/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.commons.collections4;
  
  import java.lang.reflect.Array;
  import java.util.ArrayList;
  import java.util.Collection;
  import java.util.Collections;
  import java.util.Comparator;
  import java.util.Enumeration;
  import java.util.HashMap;
  import java.util.HashSet;
  import java.util.Iterator;
  import java.util.List;
  import java.util.ListIterator;
  import java.util.Map;
  import java.util.Objects;
  import java.util.Set;
  
  import org.apache.commons.collections4.bag.HashBag;
  import org.apache.commons.collections4.collection.PredicatedCollection;
  import org.apache.commons.collections4.collection.SynchronizedCollection;
  import org.apache.commons.collections4.collection.TransformedCollection;
  import org.apache.commons.collections4.collection.UnmodifiableBoundedCollection;
  import org.apache.commons.collections4.collection.UnmodifiableCollection;
  import org.apache.commons.collections4.functors.TruePredicate;
  import org.apache.commons.collections4.iterators.CollatingIterator;
  import org.apache.commons.collections4.iterators.PermutationIterator;
  
  /**
   * Provides utility methods and decorators for {@link Collection} instances.
   * <p>
   * Various utility methods might put the input objects into a Set/Map/Bag. In case
   * the input objects override {@link Object#equals(Object)}, it is mandatory that
   * the general contract of the {@link Object#hashCode()} method is maintained.
   * </p>
   * <p>
   * NOTE: From 4.0, method parameters will take {@link Iterable} objects when possible.
   * </p>
   *
   * @since 1.0
   */
  public class CollectionUtils {
  
      /**
       * Helper class to easily access cardinality properties of two collections.
       * @param <O>  the element type
       */
      private static class CardinalityHelper<O> {
  
          /** Contains the cardinality for each object in collection A. */
          final Map<O, Integer> cardinalityA;
  
          /** Contains the cardinality for each object in collection B. */
          final Map<O, Integer> cardinalityB;
  
          /**
           * Create a new CardinalityHelper for two collections.
           * @param a  the first collection
           * @param b  the second collection
           */
          CardinalityHelper(final Iterable<? extends O> a, final Iterable<? extends O> b) {
              cardinalityA = CollectionUtils.<O>getCardinalityMap(a);
              cardinalityB = CollectionUtils.<O>getCardinalityMap(b);
          }
  
          /**
           * Returns the frequency of this object in collection A.
           * @param obj  the object
           * @return the frequency of the object in collection A
           */
          public int freqA(final Object obj) {
              return getFreq(obj, cardinalityA);
          }
  
          /**
           * Returns the frequency of this object in collection B.
           * @param obj  the object
           * @return the frequency of the object in collection B
           */
          public int freqB(final Object obj) {
              return getFreq(obj, cardinalityB);
          }
  
          private int getFreq(final Object obj, final Map<?, Integer> freqMap) {
             final Integer count = freqMap.get(obj);
             if (count != null) {
                 return count.intValue();
             }
             return 0;
         }
 
         /**
          * Returns the maximum frequency of an object.
          * @param obj  the object
          * @return the maximum frequency of the object
          */
         public final int max(final Object obj) {
             return Math.max(freqA(obj), freqB(obj));
         }
 
         /**
          * Returns the minimum frequency of an object.
          * @param obj  the object
          * @return the minimum frequency of the object
          */
         public final int min(final Object obj) {
             return Math.min(freqA(obj), freqB(obj));
         }
     }
 
     /**
      * Wraps another object and uses the provided Equator to implement
      * {@link #equals(Object)} and {@link #hashCode()}.
      * <p>
      * This class can be used to store objects into a Map.
      * </p>
      *
      * @param <O>  the element type
      * @since 4.0
      */
     private static final class EquatorWrapper<O> {
         private final Equator<? super O> equator;
         private final O object;
 
         EquatorWrapper(final Equator<? super O> equator, final O object) {
             this.equator = equator;
             this.object = object;
         }
 
         @Override
         public boolean equals(final Object obj) {
             if (!(obj instanceof EquatorWrapper)) {
                 return false;
             }
             @SuppressWarnings("unchecked")
             final EquatorWrapper<O> otherObj = (EquatorWrapper<O>) obj;
             return equator.equate(object, otherObj.getObject());
         }
 
         public O getObject() {
             return object;
         }
 
         @Override
         public int hashCode() {
             return equator.hash(object);
         }
     }
 
     /**
      * Helper class for set-related operations, e.g. union, subtract, intersection.
      * @param <O>  the element type
      */
     private static final class SetOperationCardinalityHelper<O> extends CardinalityHelper<O> implements Iterable<O> {
 
         /** Contains the unique elements of the two collections. */
         private final Set<O> elements;
 
         /** Output collection. */
         private final List<O> newList;
 
         /**
          * Create a new set operation helper from the two collections.
          * @param a  the first collection
          * @param b  the second collection
          */
         SetOperationCardinalityHelper(final Iterable<? extends O> a, final Iterable<? extends O> b) {
             super(a, b);
             elements = new HashSet<>();
             addAll(elements, a);
             addAll(elements, b);
             // the resulting list must contain at least each unique element, but may grow
             newList = new ArrayList<>(elements.size());
         }
 
         @Override
         public Iterator<O> iterator() {
             return elements.iterator();
         }
 
