * Any attempt to insert an element of the wrong type will result in
     * an immediate {@link ClassCastException}.  Assuming a set contains
     * no incorrectly typed elements prior to the time a dynamically typesafe
     * view is generated, and that all subsequent access to the set
     * takes place through the view, it is <i>guaranteed</i> that the
     * set cannot contain an incorrectly typed element.
     *
     * <p>A discussion of the use of dynamically typesafe views may be
     * found in the documentation for the {@link #checkedCollection
     * checkedCollection} method.
     *
     * <p>The returned set will be serializable if the specified set is
     * serializable.
     *
     * <p>Since {@code null} is considered to be a value of any reference
     * type, the returned set permits insertion of null elements whenever
     * the backing set does.
     *
     * @param <E> the class of the objects in the set
     * @param s the set for which a dynamically typesafe view is to be
     *          returned
     * @param type the type of element that {@code s} is permitted to hold
     * @return a dynamically typesafe view of the specified set
     * @since 1.5
     */
    public static <E> Set<E> checkedSet(Set<E> s, Class<E> type) {
        return new CheckedSet<>(s, type);
    }

    /**
     * @serial include
     */
    static class CheckedSet<E> extends CheckedCollection<E>
                                 implements Set<E>, Serializable
    {
        private static final long serialVersionUID = 4694047833775013803L;

        CheckedSet(Set<E> s, Class<E> elementType) { super(s, elementType); }

        public boolean equals(Object o) { return o == this || c.equals(o); }
        public int hashCode()           { return c.hashCode(); }
    }

    /**
     * Returns a dynamically typesafe view of the specified sorted set.
     * Any attempt to insert an element of the wrong type will result in an
     * immediate {@link ClassCastException}.  Assuming a sorted set
     * contains no incorrectly typed elements prior to the time a
     * dynamically typesafe view is generated, and that all subsequent
     * access to the sorted set takes place through the view, it is
     * <i>guaranteed</i> that the sorted set cannot contain an incorrectly
     * typed element.
     *
     * <p>A discussion of the use of dynamically typesafe views may be
     * found in the documentation for the {@link #checkedCollection
     * checkedCollection} method.
     *
     * <p>The returned sorted set will be serializable if the specified sorted
     * set is serializable.
     *
     * <p>Since {@code null} is considered to be a value of any reference
     * type, the returned sorted set permits insertion of null elements
     * whenever the backing sorted set does.
     *
     * @param <E> the class of the objects in the set
     * @param s the sorted set for which a dynamically typesafe view is to be
     *          returned
     * @param type the type of element that {@code s} is permitted to hold
     * @return a dynamically typesafe view of the specified sorted set
     * @since 1.5
     */
    public static <E> SortedSet<E> checkedSortedSet(SortedSet<E> s,
                                                    Class<E> type) {
        return new CheckedSortedSet<>(s, type);
    }

    /**
     * @serial include
     */
    static class CheckedSortedSet<E> extends CheckedSet<E>
        implements SortedSet<E>, Serializable
    {
        private static final long serialVersionUID = 1599911165492914959L;

        private final SortedSet<E> ss;

        CheckedSortedSet(SortedSet<E> s, Class<E> type) {
            super(s, type);
            ss = s;
        }

        public Comparator<? super E> comparator() { return ss.comparator(); }
        public E first()                   { return ss.first(); }
        public E last()                    { return ss.last(); }

        public SortedSet<E> subSet(E fromElement, E toElement) {
            return checkedSortedSet(ss.subSet(fromElement,toElement), type);
        }
        public SortedSet<E> headSet(E toElement) {
            return checkedSortedSet(ss.headSet(toElement), type);
        }
        public SortedSet<E> tailSet(E fromElement) {
            return checkedSortedSet(ss.tailSet(fromElement), type);
        }
    }

    /**
     * Returns a dynamically typesafe view of the specified list.
     * Any attempt to insert an element of the wrong type will result in
     * an immediate {@link ClassCastException}.  Assuming a list contains
     * no incorrectly typed elements prior to the time a dynamically typesafe
     * view is generated, and that all subsequent access to the list
     * takes place through the view, it is <i>guaranteed</i> that the
     * list cannot contain an incorrectly typed element.
     *
     * <p>A discussion of the use of dynamically typesafe views may be
     * found in the documentation for the {@link #checkedCollection
     * checkedCollection} method.
     *
     * <p>The returned list will be serializable if the specified list
     * is serializable.
     *
     * <p>Since {@code null} is considered to be a value of any reference
     * type, the returned list permits insertion of null elements whenever
     * the backing list does.
     *
     * @param <E> the class of the objects in the list
     * @param list the list for which a dynamically typesafe view is to be
     *             returned
     * @param type the type of element that {@code list} is permitted to hold
     * @return a dynamically typesafe view of the specified list
     * @since 1.5
     */
    public static <E> List<E> checkedList(List<E> list, Class<E> type) {
        return (list instanceof RandomAccess ?
                new CheckedRandomAccessList<>(list, type) :
                new CheckedList<>(list, type));
    }

    /**
     * @serial include
     */
    static class CheckedList<E>
        extends CheckedCollection<E>
        implements List<E>
    {
        private static final long serialVersionUID = 65247728283967356L;
        final List<E> list;

        CheckedList(List<E> list, Class<E> type) {
            super(list, type);
            this.list = list;
        }

        public boolean equals(Object o)  { return o == this || list.equals(o); }
        public int hashCode()            { return list.hashCode(); }
        public E get(int index)          { return list.get(index); }
        public E remove(int index)       { return list.remove(index); }
        public int indexOf(Object o)     { return list.indexOf(o); }
        public int lastIndexOf(Object o) { return list.lastIndexOf(o); }

        public E set(int index, E element) {
            typeCheck(element);
            return list.set(index, element);
        }

        public void add(int index, E element) {
            typeCheck(element);
            list.add(index, element);
        }

        public boolean addAll(int index, Collection<? extends E> c) {
            return list.addAll(index, checkedCopyOf(c));
        }
        public ListIterator<E> listIterator()   { return listIterator(0); }

        public ListIterator<E> listIterator(final int index) {
            final ListIterator<E> i = list.listIterator(index);

            return new ListIterator<E>() {
                public boolean hasNext()     { return i.hasNext(); }
                public E next()              { return i.next(); }
                public boolean hasPrevious() { return i.hasPrevious(); }
                public E previous()          { return i.previous(); }
                public int nextIndex()       { return i.nextIndex(); }
                public int previousIndex()   { return i.previousIndex(); }
                public void remove()         {        i.remove(); }

                public void set(E e) {
                    typeCheck(e);
                    i.set(e);
                }

                public void add(E e) {
                    typeCheck(e);
                    i.add(e);
                }

