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    * 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
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   */
  
  package java.util;
  import java.io.Serializable;
  import java.io.ObjectOutputStream;
  import java.io.IOException;
  import java.lang.reflect.Array;
  
  /**
   * 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 techiques 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  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
      */
     public static <T extends Comparable<? super T>> void sort(List<T> list) {
         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 techiques 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  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
      */
     public static <T> void sort(List<T> list, Comparator<? super T> c) {
         Object[] a = list.toArray();
         Arrays.sort(a, (Comparator)c);
         ListIterator i = list.listIterator();
         for (int j=0; j<a.length; j++) {
             i.next();
             i.set(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  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  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.
      */
     public static <T> int binarySearch(List<? extends T> list, T key, Comparator<? super T> c) {
         if (c==null)
             return binarySearch((List) 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
     }
 
     private interface SelfComparable extends Comparable<SelfComparable> {}
 
 
     /**
      * 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.
      */
     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 {
             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();
         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.
      */
     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
             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
      */
     public static void swap(List<?> list, int i, int j) {
         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  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  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  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  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
      */
     public static <T> T min(Collection<? extends T> coll, Comparator<? super T> comp) {
         if (comp==null)
             return (T)min((Collection<SelfComparable>) (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  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  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
      */
     public static <T> T max(Collection<? extends T> coll, Comparator<? super T> comp) {
         if (comp==null)
             return (T)max((Collection<SelfComparable>) (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 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 <tt>source.subList(i, i+target.size()).equals(target)</tt>,
      * or -1 if there is no such index.  (Returns -1 if
      * <tt>target.size() > source.size()</tt>.)
      *
      * <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 <tt>source.subList(i, i+target.size()).equals(target)</tt>,
      * or -1 if there is no such index.  (Returns -1 if
      * <tt>target.size() > source.size()</tt>.)
      *
      * <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  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();
                 }
             };
         }
 
         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();
         }
     }
 
     /**
      * 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  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 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  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();
                 }
             };
         }
 
         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  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();}
 
         /**
          * 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;
 
             UnmodifiableEntrySet(Set<? extends Map.Entry<? extends K, ? extends V>> s) {
                 super((Set)s);
             }
             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();
                     }
                 };
             }
 
             public Object[] toArray() {
                 Object[] a = c.toArray();
                 for (int i=0; i<a.length; i++)
                     a[i] = new UnmodifiableEntry<>((Map.Entry<K,V>)a[i]);
                 return a;
             }
 
             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<K,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 = 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 (!(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 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
 
     /**
      * 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 iterating over it:
      * <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 <tt>hashCode</tt>
      * and <tt>equals</tt> operations through to the backing collection, but
      * relies on <tt>Object</tt>'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  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) {
             if (c==null)
                 throw new NullPointerException();
             this.c = c;
             mutex = this;
         }
         SynchronizedCollection(Collection<E> c, Object mutex) {
             this.c = c;
             this.mutex = 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();}
         }
         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  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) {
             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  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  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) {
             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  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) {
             if (m==null)
                 throw new NullPointerException();
             this.m = 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) {
             synchronized (mutex) {return m.equals(o);}
         }
         public int hashCode() {
             synchronized (mutex) {return m.hashCode();}
         }
         public String toString() {
             synchronized (mutex) {return m.toString();}
         }
         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  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<String>();
      * }</pre>
      * may be replaced temporarily by this one:
      *  <pre> {@code
      *     Collection<String> c = Collections.checkedCollection(
      *         new HashSet<String>(), 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 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() {
             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(); }};
         }
 
         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));
         }
     }
 
     /**
      * 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 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 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 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);
                 }
             };
         }
 
         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 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 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) {
             if (m == null || keyType == null || valueType == null)
                 throw new NullPointerException();
             this.m = m;
             this.keyType = keyType;
             this.valueType = 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;
         }
 
         /**
          * 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);
                     }
                 };
             }
 
             @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) {
                 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 = e;
                     this.valueType = 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 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 compact>
      *
      * <li>{@link Iterator#hasNext hasNext} always returns {@code
      * false}.
      *
      * <li>{@link Iterator#next next} always throws {@link
      * NoSuchElementException}.
      *
      * <li>{@link Iterator#remove remove} always throws {@link
      * IllegalStateException}.
      *
      * </ul>
      *
      * <p>Implementations of this method are permitted, but not
      * required, to return the same object from multiple invocations.
      *
      * @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(); }
     }
 
     /**
      * Returns a list iterator that has no elements.  More precisely,
      *
      * <ul compact>
      *
      * <li>{@link Iterator#hasNext hasNext} and {@link
      * ListIterator#hasPrevious hasPrevious} always return {@code
      * false}.
      *
      * <li>{@link Iterator#next next} and {@link ListIterator#previous
      * previous} always throw {@link NoSuchElementException}.
      *
      * <li>{@link Iterator#remove remove} and {@link ListIterator#set
      * set} always throw {@link IllegalStateException}.
      *
      * <li>{@link ListIterator#add add} always throws {@link
      * UnsupportedOperationException}.
      *
      * <li>{@link ListIterator#nextIndex nextIndex} always returns
      * {@code 0} .
      *
      * <li>{@link ListIterator#previousIndex previousIndex} always
      * returns {@code -1}.
      *
      * </ul>
      *
      * <p>Implementations of this method are permitted, but not
      * required, to return the same object from multiple invocations.
      *
      * @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 compact>
      *
      * <li>{@link Enumeration#hasMoreElements hasMoreElements} always
      * returns {@code false}.
      *
      * <li> {@link Enumeration#nextElement nextElement} always throws
      * {@link NoSuchElementException}.
      *
      * </ul>
      *
      * <p>Implementations of this method are permitted, but not
      * required, to return the same object from multiple invocations.
      *
      * @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("unchecked")
     public static final Set EMPTY_SET = new EmptySet<>();
 
     /**
      * Returns the 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>
      * Implementation note:  Implementations of this method need not
      * create a separate <tt>Set</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.)
      *
      * @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;
         }
 
         // Preserves singleton property
         private Object readResolve() {
             return EMPTY_SET;
         }
     }
 
     /**
      * The empty list (immutable).  This list is serializable.
      *
      * @see #emptyList()
      */
     @SuppressWarnings("unchecked")
     public static final List EMPTY_LIST = new EmptyList<>();
 
     /**
      * Returns the 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.)
      *
      * @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; }
 
         // Preserves singleton property
         private Object readResolve() {
             return EMPTY_LIST;
         }
     }
 
     /**
      * The empty map (immutable).  This map is serializable.
      *
      * @see #emptyMap()
      * @since 1.3
      */
     @SuppressWarnings("unchecked")
     public static final Map EMPTY_MAP = new EmptyMap<>();
 
     /**
      * Returns the empty map (immutable).  This map is serializable.
      *
      * <p>This example illustrates the type-safe way to obtain an empty set:
      * <pre>
      *     Map&lt;String, Date&gt; s = Collections.emptyMap();
      * </pre>
      * Implementation note:  Implementations of this method need not
      * create a separate <tt>Map</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.)
      *
      * @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;}
 
         // 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 <T> Set<T> singleton(T 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();
             }
         };
     }
 
     /**
      * @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);}
     }
 
     /**
      * 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 <T> List<T> singletonList(T 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;
         }
     }
 
     /**
      * 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;
         }
 
     }
 
     // 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(); }
     }
 
     /**
      * 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;
         }
     }
 
     /**
      * 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;
 
         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
     }
 }