         /**
          * Returns the resulting collection.
          * @return the result
          */
         public Collection<O> list() {
             return newList;
         }
 
         /**
          * Add the object {@code count} times to the result collection.
          * @param obj  the object to add
          * @param count  the count
          */
         public void setCardinality(final O obj, final int count) {
             for (int i = 0; i < count; i++) {
                 newList.add(obj);
             }
         }
 
     }
 
     /**
      * The index value when an element is not found in a collection or array: {@code -1}.
      *
      * @since 4.5
      */
     public static final int INDEX_NOT_FOUND = -1;
     /**
      * Default prefix used while converting an Iterator to its String representation.
      *
      * @since 4.5
      */
     public static final String DEFAULT_TOSTRING_PREFIX = "[";
 
     /**
      * Default suffix used while converting an Iterator to its String representation.
      *
      * @since 4.5
      */
     public static final String DEFAULT_TOSTRING_SUFFIX = "]";
 
     /**
      * A String for Colon  (":").
      *
      * @since 4.5
      */
     public static final String COLON = ":";
 
     /**
      * A String for Comma (",").
      *
      * @since 4.5
      */
     public static final String COMMA = ",";
 
     /**
      * An empty unmodifiable collection.
      * The JDK provides empty Set and List implementations which could be used for
      * this purpose. However they could be cast to Set or List which might be
      * undesirable. This implementation only implements Collection.
      */
     @SuppressWarnings("rawtypes") // we deliberately use the raw type here
     public static final Collection EMPTY_COLLECTION = Collections.emptyList();
 
     /**
      * Adds all elements in the array to the given collection.
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection to add to, must not be null
      * @param elements  the array of elements to add, must not be null
      * @return {@code true} if the collection was changed, {@code false} otherwise
      * @throws NullPointerException if the collection or elements is null
      */
     public static <C> boolean addAll(final Collection<C> collection, final C... elements) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(elements, "elements");
         boolean changed = false;
         for (final C element : elements) {
             changed |= collection.add(element);
         }
         return changed;
     }
 
     /**
      * Adds all elements in the enumeration to the given collection.
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection to add to, must not be null
      * @param enumeration  the enumeration of elements to add, must not be null
      * @return {@code true} if the collections was changed, {@code false} otherwise
      * @throws NullPointerException if the collection or enumeration is null
      */
     public static <C> boolean addAll(final Collection<C> collection, final Enumeration<? extends C> enumeration) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(enumeration, "enumeration");
         boolean changed = false;
         while (enumeration.hasMoreElements()) {
             changed |= collection.add(enumeration.nextElement());
         }
         return changed;
     }
 
     /**
      * Adds all elements in the {@link Iterable} to the given collection. If the
      * {@link Iterable} is a {@link Collection} then it is cast and will be
      * added using {@link Collection#addAll(Collection)} instead of iterating.
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection to add to, must not be null
      * @param iterable  the iterable of elements to add, must not be null
      * @return a boolean indicating whether the collection has changed or not.
      * @throws NullPointerException if the collection or iterable is null
      */
     public static <C> boolean addAll(final Collection<C> collection, final Iterable<? extends C> iterable) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(iterable, "iterable");
         if (iterable instanceof Collection<?>) {
             return collection.addAll((Collection<? extends C>) iterable);
         }
         return addAll(collection, iterable.iterator());
     }
 
     /**
      * Adds all elements in the iteration to the given collection.
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection to add to, must not be null
      * @param iterator  the iterator of elements to add, must not be null
      * @return a boolean indicating whether the collection has changed or not.
      * @throws NullPointerException if the collection or iterator is null
      */
     public static <C> boolean addAll(final Collection<C> collection, final Iterator<? extends C> iterator) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(iterator, "iterator");
         boolean changed = false;
         while (iterator.hasNext()) {
             changed |= collection.add(iterator.next());
         }
         return changed;
     }
 
     /**
      * Adds an element to the collection unless the element is null.
      *
      * @param <T>  the type of object the {@link Collection} contains
      * @param collection  the collection to add to, must not be null
      * @param object  the object to add, if null it will not be added
      * @return true if the collection changed
      * @throws NullPointerException if the collection is null
      * @since 3.2
      */
     public static <T> boolean addIgnoreNull(final Collection<T> collection, final T object) {
         Objects.requireNonNull(collection, "collection");
         return object != null && collection.add(object);
     }
 
     /**
      * Returns the number of occurrences of <i>obj</i> in <i>coll</i>.
      *
      * @param obj the object to find the cardinality of
      * @param collection the {@link Iterable} to search
      * @param <O> the type of object that the {@link Iterable} may contain.
      * @return the number of occurrences of obj in coll
      * @throws NullPointerException if collection is null
      * @deprecated since 4.1, use {@link IterableUtils#frequency(Iterable, Object)} instead.
      *   Be aware that the order of parameters has changed.
      */
     @Deprecated
     public static <O> int cardinality(final O obj, final Iterable<? super O> collection) {
         return IterableUtils.frequency(Objects.requireNonNull(collection, "collection"), obj);
     }
 
     /**
      * Ensures an index is not negative.
      * @param index the index to check.
      * @throws IndexOutOfBoundsException if the index is negative.
      */
     static void checkIndexBounds(final int index) {
         if (index < 0) {
             throw new IndexOutOfBoundsException("Index cannot be negative: " + index);
         }
     }
 