                @Override
                public void forEachRemaining(Consumer<? super E> action) {
                    i.forEachRemaining(action);
                }
            };
        }

        public List<E> subList(int fromIndex, int toIndex) {
            return new CheckedList<>(list.subList(fromIndex, toIndex), type);
        }
    }

    /**
     * @serial include
     */
    static class CheckedRandomAccessList<E> extends CheckedList<E>
                                            implements RandomAccess
    {
        private static final long serialVersionUID = 1638200125423088369L;

        CheckedRandomAccessList(List<E> list, Class<E> type) {
            super(list, type);
        }

        public List<E> subList(int fromIndex, int toIndex) {
            return new CheckedRandomAccessList<>(
                    list.subList(fromIndex, toIndex), type);
        }
    }

    /**
     * Returns a dynamically typesafe view of the specified map.
     * Any attempt to insert a mapping whose key or value have the wrong
     * type will result in an immediate {@link ClassCastException}.
     * Similarly, any attempt to modify the value currently associated with
     * a key will result in an immediate {@link ClassCastException},
     * whether the modification is attempted directly through the map
     * itself, or through a {@link Map.Entry} instance obtained from the
     * map's {@link Map#entrySet() entry set} view.
     *
     * <p>Assuming a map contains no incorrectly typed keys or values
     * prior to the time a dynamically typesafe view is generated, and
     * that all subsequent access to the map takes place through the view
     * (or one of its collection views), it is <i>guaranteed</i> that the
     * map cannot contain an incorrectly typed key or value.
     *
     * <p>A discussion of the use of dynamically typesafe views may be
     * found in the documentation for the {@link #checkedCollection
     * checkedCollection} method.
     *
     * <p>The returned map will be serializable if the specified map is
     * serializable.
     *
     * <p>Since {@code null} is considered to be a value of any reference
     * type, the returned map permits insertion of null keys or values
     * whenever the backing map does.
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @param m the map for which a dynamically typesafe view is to be
     *          returned
     * @param keyType the type of key that {@code m} is permitted to hold
     * @param valueType the type of value that {@code m} is permitted to hold
     * @return a dynamically typesafe view of the specified map
     * @since 1.5
     */
    public static <K, V> Map<K, V> checkedMap(Map<K, V> m,
                                              Class<K> keyType,
                                              Class<V> valueType) {
        return new CheckedMap<>(m, keyType, valueType);
    }


    /**
     * @serial include
     */
    private static class CheckedMap<K,V>
        implements Map<K,V>, Serializable
    {
        private static final long serialVersionUID = 5742860141034234728L;

        private final Map<K, V> m;
        final Class<K> keyType;
        final Class<V> valueType;

        private void typeCheck(Object key, Object value) {
            if (key != null && !keyType.isInstance(key))
                throw new ClassCastException(badKeyMsg(key));

            if (value != null && !valueType.isInstance(value))
                throw new ClassCastException(badValueMsg(value));
        }

        private BiFunction<? super K, ? super V, ? extends V> typeCheck(
                BiFunction<? super K, ? super V, ? extends V> func) {
            Objects.requireNonNull(func);
            return (k, v) -> {
                V newValue = func.apply(k, v);
                typeCheck(k, newValue);
                return newValue;
            };
        }

        private String badKeyMsg(Object key) {
            return "Attempt to insert " + key.getClass() +
                " key into map with key type " + keyType;
        }

        private String badValueMsg(Object value) {
            return "Attempt to insert " + value.getClass() +
                " value into map with value type " + valueType;
        }

        CheckedMap(Map<K, V> m, Class<K> keyType, Class<V> valueType) {
            this.m = Objects.requireNonNull(m);
            this.keyType = Objects.requireNonNull(keyType);
            this.valueType = Objects.requireNonNull(valueType);
        }

        public int size()                      { return m.size(); }
        public boolean isEmpty()               { return m.isEmpty(); }
        public boolean containsKey(Object key) { return m.containsKey(key); }
        public boolean containsValue(Object v) { return m.containsValue(v); }
        public V get(Object key)               { return m.get(key); }
        public V remove(Object key)            { return m.remove(key); }
        public void clear()                    { m.clear(); }
        public Set<K> keySet()                 { return m.keySet(); }
        public Collection<V> values()          { return m.values(); }
        public boolean equals(Object o)        { return o == this || m.equals(o); }
        public int hashCode()                  { return m.hashCode(); }
        public String toString()               { return m.toString(); }

        public V put(K key, V value) {
            typeCheck(key, value);
            return m.put(key, value);
        }

        @SuppressWarnings("unchecked")
        public void putAll(Map<? extends K, ? extends V> t) {
            // Satisfy the following goals:
            // - good diagnostics in case of type mismatch
            // - all-or-nothing semantics
            // - protection from malicious t
            // - correct behavior if t is a concurrent map
            Object[] entries = t.entrySet().toArray();
            List<Map.Entry<K,V>> checked = new ArrayList<>(entries.length);
            for (Object o : entries) {
                Map.Entry<?,?> e = (Map.Entry<?,?>) o;
                Object k = e.getKey();
                Object v = e.getValue();
                typeCheck(k, v);
                checked.add(
                        new AbstractMap.SimpleImmutableEntry<>((K)k, (V)v));
            }
            for (Map.Entry<K,V> e : checked)
                m.put(e.getKey(), e.getValue());
        }

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

        public Set<Map.Entry<K,V>> entrySet() {
            if (entrySet==null)
                entrySet = new CheckedEntrySet<>(m.entrySet(), valueType);
            return entrySet;
        }

        // Override default methods in Map
        @Override
        public void forEach(BiConsumer<? super K, ? super V> action) {
            m.forEach(action);
        }

        /**
         * We need this class in addition to CheckedSet as Map.Entry permits
         * modification of the backing Map via the setValue operation.  This
         * class is subtle: there are many possible attacks that must be
         * thwarted.
         *
         * @serial exclude
         */
        static class CheckedEntrySet<K,V> implements Set<Map.Entry<K,V>> {
            private final Set<Map.Entry<K,V>> s;
            private final Class<V> valueType;

            CheckedEntrySet(Set<Map.Entry<K, V>> s, Class<V> valueType) {
                this.s = s;
                this.valueType = valueType;
            }

            public int size()        { return s.size(); }
            public boolean isEmpty() { return s.isEmpty(); }
            public String toString() { return s.toString(); }
            public int hashCode()    { return s.hashCode(); }
            public void clear()      {        s.clear(); }

            public boolean add(Map.Entry<K, V> e) {
                throw new UnsupportedOperationException();
            }
            public boolean addAll(Collection<? extends Map.Entry<K, V>> coll) {
                throw new UnsupportedOperationException();
            }

            public Iterator<Map.Entry<K,V>> iterator() {
                final Iterator<Map.Entry<K, V>> i = s.iterator();
                final Class<V> valueType = this.valueType;

                return new Iterator<Map.Entry<K,V>>() {
                    public boolean hasNext() { return i.hasNext(); }
                    public void remove()     { i.remove(); }

                    public Map.Entry<K,V> next() {
                        return checkedEntry(i.next(), valueType);
                    }
                    // Android-note: forEachRemaining is missing checks.
                };
            }