     /**
      * Merges two sorted Collections, a and b, into a single, sorted List
      * such that the natural ordering of the elements is retained.
      * <p>
      * Uses the standard O(n) merge algorithm for combining two sorted lists.
      * </p>
      *
      * @param <O>  the element type
      * @param a  the first collection, must not be null
      * @param b  the second collection, must not be null
      * @return a new sorted List, containing the elements of Collection a and b
      * @throws NullPointerException if either collection is null
      * @since 4.0
      */
     public static <O extends Comparable<? super O>> List<O> collate(final Iterable<? extends O> a,
                                                                     final Iterable<? extends O> b) {
         return collate(a, b, ComparatorUtils.<O>naturalComparator(), true);
     }
 
     /**
      * Merges two sorted Collections, a and b, into a single, sorted List
      * such that the natural ordering of the elements is retained.
      * <p>
      * Uses the standard O(n) merge algorithm for combining two sorted lists.
      * </p>
      *
      * @param <O>  the element type
      * @param a  the first collection, must not be null
      * @param b  the second collection, must not be null
      * @param includeDuplicates  if {@code true} duplicate elements will be retained, otherwise
      *   they will be removed in the output collection
      * @return a new sorted List, containing the elements of Collection a and b
      * @throws NullPointerException if either collection is null
      * @since 4.0
      */
     public static <O extends Comparable<? super O>> List<O> collate(final Iterable<? extends O> a,
                                                                     final Iterable<? extends O> b,
                                                                     final boolean includeDuplicates) {
         return collate(a, b, ComparatorUtils.<O>naturalComparator(), includeDuplicates);
     }
 
     /**
      * Merges two sorted Collections, a and b, into a single, sorted List
      * such that the ordering of the elements according to Comparator c is retained.
      * <p>
      * Uses the standard O(n) merge algorithm for combining two sorted lists.
      * </p>
      *
      * @param <O>  the element type
      * @param a  the first collection, must not be null
      * @param b  the second collection, must not be null
      * @param c  the comparator to use for the merge.
      * @return a new sorted List, containing the elements of Collection a and b
      * @throws NullPointerException if either collection or the comparator is null
      * @since 4.0
      */
     public static <O> List<O> collate(final Iterable<? extends O> a, final Iterable<? extends O> b,
                                       final Comparator<? super O> c) {
         return collate(a, b, c, true);
     }
 
     /**
      * Merges two sorted Collections, a and b, into a single, sorted List
      * such that the ordering of the elements according to Comparator c is retained.
      * <p>
      * Uses the standard O(n) merge algorithm for combining two sorted lists.
      * </p>
      *
      * @param <O>  the element type
      * @param iterableA  the first collection, must not be null
      * @param iterableB  the second collection, must not be null
      * @param comparator  the comparator to use for the merge.
      * @param includeDuplicates  if {@code true} duplicate elements will be retained, otherwise
      *   they will be removed in the output collection
      * @return a new sorted List, containing the elements of Collection a and b
      * @throws NullPointerException if either collection or the comparator is null
      * @since 4.0
      */
     public static <O> List<O> collate(final Iterable<? extends O> iterableA, final Iterable<? extends O> iterableB,
                                       final Comparator<? super O> comparator, final boolean includeDuplicates) {
 
         Objects.requireNonNull(iterableA, "iterableA");
         Objects.requireNonNull(iterableB, "iterableB");
         Objects.requireNonNull(comparator, "comparator");
 
         // if both Iterables are a Collection, we can estimate the size
         final int totalSize = iterableA instanceof Collection<?> && iterableB instanceof Collection<?> ?
                 Math.max(1, ((Collection<?>) iterableA).size() + ((Collection<?>) iterableB).size()) : 10;
 
         final Iterator<O> iterator = new CollatingIterator<>(comparator, iterableA.iterator(), iterableB.iterator());
         if (includeDuplicates) {
             return IteratorUtils.toList(iterator, totalSize);
         }
         final ArrayList<O> mergedList = new ArrayList<>(totalSize);
 
         O lastItem = null;
         while (iterator.hasNext()) {
             final O item = iterator.next();
             if (lastItem == null || !lastItem.equals(item)) {
                 mergedList.add(item);
             }
             lastItem = item;
         }
 
         mergedList.trimToSize();
         return mergedList;
     }
 
     /**
      * Transforms all elements from input collection with the given transformer
      * and adds them to the output collection.
      * <p>
      * If the input collection or transformer is null, there is no change to the
      * output collection.
      * </p>
      *
      * @param <I>  the type of object in the input collection
      * @param <O>  the type of object in the output collection
      * @param <R>  the type of the output collection
      * @param inputCollection  the collection to get the input from, may be null
      * @param transformer  the transformer to use, may be null
      * @param outputCollection  the collection to output into, may not be null if inputCollection
      *   and transformer are not null
      * @return the output collection with the transformed input added
      * @throws NullPointerException if the outputCollection is null and both, inputCollection and
      *   transformer are not null
      */
     public static <I, O, R extends Collection<? super O>> R collect(final Iterable<? extends I> inputCollection,
             final Transformer<? super I, ? extends O> transformer, final R outputCollection) {
         if (inputCollection != null) {
             return collect(inputCollection.iterator(), transformer, outputCollection);
         }
         return outputCollection;
     }
 
     /**
      * Returns a new Collection containing all elements of the input collection
      * transformed by the given transformer.
      * <p>
      * If the input collection or transformer is null, the result is an empty list.
      * </p>
      *
      * @param <I>  the type of object in the input collection
      * @param <O>  the type of object in the output collection
      * @param inputCollection  the collection to get the input from, may not be null
      * @param transformer  the transformer to use, may be null
      * @return the transformed result (new list)
      * @throws NullPointerException if the outputCollection is null and both, inputCollection and
      *   transformer are not null
      */
     public static <I, O> Collection<O> collect(final Iterable<I> inputCollection,
                                                final Transformer<? super I, ? extends O> transformer) {
         int size = 0;
         if (null != inputCollection) {
             size = inputCollection instanceof Collection<?> ? ((Collection<?>) inputCollection).size() : 0;
         }
         final Collection<O> answer = size == 0 ? new ArrayList<>() : new ArrayList<>(size);
         return collect(inputCollection, transformer, answer);
     }
 
     /**
      * Transforms all elements from the input iterator with the given transformer
      * and adds them to the output collection.
      * <p>
      * If the input iterator or transformer is null, there is no change to the
      * output collection.
      * </p>
      *
      * @param <I>  the type of object in the input collection
      * @param <O>  the type of object in the output collection
      * @param <R>  the type of the output collection
      * @param inputIterator  the iterator to get the input from, may be null
      * @param transformer  the transformer to use, may be null
      * @param outputCollection  the collection to output into, may not be null if inputIterator
      *   and transformer are not null
      * @return the outputCollection with the transformed input added
      * @throws NullPointerException if the output collection is null and both, inputIterator and
      *   transformer are not null
      */
     public static <I, O, R extends Collection<? super O>> R collect(final Iterator<? extends I> inputIterator,
             final Transformer<? super I, ? extends O> transformer, final R outputCollection) {
         if (inputIterator != null && transformer != null) {
             while (inputIterator.hasNext()) {
                 final I item = inputIterator.next();
                 final O value = transformer.transform(item);
                 outputCollection.add(value);
             }
         }
         return outputCollection;
     }
 
     /**
      * Transforms all elements from the input iterator with the given transformer
      * and adds them to the output collection.
      * <p>
      * If the input iterator or transformer is null, the result is an empty list.
      * </p>
      *
      * @param <I>  the type of object in the input collection
      * @param <O>  the type of object in the output collection
      * @param inputIterator  the iterator to get the input from, may be null
      * @param transformer  the transformer to use, may be null
      * @return the transformed result (new list)
      */
     public static <I, O> Collection<O> collect(final Iterator<I> inputIterator,
                                                final Transformer<? super I, ? extends O> transformer) {
         return collect(inputIterator, transformer, new ArrayList<>());
     }
 
     /**
      * Returns {@code true} iff all elements of {@code coll2} are also contained
      * in {@code coll1}. The cardinality of values in {@code coll2} is not taken into account,
      * which is the same behavior as {@link Collection#containsAll(Collection)}.
      * <p>
      * In other words, this method returns {@code true} iff the
      * {@link #intersection} of <i>coll1</i> and <i>coll2</i> has the same cardinality as
      * the set of unique values from {@code coll2}. In case {@code coll2} is empty, {@code true}
      * will be returned.
      * </p>
      * <p>
      * This method is intended as a replacement for {@link Collection#containsAll(Collection)}
      * with a guaranteed runtime complexity of {@code O(n + m)}. Depending on the type of
      * {@link Collection} provided, this method will be much faster than calling
      * {@link Collection#containsAll(Collection)} instead, though this will come at the
      * cost of an additional space complexity O(n).
      * </p>
      *
      * @param coll1  the first collection, must not be null
      * @param coll2  the second collection, must not be null
      * @return {@code true} iff the intersection of the collections has the same cardinality
      *   as the set of unique elements from the second collection
      * @throws NullPointerException if coll1 or coll2 is null
      * @since 4.0
      */
     public static boolean containsAll(final Collection<?> coll1, final Collection<?> coll2) {
         Objects.requireNonNull(coll1, "coll1");
         Objects.requireNonNull(coll2, "coll2");
         if (coll2.isEmpty()) {
             return true;
         }
         final Set<Object> elementsAlreadySeen = new HashSet<>();
         for (final Object nextElement : coll2) {
             if (elementsAlreadySeen.contains(nextElement)) {
                 continue;
             }
 
             boolean foundCurrentElement = false;
             for (final Object p : coll1) {
                 elementsAlreadySeen.add(p);
                 if (Objects.equals(nextElement, p)) {
                     foundCurrentElement = true;
                     break;
                 }
             }
 
             if (!foundCurrentElement) {
                 return false;
             }
         }
         return true;
     }
 