            @SuppressWarnings("unchecked")
            public Object[] toArray() {
                Object[] source = s.toArray();

                /*
                 * Ensure that we don't get an ArrayStoreException even if
                 * s.toArray returns an array of something other than Object
                 */
                Object[] dest = (CheckedEntry.class.isInstance(
                    source.getClass().getComponentType()) ? source :
                                 new Object[source.length]);

                for (int i = 0; i < source.length; i++)
                    dest[i] = checkedEntry((Map.Entry<K,V>)source[i],
                                           valueType);
                return dest;
            }

            @SuppressWarnings("unchecked")
            public <T> T[] toArray(T[] a) {
                // We don't pass a to s.toArray, to avoid window of
                // vulnerability wherein an unscrupulous multithreaded client
                // could get his hands on raw (unwrapped) Entries from s.
                T[] arr = s.toArray(a.length==0 ? a : Arrays.copyOf(a, 0));

                for (int i=0; i<arr.length; i++)
                    arr[i] = (T) checkedEntry((Map.Entry<K,V>)arr[i],
                                              valueType);
                if (arr.length > a.length)
                    return arr;

                System.arraycopy(arr, 0, a, 0, arr.length);
                if (a.length > arr.length)
                    a[arr.length] = null;
                return a;
            }

            /**
             * This method is overridden to protect the backing set against
             * an object with a nefarious equals function that senses
             * that the equality-candidate is Map.Entry and calls its
             * setValue method.
             */
            public boolean contains(Object o) {
                if (!(o instanceof Map.Entry))
                    return false;
                Map.Entry<?,?> e = (Map.Entry<?,?>) o;
                return s.contains(
                    (e instanceof CheckedEntry) ? e : checkedEntry(e, valueType));
            }

            /**
             * The bulk collection methods are overridden to protect
             * against an unscrupulous collection whose contains(Object o)
             * method senses when o is a Map.Entry, and calls o.setValue.
             */
            public boolean containsAll(Collection<?> c) {
                for (Object o : c)
                    if (!contains(o)) // Invokes safe contains() above
                        return false;
                return true;
            }

            public boolean remove(Object o) {
                if (!(o instanceof Map.Entry))
                    return false;
                return s.remove(new AbstractMap.SimpleImmutableEntry
                                <>((Map.Entry<?,?>)o));
            }

            public boolean removeAll(Collection<?> c) {
                return batchRemove(c, false);
            }
            public boolean retainAll(Collection<?> c) {
                return batchRemove(c, true);
            }
            private boolean batchRemove(Collection<?> c, boolean complement) {
                Objects.requireNonNull(c);
                boolean modified = false;
                Iterator<Map.Entry<K,V>> it = iterator();
                while (it.hasNext()) {
                    if (c.contains(it.next()) != complement) {
                        it.remove();
                        modified = true;
                    }
                }
                return modified;
            }

            public boolean equals(Object o) {
                if (o == this)
                    return true;
                if (!(o instanceof Set))
                    return false;
                Set<?> that = (Set<?>) o;
                return that.size() == s.size()
                    && containsAll(that); // Invokes safe containsAll() above
            }

            static <K,V,T> CheckedEntry<K,V,T> checkedEntry(Map.Entry<K,V> e,
                                                            Class<T> valueType) {
                return new CheckedEntry<>(e, valueType);
            }

            /**
             * This "wrapper class" serves two purposes: it prevents
             * the client from modifying the backing Map, by short-circuiting
             * the setValue method, and it protects the backing Map against
             * an ill-behaved Map.Entry that attempts to modify another
             * Map.Entry when asked to perform an equality check.
             */
            private static class CheckedEntry<K,V,T> implements Map.Entry<K,V> {
                private final Map.Entry<K, V> e;
                private final Class<T> valueType;

                CheckedEntry(Map.Entry<K, V> e, Class<T> valueType) {
                    this.e = Objects.requireNonNull(e);
                    this.valueType = Objects.requireNonNull(valueType);
                }

                public K getKey()        { return e.getKey(); }
                public V getValue()      { return e.getValue(); }
                public int hashCode()    { return e.hashCode(); }
                public String toString() { return e.toString(); }

                public V setValue(V value) {
                    if (value != null && !valueType.isInstance(value))
                        throw new ClassCastException(badValueMsg(value));
                    return e.setValue(value);
                }

                private String badValueMsg(Object value) {
                    return "Attempt to insert " + value.getClass() +
                        " value into map with value type " + valueType;
                }

                public boolean equals(Object o) {
                    if (o == this)
                        return true;
                    if (!(o instanceof Map.Entry))
                        return false;
                    return e.equals(new AbstractMap.SimpleImmutableEntry
                                    <>((Map.Entry<?,?>)o));
                }
            }
        }
    }

    /**
     * Returns a dynamically typesafe view of the specified sorted map.
     * Any attempt to insert a mapping whose key or value have the wrong
     * type will result in an immediate {@link ClassCastException}.
     * Similarly, any attempt to modify the value currently associated with
     * a key will result in an immediate {@link ClassCastException},
     * whether the modification is attempted directly through the map
     * itself, or through a {@link Map.Entry} instance obtained from the
     * map's {@link Map#entrySet() entry set} view.
     *
     * <p>Assuming a map contains no incorrectly typed keys or values
     * prior to the time a dynamically typesafe view is generated, and
     * that all subsequent access to the map takes place through the view
     * (or one of its collection views), it is <i>guaranteed</i> that the
     * map cannot contain an incorrectly typed key or value.
     *
     * <p>A discussion of the use of dynamically typesafe views may be
     * found in the documentation for the {@link #checkedCollection
     * checkedCollection} method.
     *
     * <p>The returned map will be serializable if the specified map is
     * serializable.
     *
     * <p>Since {@code null} is considered to be a value of any reference
     * type, the returned map permits insertion of null keys or values
     * whenever the backing map does.
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @param m the map for which a dynamically typesafe view is to be
     *          returned
     * @param keyType the type of key that {@code m} is permitted to hold
     * @param valueType the type of value that {@code m} is permitted to hold
     * @return a dynamically typesafe view of the specified map
     * @since 1.5
     */
    public static <K,V> SortedMap<K,V> checkedSortedMap(SortedMap<K, V> m,
                                                        Class<K> keyType,
                                                        Class<V> valueType) {
        return new CheckedSortedMap<>(m, keyType, valueType);
    }

    /**
     * @serial include
     */
    static class CheckedSortedMap<K,V> extends CheckedMap<K,V>
        implements SortedMap<K,V>, Serializable
    {
        private static final long serialVersionUID = 1599671320688067438L;

        private final SortedMap<K, V> sm;