     /**
      * Returns {@code true} iff at least one element is in both collections.
      * <p>
      * In other words, this method returns {@code true} iff the
      * {@link #intersection} of <i>coll1</i> and <i>coll2</i> is not empty.
      * </p>
      *
      * @param coll1  the first collection, must not be null
      * @param coll2  the second collection, must not be null
      * @return {@code true} iff the intersection of the collections is non-empty
      * @throws NullPointerException if coll1 or coll2 is null
      * @since 2.1
      * @see #intersection
      */
     public static boolean containsAny(final Collection<?> coll1, final Collection<?> coll2) {
         Objects.requireNonNull(coll1, "coll1");
         Objects.requireNonNull(coll2, "coll2");
         if (coll1.size() < coll2.size()) {
             for (final Object aColl1 : coll1) {
                 if (coll2.contains(aColl1)) {
                     return true;
                 }
             }
         } else {
             for (final Object aColl2 : coll2) {
                 if (coll1.contains(aColl2)) {
                     return true;
                 }
             }
         }
         return false;
     }
 
     /**
      * Returns {@code true} iff at least one element is in both collections.
      * <p>
      * In other words, this method returns {@code true} iff the
      * {@link #intersection} of <i>coll1</i> and <i>coll2</i> is not empty.
      * </p>
      *
      * @param <T> the type of object to lookup in {@code coll1}.
      * @param coll1  the first collection, must not be null
      * @param coll2  the second collection, must not be null
      * @return {@code true} iff the intersection of the collections is non-empty
      * @throws NullPointerException if coll1 or coll2 is null
      * @since 4.2
      * @see #intersection
      */
     public static <T> boolean containsAny(final Collection<?> coll1, @SuppressWarnings("unchecked") final T... coll2) {
         Objects.requireNonNull(coll1, "coll1");
         Objects.requireNonNull(coll2, "coll2");
         if (coll1.size() < coll2.length) {
             for (final Object aColl1 : coll1) {
                 if (ArrayUtils.contains(coll2, aColl1)) {
                     return true;
                 }
             }
         } else {
             for (final Object aColl2 : coll2) {
                 if (coll1.contains(aColl2)) {
                     return true;
                 }
             }
         }
         return false;
     }
 
     /**
      * Counts the number of elements in the input collection that match the
      * predicate.
      * <p>
      * A {@code null} collection or predicate matches no elements.
      * </p>
      *
      * @param <C>  the type of object the {@link Iterable} contains
      * @param input  the {@link Iterable} to get the input from, may be null
      * @param predicate  the predicate to use, may be null
      * @return the number of matches for the predicate in the collection
      * @deprecated since 4.1, use {@link IterableUtils#countMatches(Iterable, Predicate)} instead
      */
     @Deprecated
     public static <C> int countMatches(final Iterable<C> input, final Predicate<? super C> predicate) {
         return predicate == null ? 0 : (int) IterableUtils.countMatches(input, predicate);
     }
 
     /**
      * Returns a {@link Collection} containing the exclusive disjunction
      * (symmetric difference) of the given {@link Iterable}s.
      * <p>
      * The cardinality of each element <i>e</i> in the returned
      * {@link Collection} will be equal to
      * <code>max(cardinality(<i>e</i>,<i>a</i>),cardinality(<i>e</i>,<i>b</i>)) - min(cardinality(<i>e</i>,<i>a</i>),
      * cardinality(<i>e</i>,<i>b</i>))</code>.
      * </p>
      * <p>
      * This is equivalent to
      * {@code {@link #subtract subtract}({@link #union union(a,b)},{@link #intersection intersection(a,b)})}
      * or
      * {@code {@link #union union}({@link #subtract subtract(a,b)},{@link #subtract subtract(b,a)})}.
      * </p>
      *
      * @param a the first collection, must not be null
      * @param b the second collection, must not be null
      * @param <O> the generic type that is able to represent the types contained
      *        in both input collections.
      * @return the symmetric difference of the two collections
      * @throws NullPointerException if either collection is null
      */
     public static <O> Collection<O> disjunction(final Iterable<? extends O> a, final Iterable<? extends O> b) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         final SetOperationCardinalityHelper<O> helper = new SetOperationCardinalityHelper<>(a, b);
         for (final O obj : helper) {
             helper.setCardinality(obj, helper.max(obj) - helper.min(obj));
         }
         return helper.list();
     }
 
     /**
      * Returns the immutable EMPTY_COLLECTION with generic type safety.
      *
      * @see #EMPTY_COLLECTION
      * @since 4.0
      * @param <T> the element type
      * @return immutable empty collection
      */
     @SuppressWarnings("unchecked") // OK, empty collection is compatible with any type
     public static <T> Collection<T> emptyCollection() {
         return EMPTY_COLLECTION;
     }
 
     /**
      * Returns an immutable empty collection if the argument is {@code null},
      * or the argument itself otherwise.
      *
      * @param <T> the element type
      * @param collection the collection, possibly {@code null}
      * @return an empty collection if the argument is {@code null}
      */
     public static <T> Collection<T> emptyIfNull(final Collection<T> collection) {
         return collection == null ? CollectionUtils.<T>emptyCollection() : collection;
     }
 
     /**
      * Answers true if a predicate is true for at least one element of a
      * collection.
      * <p>
      * A {@code null} collection or predicate returns false.
      * </p>
      *
      * @param <C>  the type of object the {@link Iterable} contains
      * @param input  the {@link Iterable} to get the input from, may be null
      * @param predicate  the predicate to use, may be null
      * @return true if at least one element of the collection matches the predicate
      * @deprecated since 4.1, use {@link IterableUtils#matchesAny(Iterable, Predicate)} instead
      */
     @Deprecated
     public static <C> boolean exists(final Iterable<C> input, final Predicate<? super C> predicate) {
         return predicate != null && IterableUtils.matchesAny(input, predicate);
     }
 