        CheckedSortedMap(SortedMap<K, V> m,
                         Class<K> keyType, Class<V> valueType) {
            super(m, keyType, valueType);
            sm = m;
        }

        public Comparator<? super K> comparator() { return sm.comparator(); }
        public K firstKey()                       { return sm.firstKey(); }
        public K lastKey()                        { return sm.lastKey(); }

        public SortedMap<K,V> subMap(K fromKey, K toKey) {
            return checkedSortedMap(sm.subMap(fromKey, toKey),
                                    keyType, valueType);
        }
        public SortedMap<K,V> headMap(K toKey) {
            return checkedSortedMap(sm.headMap(toKey), keyType, valueType);
        }
        public SortedMap<K,V> tailMap(K fromKey) {
            return checkedSortedMap(sm.tailMap(fromKey), keyType, valueType);
        }
    }

    // Empty collections

    /**
     * Returns an iterator that has no elements.  More precisely,
     *
     * <ul>
     * <li>{@link Iterator#hasNext hasNext} always returns {@code
     * false}.</li>
     * <li>{@link Iterator#next next} always throws {@link
     * NoSuchElementException}.</li>
     * <li>{@link Iterator#remove remove} always throws {@link
     * IllegalStateException}.</li>
     * </ul>
     *
     * <p>Implementations of this method are permitted, but not
     * required, to return the same object from multiple invocations.
     *
     * @param <T> type of elements, if there were any, in the iterator
     * @return an empty iterator
     * @since 1.7
     */
    @SuppressWarnings("unchecked")
    public static <T> Iterator<T> emptyIterator() {
        return (Iterator<T>) EmptyIterator.EMPTY_ITERATOR;
    }

    private static class EmptyIterator<E> implements Iterator<E> {
        static final EmptyIterator<Object> EMPTY_ITERATOR
            = new EmptyIterator<>();

        public boolean hasNext() { return false; }
        public E next() { throw new NoSuchElementException(); }
        public void remove() { throw new IllegalStateException(); }
        @Override
        public void forEachRemaining(Consumer<? super E> action) {
            Objects.requireNonNull(action);
        }
    }

    /**
     * Returns a list iterator that has no elements.  More precisely,
     *
     * <ul>
     * <li>{@link Iterator#hasNext hasNext} and {@link
     * ListIterator#hasPrevious hasPrevious} always return {@code
     * false}.</li>
     * <li>{@link Iterator#next next} and {@link ListIterator#previous
     * previous} always throw {@link NoSuchElementException}.</li>
     * <li>{@link Iterator#remove remove} and {@link ListIterator#set
     * set} always throw {@link IllegalStateException}.</li>
     * <li>{@link ListIterator#add add} always throws {@link
     * UnsupportedOperationException}.</li>
     * <li>{@link ListIterator#nextIndex nextIndex} always returns
     * {@code 0}.</li>
     * <li>{@link ListIterator#previousIndex previousIndex} always
     * returns {@code -1}.</li>
     * </ul>
     *
     * <p>Implementations of this method are permitted, but not
     * required, to return the same object from multiple invocations.
     *
     * @param <T> type of elements, if there were any, in the iterator
     * @return an empty list iterator
     * @since 1.7
     */
    @SuppressWarnings("unchecked")
    public static <T> ListIterator<T> emptyListIterator() {
        return (ListIterator<T>) EmptyListIterator.EMPTY_ITERATOR;
    }

    private static class EmptyListIterator<E>
        extends EmptyIterator<E>
        implements ListIterator<E>
    {
        static final EmptyListIterator<Object> EMPTY_ITERATOR
            = new EmptyListIterator<>();

        public boolean hasPrevious() { return false; }
        public E previous() { throw new NoSuchElementException(); }
        public int nextIndex()     { return 0; }
        public int previousIndex() { return -1; }
        public void set(E e) { throw new IllegalStateException(); }
        public void add(E e) { throw new UnsupportedOperationException(); }
    }

    /**
     * Returns an enumeration that has no elements.  More precisely,
     *
     * <ul>
     * <li>{@link Enumeration#hasMoreElements hasMoreElements} always
     * returns {@code false}.</li>
     * <li> {@link Enumeration#nextElement nextElement} always throws
     * {@link NoSuchElementException}.</li>
     * </ul>
     *
     * <p>Implementations of this method are permitted, but not
     * required, to return the same object from multiple invocations.
     *
     * @param  <T> the class of the objects in the enumeration
     * @return an empty enumeration
     * @since 1.7
     */
    @SuppressWarnings("unchecked")
    public static <T> Enumeration<T> emptyEnumeration() {
        return (Enumeration<T>) EmptyEnumeration.EMPTY_ENUMERATION;
    }

    private static class EmptyEnumeration<E> implements Enumeration<E> {
        static final EmptyEnumeration<Object> EMPTY_ENUMERATION
            = new EmptyEnumeration<>();

        public boolean hasMoreElements() { return false; }
        public E nextElement() { throw new NoSuchElementException(); }
    }

    /**
     * The empty set (immutable).  This set is serializable.
     *
     * @see #emptySet()
     */
    @SuppressWarnings("rawtypes")
    public static final Set EMPTY_SET = new EmptySet<>();

    /**
     * Returns an empty set (immutable).  This set is serializable.
     * Unlike the like-named field, this method is parameterized.
     *
     * <p>This example illustrates the type-safe way to obtain an empty set:
     * <pre>
     *     Set&lt;String&gt; s = Collections.emptySet();
     * </pre>
     * @implNote Implementations of this method need not create a separate
     * {@code Set} object for each call.  Using this method is likely to have
     * comparable cost to using the like-named field.  (Unlike this method, the
     * field does not provide type safety.)
     *
     * @param  <T> the class of the objects in the set
     * @return the empty set
     *
     * @see #EMPTY_SET
     * @since 1.5
     */
    @SuppressWarnings("unchecked")
    public static final <T> Set<T> emptySet() {
        return (Set<T>) EMPTY_SET;
    }

    /**
     * @serial include
     */
    private static class EmptySet<E>
        extends AbstractSet<E>
        implements Serializable
    {
        private static final long serialVersionUID = 1582296315990362920L;

        public Iterator<E> iterator() { return emptyIterator(); }

        public int size() {return 0;}
        public boolean isEmpty() {return true;}

        public boolean contains(Object obj) {return false;}
        public boolean containsAll(Collection<?> c) { return c.isEmpty(); }

        public Object[] toArray() { return new Object[0]; }

        public <T> T[] toArray(T[] a) {
            if (a.length > 0)
                a[0] = null;
            return a;
        }

        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> action) {
            Objects.requireNonNull(action);
        }
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            Objects.requireNonNull(filter);
            return false;
        }
        @Override
        public Spliterator<E> spliterator() { return Spliterators.emptySpliterator(); }

        // Preserves singleton property
        private Object readResolve() {
            return EMPTY_SET;
        }