     /**
      * Extract the lone element of the specified Collection.
      *
      * @param <E> collection type
      * @param collection to read
      * @return sole member of collection
      * @throws NullPointerException if collection is null
      * @throws IllegalArgumentException if collection is empty or contains more than one element
      * @since 4.0
      */
     public static <E> E extractSingleton(final Collection<E> collection) {
         Objects.requireNonNull(collection, "collection");
         if (collection.size() != 1) {
             throw new IllegalArgumentException("Can extract singleton only when collection size == 1");
         }
         return collection.iterator().next();
     }
 
     /**
      * Filter the collection by applying a Predicate to each element. If the
      * predicate returns false, remove the element.
      * <p>
      * If the input collection or predicate is null, there is no change made.
      * </p>
      *
      * @param <T>  the type of object the {@link Iterable} contains
      * @param collection  the collection to get the input from, may be null
      * @param predicate  the predicate to use as a filter, may be null
      * @return true if the collection is modified by this call, false otherwise.
      */
     public static <T> boolean filter(final Iterable<T> collection, final Predicate<? super T> predicate) {
         boolean result = false;
         if (collection != null && predicate != null) {
             for (final Iterator<T> it = collection.iterator(); it.hasNext();) {
                 if (!predicate.evaluate(it.next())) {
                     it.remove();
                     result = true;
                 }
             }
         }
         return result;
     }
 
     /**
      * Filter the collection by applying a Predicate to each element. If the
      * predicate returns true, remove the element.
      * <p>
      * This is equivalent to {@code filter(collection, PredicateUtils.notPredicate(predicate))}
      * if predicate is != null.
      * </p>
      * <p>
      * If the input collection or predicate is null, there is no change made.
      * </p>
      *
      * @param <T>  the type of object the {@link Iterable} contains
      * @param collection  the collection to get the input from, may be null
      * @param predicate  the predicate to use as a filter, may be null
      * @return true if the collection is modified by this call, false otherwise.
      */
     public static <T> boolean filterInverse(final Iterable<T> collection, final Predicate<? super T> predicate) {
         return filter(collection, predicate == null ? null : PredicateUtils.notPredicate(predicate));
     }
 
     /**
      * Finds the first element in the given collection which matches the given predicate.
      * <p>
      * If the input collection or predicate is null, or no element of the collection
      * matches the predicate, null is returned.
      * </p>
      *
      * @param <T>  the type of object the {@link Iterable} contains
      * @param collection  the collection to search, may be null
      * @param predicate  the predicate to use, may be null
      * @return the first element of the collection which matches the predicate or null if none could be found
      * @deprecated since 4.1, use {@link IterableUtils#find(Iterable, Predicate)} instead
      */
     @Deprecated
     public static <T> T find(final Iterable<T> collection, final Predicate<? super T> predicate) {
         return predicate != null ? IterableUtils.find(collection, predicate) : null;
     }
 
     /**
      * Executes the given closure on each but the last element in the collection.
      * <p>
      * If the input collection or closure is null, there is no change made.
      * </p>
      *
      * @param <T>  the type of object the {@link Iterable} contains
      * @param <C>  the closure type
      * @param collection  the collection to get the input from, may be null
      * @param closure  the closure to perform, may be null
      * @return the last element in the collection, or null if either collection or closure is null
      * @since 4.0
      * @deprecated since 4.1, use {@link IterableUtils#forEachButLast(Iterable, Closure)} instead
      */
     @Deprecated
     public static <T, C extends Closure<? super T>> T forAllButLastDo(final Iterable<T> collection,
                                                                       final C closure) {
         return closure != null ? IterableUtils.forEachButLast(collection, closure) : null;
     }
 
     /**
      * Executes the given closure on each but the last element in the collection.
      * <p>
      * If the input collection or closure is null, there is no change made.
      * </p>
      *
      * @param <T>  the type of object the {@link Collection} contains
      * @param <C>  the closure type
      * @param iterator  the iterator to get the input from, may be null
      * @param closure  the closure to perform, may be null
      * @return the last element in the collection, or null if either iterator or closure is null
      * @since 4.0
      * @deprecated since 4.1, use {@link IteratorUtils#forEachButLast(Iterator, Closure)} instead
      */
     @Deprecated
     public static <T, C extends Closure<? super T>> T forAllButLastDo(final Iterator<T> iterator, final C closure) {
         return closure != null ? IteratorUtils.forEachButLast(iterator, closure) : null;
     }
 
     /**
      * Executes the given closure on each element in the collection.
      * <p>
      * If the input collection or closure is null, there is no change made.
      * </p>
      *
      * @param <T>  the type of object the {@link Iterable} contains
      * @param <C>  the closure type
      * @param collection  the collection to get the input from, may be null
      * @param closure  the closure to perform, may be null
      * @return closure
      * @deprecated since 4.1, use {@link IterableUtils#forEach(Iterable, Closure)} instead
      */
     @Deprecated
     public static <T, C extends Closure<? super T>> C forAllDo(final Iterable<T> collection, final C closure) {
         if (closure != null) {
             IterableUtils.forEach(collection, closure);
         }
         return closure;
     }
 