    }

    /**
     * The empty list (immutable).  This list is serializable.
     *
     * @see #emptyList()
     */
    @SuppressWarnings("rawtypes")
    public static final List EMPTY_LIST = new EmptyList<>();

    /**
     * Returns an empty list (immutable).  This list is serializable.
     *
     * <p>This example illustrates the type-safe way to obtain an empty list:
     * <pre>
     *     List&lt;String&gt; s = Collections.emptyList();
     * </pre>
     * Implementation note:  Implementations of this method need not
     * create a separate <tt>List</tt> object for each call.   Using this
     * method is likely to have comparable cost to using the like-named
     * field.  (Unlike this method, the field does not provide type safety.)
     *
     * @param <T> type of elements, if there were any, in the list
     * @return an empty immutable list
     *
     * @see #EMPTY_LIST
     * @since 1.5
     */
    @SuppressWarnings("unchecked")
    public static final <T> List<T> emptyList() {
        return (List<T>) EMPTY_LIST;
    }

    /**
     * @serial include
     */
    private static class EmptyList<E>
        extends AbstractList<E>
        implements RandomAccess, Serializable {
        private static final long serialVersionUID = 8842843931221139166L;

        public Iterator<E> iterator() {
            return emptyIterator();
        }
        public ListIterator<E> listIterator() {
            return emptyListIterator();
        }

        public int size() {return 0;}
        public boolean isEmpty() {return true;}

        public boolean contains(Object obj) {return false;}
        public boolean containsAll(Collection<?> c) { return c.isEmpty(); }

        public Object[] toArray() { return new Object[0]; }

        public <T> T[] toArray(T[] a) {
            if (a.length > 0)
                a[0] = null;
            return a;
        }

        public E get(int index) {
            throw new IndexOutOfBoundsException("Index: "+index);
        }

        public boolean equals(Object o) {
            return (o instanceof List) && ((List<?>)o).isEmpty();
        }

        public int hashCode() { return 1; }

        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            Objects.requireNonNull(filter);
            return false;
        }

        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> action) {
            Objects.requireNonNull(action);
        }

        @Override
        public Spliterator<E> spliterator() { return Spliterators.emptySpliterator(); }

        // Preserves singleton property
        private Object readResolve() {
            return EMPTY_LIST;
        }
    }

    /**
     * The empty map (immutable).  This map is serializable.
     *
     * @see #emptyMap()
     * @since 1.3
     */
    @SuppressWarnings("rawtypes")
    public static final Map EMPTY_MAP = new EmptyMap<>();

    /**
     * Returns an empty map (immutable).  This map is serializable.
     *
     * <p>This example illustrates the type-safe way to obtain an empty map:
     * <pre>
     *     Map&lt;String, Date&gt; s = Collections.emptyMap();
     * </pre>
     * @implNote Implementations of this method need not create a separate
     * {@code Map} object for each call.  Using this method is likely to have
     * comparable cost to using the like-named field.  (Unlike this method, the
     * field does not provide type safety.)
     *
     * @param <K> the class of the map keys
     * @param <V> the class of the map values
     * @return an empty map
     * @see #EMPTY_MAP
     * @since 1.5
     */
    @SuppressWarnings("unchecked")
    public static final <K,V> Map<K,V> emptyMap() {
        return (Map<K,V>) EMPTY_MAP;
    }

    /**
     * @serial include
     */
    private static class EmptyMap<K,V>
        extends AbstractMap<K,V>
        implements Serializable
    {
        private static final long serialVersionUID = 6428348081105594320L;

        public int size()                          {return 0;}
        public boolean isEmpty()                   {return true;}
        public boolean containsKey(Object key)     {return false;}
        public boolean containsValue(Object value) {return false;}
        public V get(Object key)                   {return null;}
        public Set<K> keySet()                     {return emptySet();}
        public Collection<V> values()              {return emptySet();}
        public Set<Map.Entry<K,V>> entrySet()      {return emptySet();}

        public boolean equals(Object o) {
            return (o instanceof Map) && ((Map<?,?>)o).isEmpty();
        }

        public int hashCode()                      {return 0;}

        // Override default methods in Map
        @Override
        public void forEach(BiConsumer<? super K, ? super V> action) {
            Objects.requireNonNull(action);
        }

        // Preserves singleton property
        private Object readResolve() {
            return EMPTY_MAP;
        }
    }

    // Singleton collections

    /**
     * Returns an immutable set containing only the specified object.
     * The returned set is serializable.
     *
     * @param o the sole object to be stored in the returned set.
     * @return an immutable set containing only the specified object.
     */
    public static <E> Set<E> singleton(E o) {
        return new SingletonSet<>(o);
    }

    static <E> Iterator<E> singletonIterator(final E e) {
        return new Iterator<E>() {
            private boolean hasNext = true;
            public boolean hasNext() {
                return hasNext;
            }
            public E next() {
                if (hasNext) {
                    hasNext = false;
                    return e;
                }
                throw new NoSuchElementException();
            }
            public void remove() {
                throw new UnsupportedOperationException();
            }
            @Override
            public void forEachRemaining(Consumer<? super E> action) {
                Objects.requireNonNull(action);
                if (hasNext) {
                    action.accept(e);
                    hasNext = false;
                }
            }
        };
    }

    /**
     * @serial include
     */
    private static class SingletonSet<E>
        extends AbstractSet<E>
        implements Serializable
    {
        private static final long serialVersionUID = 3193687207550431679L;

        private final E element;

        SingletonSet(E e) {element = e;}

        public Iterator<E> iterator() {
            return singletonIterator(element);
        }

        public int size() {return 1;}

        public boolean contains(Object o) {return eq(o, element);}

        // Override default methods for Collection
        @Override
        public void forEach(Consumer<? super E> action) {
            action.accept(element);
        }
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Returns an immutable list containing only the specified object.
     * The returned list is serializable.
     *
     * @param o the sole object to be stored in the returned list.
     * @return an immutable list containing only the specified object.
     * @since 1.3
     */
    public static <E> List<E> singletonList(E o) {
        return new SingletonList<>(o);
    }

    /**
     * @serial include
     */
    private static class SingletonList<E>
        extends AbstractList<E>
        implements RandomAccess, Serializable {

        private static final long serialVersionUID = 3093736618740652951L;

        private final E element;

        SingletonList(E obj)                {element = obj;}

        public Iterator<E> iterator() {
            return singletonIterator(element);
        }

        public int size()                   {return 1;}

        public boolean contains(Object obj) {return eq(obj, element);}

        public E get(int index) {
            if (index != 0)
              throw new IndexOutOfBoundsException("Index: "+index+", Size: 1");
            return element;
        }

        // Override default methods for Collection
        @Override
        public void forEach(Consumer<? super E> action) {
            action.accept(element);
        }
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            throw new UnsupportedOperationException();
        }
    }

    /**
     * Returns an immutable map, mapping only the specified key to the
     * specified value.  The returned map is serializable.
     *
     * @param key the sole key to be stored in the returned map.
     * @param value the value to which the returned map maps <tt>key</tt>.
     * @return an immutable map containing only the specified key-value
     *         mapping.
     * @since 1.3
     */
    public static <K,V> Map<K,V> singletonMap(K key, V value) {
        return new SingletonMap<>(key, value);
    }

    /**
     * @serial include
     */
    private static class SingletonMap<K,V>
          extends AbstractMap<K,V>
          implements Serializable {
        private static final long serialVersionUID = -6979724477215052911L;

        private final K k;
        private final V v;

        SingletonMap(K key, V value) {
            k = key;
            v = value;
        }

        public int size()                          {return 1;}

        public boolean isEmpty()                   {return false;}

        public boolean containsKey(Object key)     {return eq(key, k);}

        public boolean containsValue(Object value) {return eq(value, v);}

        public V get(Object key)                   {return (eq(key, k) ? v : null);}

        private transient Set<K> keySet = null;
        private transient Set<Map.Entry<K,V>> entrySet = null;
        private transient Collection<V> values = null;

        public Set<K> keySet() {
            if (keySet==null)
                keySet = singleton(k);
            return keySet;
        }

        public Set<Map.Entry<K,V>> entrySet() {
            if (entrySet==null)
                entrySet = Collections.<Map.Entry<K,V>>singleton(
                    new SimpleImmutableEntry<>(k, v));
            return entrySet;
        }

        public Collection<V> values() {
            if (values==null)
                values = singleton(v);
            return values;
        }

        // Override default methods in Map
        @Override
        public void forEach(BiConsumer<? super K, ? super V> action) {
            action.accept(k, v);
        }

    }

    // Miscellaneous

    /**
     * Returns an immutable list consisting of <tt>n</tt> copies of the
     * specified object.  The newly allocated data object is tiny (it contains
     * a single reference to the data object).  This method is useful in
     * combination with the <tt>List.addAll</tt> method to grow lists.
     * The returned list is serializable.
     *
     * @param  n the number of elements in the returned list.
     * @param  o the element to appear repeatedly in the returned list.
     * @return an immutable list consisting of <tt>n</tt> copies of the
     *         specified object.
     * @throws IllegalArgumentException if {@code n < 0}
     * @see    List#addAll(Collection)
     * @see    List#addAll(int, Collection)
     */
    public static <T> List<T> nCopies(int n, T o) {
        if (n < 0)
            throw new IllegalArgumentException("List length = " + n);
        return new CopiesList<>(n, o);
    }

    /**
     * @serial include
     */
    private static class CopiesList<E>
        extends AbstractList<E>
        implements RandomAccess, Serializable
    {
        private static final long serialVersionUID = 2739099268398711800L;

        final int n;
        final E element;

        CopiesList(int n, E e) {
            assert n >= 0;
            this.n = n;
            element = e;
        }

        public int size() {
            return n;
        }

        public boolean contains(Object obj) {
            return n != 0 && eq(obj, element);
        }

        public int indexOf(Object o) {
            return contains(o) ? 0 : -1;
        }

        public int lastIndexOf(Object o) {
            return contains(o) ? n - 1 : -1;
        }

        public E get(int index) {
            if (index < 0 || index >= n)
                throw new IndexOutOfBoundsException("Index: "+index+
                                                    ", Size: "+n);
            return element;
        }

        public Object[] toArray() {
            final Object[] a = new Object[n];
            if (element != null)
                Arrays.fill(a, 0, n, element);
            return a;
        }

        public <T> T[] toArray(T[] a) {
            final int n = this.n;
            if (a.length < n) {
                a = (T[])java.lang.reflect.Array
                    .newInstance(a.getClass().getComponentType(), n);
                if (element != null)
                    Arrays.fill(a, 0, n, element);
            } else {
                Arrays.fill(a, 0, n, element);
                if (a.length > n)
                    a[n] = null;
            }
            return a;
        }

        public List<E> subList(int fromIndex, int toIndex) {
            if (fromIndex < 0)
                throw new IndexOutOfBoundsException("fromIndex = " + fromIndex);
            if (toIndex > n)
                throw new IndexOutOfBoundsException("toIndex = " + toIndex);
            if (fromIndex > toIndex)
                throw new IllegalArgumentException("fromIndex(" + fromIndex +
                                                   ") > toIndex(" + toIndex + ")");
            return new CopiesList<>(toIndex - fromIndex, element);
        }
    }

    /**
     * Returns a comparator that imposes the reverse of the <em>natural
     * ordering</em> on a collection of objects that implement the
     * {@code Comparable} interface.  (The natural ordering is the ordering
     * imposed by the objects' own {@code compareTo} method.)  This enables a
     * simple idiom for sorting (or maintaining) collections (or arrays) of
     * objects that implement the {@code Comparable} interface in
     * reverse-natural-order.  For example, suppose {@code a} is an array of
     * strings. Then: <pre>
     *          Arrays.sort(a, Collections.reverseOrder());
     * </pre> sorts the array in reverse-lexicographic (alphabetical) order.<p>
     *
     * The returned comparator is serializable.
     *
     * @return A comparator that imposes the reverse of the <i>natural
     *         ordering</i> on a collection of objects that implement
     *         the <tt>Comparable</tt> interface.
     * @see Comparable
     */
    public static <T> Comparator<T> reverseOrder() {
        return (Comparator<T>) ReverseComparator.REVERSE_ORDER;
    }

    /**
     * @serial include
     */
    private static class ReverseComparator
        implements Comparator<Comparable<Object>>, Serializable {

        private static final long serialVersionUID = 7207038068494060240L;

        static final ReverseComparator REVERSE_ORDER
            = new ReverseComparator();

        public int compare(Comparable<Object> c1, Comparable<Object> c2) {
            return c2.compareTo(c1);
        }

        private Object readResolve() { return reverseOrder(); }

        @Override
        public Comparator<Comparable<Object>> reversed() {
            return Comparator.naturalOrder();
        }
    }

    /**
     * Returns a comparator that imposes the reverse ordering of the specified
     * comparator.  If the specified comparator is {@code null}, this method is
     * equivalent to {@link #reverseOrder()} (in other words, it returns a
     * comparator that imposes the reverse of the <em>natural ordering</em> on
     * a collection of objects that implement the Comparable interface).
     *
     * <p>The returned comparator is serializable (assuming the specified
     * comparator is also serializable or {@code null}).
     *
     * @param cmp a comparator who's ordering is to be reversed by the returned
     * comparator or {@code null}
     * @return A comparator that imposes the reverse ordering of the
     *         specified comparator.
     * @since 1.5
     */
    public static <T> Comparator<T> reverseOrder(Comparator<T> cmp) {
        if (cmp == null)
            return reverseOrder();

        if (cmp instanceof ReverseComparator2)
            return ((ReverseComparator2<T>)cmp).cmp;

        return new ReverseComparator2<>(cmp);
    }

    /**
     * @serial include
     */
    private static class ReverseComparator2<T> implements Comparator<T>,
        Serializable
    {
        private static final long serialVersionUID = 4374092139857L;