     /**
      * Executes the given closure on each element in the collection.
      * <p>
      * If the input collection or closure is null, there is no change made.
      * </p>
      *
      * @param <T>  the type of object the {@link Iterator} contains
      * @param <C>  the closure type
      * @param iterator  the iterator to get the input from, may be null
      * @param closure  the closure to perform, may be null
      * @return closure
      * @since 4.0
      * @deprecated since 4.1, use {@link IteratorUtils#forEach(Iterator, Closure)} instead
      */
     @Deprecated
     public static <T, C extends Closure<? super T>> C forAllDo(final Iterator<T> iterator, final C closure) {
         if (closure != null) {
             IteratorUtils.forEach(iterator, closure);
         }
         return closure;
     }
 
     /**
      * Returns the {@code index}-th value in the {@code iterable}'s {@link Iterator}, throwing
      * {@code IndexOutOfBoundsException} if there is no such element.
      * <p>
      * If the {@link Iterable} is a {@link List}, then it will use {@link List#get(int)}.
      * </p>
      *
      * @param iterable  the {@link Iterable} to get a value from
      * @param index  the index to get
      * @param <T> the type of object in the {@link Iterable}.
      * @return the object at the specified index
      * @throws IndexOutOfBoundsException if the index is invalid
      * @deprecated since 4.1, use {@code IterableUtils.get(Iterable, int)} instead
      */
     @Deprecated
     public static <T> T get(final Iterable<T> iterable, final int index) {
         Objects.requireNonNull(iterable, "iterable");
         return IterableUtils.get(iterable, index);
     }
 
     /**
      * Returns the {@code index}-th value in {@link Iterator}, throwing
      * {@code IndexOutOfBoundsException} if there is no such element.
      * <p>
      * The Iterator is advanced to {@code index} (or to the end, if
      * {@code index} exceeds the number of entries) as a side effect of this method.
      * </p>
      *
      * @param iterator  the iterator to get a value from
      * @param index  the index to get
      * @param <T> the type of object in the {@link Iterator}
      * @return the object at the specified index
      * @throws IndexOutOfBoundsException if the index is invalid
      * @throws IllegalArgumentException if the object type is invalid
      * @throws NullPointerException if iterator is null
      * @deprecated since 4.1, use {@code IteratorUtils.get(Iterator, int)} instead
      */
     @Deprecated
     public static <T> T get(final Iterator<T> iterator, final int index) {
         Objects.requireNonNull(iterator, "iterator");
         return IteratorUtils.get(iterator, index);
     }
 
     /**
      * Returns the {@code index}-th {@code Map.Entry} in the {@code map}'s {@code entrySet},
      * throwing {@code IndexOutOfBoundsException} if there is no such element.
      *
      * @param <K>  the key type in the {@link Map}
      * @param <V>  the value type in the {@link Map}
      * @param map  the object to get a value from
      * @param index  the index to get
      * @return the object at the specified index
      * @throws IndexOutOfBoundsException if the index is invalid
      */
     public static <K, V> Map.Entry<K, V> get(final Map<K, V> map, final int index) {
         Objects.requireNonNull(map, "map");
         checkIndexBounds(index);
         return get(map.entrySet(), index);
     }
 
     /**
      * Returns the {@code index}-th value in {@code object}, throwing
      * {@code IndexOutOfBoundsException} if there is no such element or
      * {@code IllegalArgumentException} if {@code object} is not an
      * instance of one of the supported types.
      * <p>
      * The supported types, and associated semantics are:
      * </p>
      * <ul>
      * <li> Map -- the value returned is the {@code Map.Entry} in position
      *      {@code index} in the map's {@code entrySet} iterator,
      *      if there is such an entry.</li>
      * <li> List -- this method is equivalent to the list's get method.</li>
      * <li> Array -- the {@code index}-th array entry is returned,
      *      if there is such an entry; otherwise an {@code IndexOutOfBoundsException}
      *      is thrown.</li>
      * <li> Collection -- the value returned is the {@code index}-th object
      *      returned by the collection's default iterator, if there is such an element.</li>
      * <li> Iterator or Enumeration -- the value returned is the
      *      {@code index}-th object in the Iterator/Enumeration, if there
      *      is such an element.  The Iterator/Enumeration is advanced to
      *      {@code index} (or to the end, if {@code index} exceeds the
      *      number of entries) as a side effect of this method.</li>
      * </ul>
      *
      * @param object  the object to get a value from
      * @param index  the index to get
      * @return the object at the specified index
      * @throws IndexOutOfBoundsException if the index is invalid
      * @throws IllegalArgumentException if the object type is invalid
      */
     public static Object get(final Object object, final int index) {
         final int i = index;
         if (i < 0) {
             throw new IndexOutOfBoundsException("Index cannot be negative: " + i);
         }
         if (object instanceof Map<?, ?>) {
             final Map<?, ?> map = (Map<?, ?>) object;
             final Iterator<?> iterator = map.entrySet().iterator();
             return IteratorUtils.get(iterator, i);
         }
         if (object instanceof Object[]) {
             return ((Object[]) object)[i];
         }
         if (object instanceof Iterator<?>) {
             final Iterator<?> it = (Iterator<?>) object;
             return IteratorUtils.get(it, i);
         }
         if (object instanceof Iterable<?>) {
             final Iterable<?> iterable = (Iterable<?>) object;
             return IterableUtils.get(iterable, i);
         }
         if (object instanceof Enumeration<?>) {
             final Enumeration<?> it = (Enumeration<?>) object;
             return EnumerationUtils.get(it, i);
         }
         if (object == null) {
             throw new IllegalArgumentException("Unsupported object type: null");
         }
         try {
             return Array.get(object, i);
         } catch (final IllegalArgumentException ex) {
             throw new IllegalArgumentException("Unsupported object type: " + object.getClass().getName());
         }
     }
 