        /**
         * The comparator specified in the static factory.  This will never
         * be null, as the static factory returns a ReverseComparator
         * instance if its argument is null.
         *
         * @serial
         */
        final Comparator<T> cmp;

        ReverseComparator2(Comparator<T> cmp) {
            assert cmp != null;
            this.cmp = cmp;
        }

        public int compare(T t1, T t2) {
            return cmp.compare(t2, t1);
        }

        public boolean equals(Object o) {
            return (o == this) ||
                (o instanceof ReverseComparator2 &&
                 cmp.equals(((ReverseComparator2)o).cmp));
        }

        public int hashCode() {
            return cmp.hashCode() ^ Integer.MIN_VALUE;
        }

        @Override
        public Comparator<T> reversed() {
            return cmp;
        }
    }

    /**
     * Returns an enumeration over the specified collection.  This provides
     * interoperability with legacy APIs that require an enumeration
     * as input.
     *
     * @param c the collection for which an enumeration is to be returned.
     * @return an enumeration over the specified collection.
     * @see Enumeration
     */
    public static <T> Enumeration<T> enumeration(final Collection<T> c) {
        return new Enumeration<T>() {
            private final Iterator<T> i = c.iterator();

            public boolean hasMoreElements() {
                return i.hasNext();
            }

            public T nextElement() {
                return i.next();
            }
        };
    }

    /**
     * Returns an array list containing the elements returned by the
     * specified enumeration in the order they are returned by the
     * enumeration.  This method provides interoperability between
     * legacy APIs that return enumerations and new APIs that require
     * collections.
     *
     * @param e enumeration providing elements for the returned
     *          array list
     * @return an array list containing the elements returned
     *         by the specified enumeration.
     * @since 1.4
     * @see Enumeration
     * @see ArrayList
     */
    public static <T> ArrayList<T> list(Enumeration<T> e) {
        ArrayList<T> l = new ArrayList<>();
        while (e.hasMoreElements())
            l.add(e.nextElement());
        return l;
    }

    /**
     * Returns true if the specified arguments are equal, or both null.
     */
    static boolean eq(Object o1, Object o2) {
        return o1==null ? o2==null : o1.equals(o2);
    }

    /**
     * Returns the number of elements in the specified collection equal to the
     * specified object.  More formally, returns the number of elements
     * <tt>e</tt> in the collection such that
     * <tt>(o == null ? e == null : o.equals(e))</tt>.
     *
     * @param c the collection in which to determine the frequency
     *     of <tt>o</tt>
     * @param o the object whose frequency is to be determined
     * @throws NullPointerException if <tt>c</tt> is null
     * @since 1.5
     */
    public static int frequency(Collection<?> c, Object o) {
        int result = 0;
        if (o == null) {
            for (Object e : c)
                if (e == null)
                    result++;
        } else {
            for (Object e : c)
                if (o.equals(e))
                    result++;
        }
        return result;
    }

    /**
     * Returns {@code true} if the two specified collections have no
     * elements in common.
     *
     * <p>Care must be exercised if this method is used on collections that
     * do not comply with the general contract for {@code Collection}.
     * Implementations may elect to iterate over either collection and test
     * for containment in the other collection (or to perform any equivalent
     * computation).  If either collection uses a nonstandard equality test
     * (as does a {@link SortedSet} whose ordering is not <em>compatible with
     * equals</em>, or the key set of an {@link IdentityHashMap}), both
     * collections must use the same nonstandard equality test, or the
     * result of this method is undefined.
     *
     * <p>Care must also be exercised when using collections that have
     * restrictions on the elements that they may contain. Collection
     * implementations are allowed to throw exceptions for any operation
     * involving elements they deem ineligible. For absolute safety the
     * specified collections should contain only elements which are
     * eligible elements for both collections.
     *
     * <p>Note that it is permissible to pass the same collection in both
     * parameters, in which case the method will return {@code true} if and
     * only if the collection is empty.
     *
     * @param c1 a collection
     * @param c2 a collection
     * @return {@code true} if the two specified collections have no
     * elements in common.
     * @throws NullPointerException if either collection is {@code null}.
     * @throws NullPointerException if one collection contains a {@code null}
     * element and {@code null} is not an eligible element for the other collection.
     * (<a href="Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if one collection contains an element that is
     * of a type which is ineligible for the other collection.
     * (<a href="Collection.html#optional-restrictions">optional</a>)
     * @since 1.5
     */
    public static boolean disjoint(Collection<?> c1, Collection<?> c2) {
        // The collection to be used for contains(). Preference is given to
        // the collection who's contains() has lower O() complexity.
        Collection<?> contains = c2;
        // The collection to be iterated. If the collections' contains() impl
        // are of different O() complexity, the collection with slower
        // contains() will be used for iteration. For collections who's
        // contains() are of the same complexity then best performance is
        // achieved by iterating the smaller collection.
        Collection<?> iterate = c1;

        // Performance optimization cases. The heuristics:
        //   1. Generally iterate over c1.
        //   2. If c1 is a Set then iterate over c2.
        //   3. If either collection is empty then result is always true.
        //   4. Iterate over the smaller Collection.
        if (c1 instanceof Set) {
            // Use c1 for contains as a Set's contains() is expected to perform
            // better than O(N/2)
            iterate = c2;
            contains = c1;
        } else if (!(c2 instanceof Set)) {
            // Both are mere Collections. Iterate over smaller collection.
            // Example: If c1 contains 3 elements and c2 contains 50 elements and
            // assuming contains() requires ceiling(N/2) comparisons then
            // checking for all c1 elements in c2 would require 75 comparisons
            // (3 * ceiling(50/2)) vs. checking all c2 elements in c1 requiring
            // 100 comparisons (50 * ceiling(3/2)).
            int c1size = c1.size();
            int c2size = c2.size();
            if (c1size == 0 || c2size == 0) {
                // At least one collection is empty. Nothing will match.
                return true;
            }

            if (c1size > c2size) {
                iterate = c2;
                contains = c1;
            }
        }

        for (Object e : iterate) {
            if (contains.contains(e)) {
               // Found a common element. Collections are not disjoint.
                return false;
            }
        }

        // No common elements were found.
        return true;
    }

    /**
     * Adds all of the specified elements to the specified collection.
     * Elements to be added may be specified individually or as an array.
     * The behavior of this convenience method is identical to that of
     * <tt>c.addAll(Arrays.asList(elements))</tt>, but this method is likely
     * to run significantly faster under most implementations.
     *
     * <p>When elements are specified individually, this method provides a
     * convenient way to add a few elements to an existing collection:
     * <pre>
     *     Collections.addAll(flavors, "Peaches 'n Plutonium", "Rocky Racoon");
     * </pre>
     *
     * @param c the collection into which <tt>elements</tt> are to be inserted
     * @param elements the elements to insert into <tt>c</tt>
     * @return <tt>true</tt> if the collection changed as a result of the call
     * @throws UnsupportedOperationException if <tt>c</tt> does not support
     *         the <tt>add</tt> operation
     * @throws NullPointerException if <tt>elements</tt> contains one or more
     *         null values and <tt>c</tt> does not permit null elements, or
     *         if <tt>c</tt> or <tt>elements</tt> are <tt>null</tt>
     * @throws IllegalArgumentException if some property of a value in
     *         <tt>elements</tt> prevents it from being added to <tt>c</tt>
     * @see Collection#addAll(Collection)
     * @since 1.5
     */
    @SafeVarargs
    public static <T> boolean addAll(Collection<? super T> c, T... elements) {
        boolean result = false;
        for (T element : elements)
            result |= c.add(element);
        return result;
    }

    /**
     * Returns a set backed by the specified map.  The resulting set displays
     * the same ordering, concurrency, and performance characteristics as the
     * backing map.  In essence, this factory method provides a {@link Set}
     * implementation corresponding to any {@link Map} implementation.  There
     * is no need to use this method on a {@link Map} implementation that
     * already has a corresponding {@link Set} implementation (such as {@link
     * HashMap} or {@link TreeMap}).
     *
     * <p>Each method invocation on the set returned by this method results in
     * exactly one method invocation on the backing map or its <tt>keySet</tt>
     * view, with one exception.  The <tt>addAll</tt> method is implemented
     * as a sequence of <tt>put</tt> invocations on the backing map.
     *
     * <p>The specified map must be empty at the time this method is invoked,
     * and should not be accessed directly after this method returns.  These
     * conditions are ensured if the map is created empty, passed directly
     * to this method, and no reference to the map is retained, as illustrated
     * in the following code fragment:
     * <pre>
     *    Set&lt;Object&gt; weakHashSet = Collections.newSetFromMap(
     *        new WeakHashMap&lt;Object, Boolean&gt;());
     * </pre>
     *
     * @param map the backing map
     * @return the set backed by the map
     * @throws IllegalArgumentException if <tt>map</tt> is not empty
     * @since 1.6
     */
    public static <E> Set<E> newSetFromMap(Map<E, Boolean> map) {
        return new SetFromMap<>(map);
    }

    /**
     * @serial include
     */
    private static class SetFromMap<E> extends AbstractSet<E>
        implements Set<E>, Serializable
    {
        private final Map<E, Boolean> m;  // The backing map
        private transient Set<E> s;       // Its keySet

        SetFromMap(Map<E, Boolean> map) {
            if (!map.isEmpty())
                throw new IllegalArgumentException("Map is non-empty");
            m = map;
            s = map.keySet();
        }

        public void clear()               {        m.clear(); }
        public int size()                 { return m.size(); }
        public boolean isEmpty()          { return m.isEmpty(); }
        public boolean contains(Object o) { return m.containsKey(o); }
        public boolean remove(Object o)   { return m.remove(o) != null; }
        public boolean add(E e) { return m.put(e, Boolean.TRUE) == null; }
        public Iterator<E> iterator()     { return s.iterator(); }
        public Object[] toArray()         { return s.toArray(); }
        public <T> T[] toArray(T[] a)     { return s.toArray(a); }
        public String toString()          { return s.toString(); }
        public int hashCode()             { return s.hashCode(); }
        public boolean equals(Object o)   { return o == this || s.equals(o); }
        public boolean containsAll(Collection<?> c) {return s.containsAll(c);}
        public boolean removeAll(Collection<?> c)   {return s.removeAll(c);}
        public boolean retainAll(Collection<?> c)   {return s.retainAll(c);}
        // addAll is the only inherited implementation

        private static final long serialVersionUID = 2454657854757543876L;

        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> action) {
            s.forEach(action);
        }
        @Override
        public boolean removeIf(Predicate<? super E> filter) {
            return s.removeIf(filter);
        }

        private void readObject(java.io.ObjectInputStream stream)
            throws IOException, ClassNotFoundException
        {
            stream.defaultReadObject();
            s = m.keySet();
        }
    }

    /**
     * Returns a view of a {@link Deque} as a Last-in-first-out (Lifo)
     * {@link Queue}. Method <tt>add</tt> is mapped to <tt>push</tt>,
     * <tt>remove</tt> is mapped to <tt>pop</tt> and so on. This
     * view can be useful when you would like to use a method
     * requiring a <tt>Queue</tt> but you need Lifo ordering.
     *
     * <p>Each method invocation on the queue returned by this method
     * results in exactly one method invocation on the backing deque, with
     * one exception.  The {@link Queue#addAll addAll} method is
     * implemented as a sequence of {@link Deque#addFirst addFirst}
     * invocations on the backing deque.
     *
     * @param deque the deque
     * @return the queue
     * @since  1.6
     */
    public static <T> Queue<T> asLifoQueue(Deque<T> deque) {
        return new AsLIFOQueue<>(deque);
    }

    /**
     * @serial include
     */
    static class AsLIFOQueue<E> extends AbstractQueue<E>
        implements Queue<E>, Serializable {
        private static final long serialVersionUID = 1802017725587941708L;
        private final Deque<E> q;
        AsLIFOQueue(Deque<E> q)           { this.q = q; }
        public boolean add(E e)           { q.addFirst(e); return true; }
        public boolean offer(E e)         { return q.offerFirst(e); }
        public E poll()                   { return q.pollFirst(); }
        public E remove()                 { return q.removeFirst(); }
        public E peek()                   { return q.peekFirst(); }
        public E element()                { return q.getFirst(); }
        public void clear()               {        q.clear(); }
        public int size()                 { return q.size(); }
        public boolean isEmpty()          { return q.isEmpty(); }
        public boolean contains(Object o) { return q.contains(o); }
        public boolean remove(Object o)   { return q.remove(o); }
        public Iterator<E> iterator()     { return q.iterator(); }
        public Object[] toArray()         { return q.toArray(); }
        public <T> T[] toArray(T[] a)     { return q.toArray(a); }
        public String toString()          { return q.toString(); }
        public boolean containsAll(Collection<?> c) {return q.containsAll(c);}
        public boolean removeAll(Collection<?> c)   {return q.removeAll(c);}
        public boolean retainAll(Collection<?> c)   {return q.retainAll(c);}
        // We use inherited addAll; forwarding addAll would be wrong

        // Override default methods in Collection
        @Override
        public void forEach(Consumer<? super E> action) {q.forEach(action);}
        public boolean removeIf(Predicate<? super E> filter) {
            return q.removeIf(filter);
        }
    }
}