     /**
      * Returns a {@link Map} mapping each unique element in the given
      * {@link Collection} to an {@link Integer} representing the number
      * of occurrences of that element in the {@link Collection}.
      * <p>
      * Only those elements present in the collection will appear as
      * keys in the map.
      * </p>
      *
      * @param <O>  the type of object in the returned {@link Map}. This is a super type of &lt;I&gt;.
      * @param coll  the collection to get the cardinality map for, must not be null
      * @return the populated cardinality map
      * @throws NullPointerException if coll is null
      */
     public static <O> Map<O, Integer> getCardinalityMap(final Iterable<? extends O> coll) {
         Objects.requireNonNull(coll, "coll");
         final Map<O, Integer> count = new HashMap<>();
         for (final O obj : coll) {
             final Integer c = count.get(obj);
             if (c == null) {
                 count.put(obj, Integer.valueOf(1));
             } else {
                 count.put(obj, Integer.valueOf(c.intValue() + 1));
             }
         }
         return count;
     }
 
     /**
      * Returns the hash code of the input collection using the hash method of an equator.
      *
      * <p>
      * Returns 0 if the input collection is {@code null}.
      * </p>
      *
      * @param <E>  the element type
      * @param collection  the input collection
      * @param equator  the equator used for generate hashCode
      * @return the hash code of the input collection using the hash method of an equator
      * @throws NullPointerException if the equator is {@code null}
      * @since 4.5
      */
     public static <E> int hashCode(final Collection<? extends E> collection,
             final Equator<? super E> equator) {
         Objects.requireNonNull(equator, "equator");
         if (null == collection) {
             return 0;
         }
         int hashCode = 1;
         for (final E e : collection) {
             hashCode = 31 * hashCode + equator.hash(e);
         }
         return hashCode;
     }
 
     /**
      * Returns a {@link Collection} containing the intersection of the given
      * {@link Iterable}s.
      * <p>
      * The cardinality of each element in the returned {@link Collection} will
      * be equal to the minimum of the cardinality of that element in the two
      * given {@link Iterable}s.
      * </p>
      *
      * @param a the first collection, must not be null
      * @param b the second collection, must not be null
      * @param <O> the generic type that is able to represent the types contained
      *        in both input collections.
      * @return the intersection of the two collections
      * @throws NullPointerException if either collection is null
      * @see Collection#retainAll
      * @see #containsAny
      */
     public static <O> Collection<O> intersection(final Iterable<? extends O> a, final Iterable<? extends O> b) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         final SetOperationCardinalityHelper<O> helper = new SetOperationCardinalityHelper<>(a, b);
         for (final O obj : helper) {
             helper.setCardinality(obj, helper.min(obj));
         }
         return helper.list();
     }
 
     /**
      * Null-safe check if the specified collection is empty.
      * <p>
      * Null returns true.
      * </p>
      *
      * @param coll  the collection to check, may be null
      * @return true if empty or null
      * @since 3.2
      */
     public static boolean isEmpty(final Collection<?> coll) {
         return coll == null || coll.isEmpty();
     }
 
     /**
      * Returns {@code true} iff the given {@link Collection}s contain
      * exactly the same elements with exactly the same cardinalities.
      * <p>
      * That is, iff the cardinality of <i>e</i> in <i>a</i> is
      * equal to the cardinality of <i>e</i> in <i>b</i>,
      * for each element <i>e</i> in <i>a</i> or <i>b</i>.
      * </p>
      *
      * @param a  the first collection, must not be null
      * @param b  the second collection, must not be null
      * @return {@code true} iff the collections contain the same elements with the same cardinalities.
      * @throws NullPointerException if either collection is null
      */
     public static boolean isEqualCollection(final Collection<?> a, final Collection<?> b) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         if (a.size() != b.size()) {
             return false;
         }
         final CardinalityHelper<Object> helper = new CardinalityHelper<>(a, b);
         if (helper.cardinalityA.size() != helper.cardinalityB.size()) {
             return false;
         }
         for (final Object obj : helper.cardinalityA.keySet()) {
             if (helper.freqA(obj) != helper.freqB(obj)) {
                 return false;
             }
         }
         return true;
     }
 
     /**
      * Returns {@code true} iff the given {@link Collection}s contain
      * exactly the same elements with exactly the same cardinalities.
      * <p>
      * That is, iff the cardinality of <i>e</i> in <i>a</i> is
      * equal to the cardinality of <i>e</i> in <i>b</i>,
      * for each element <i>e</i> in <i>a</i> or <i>b</i>.
      * </p>
      * <p>
      * <b>Note:</b> from version 4.1 onwards this method requires the input
      * collections and equator to be of compatible type (using bounded wildcards).
      * Providing incompatible arguments (e.g. by casting to their rawtypes)
      * will result in a {@code ClassCastException} thrown at runtime.
      * </p>
      *
      * @param <E>  the element type
      * @param a  the first collection, must not be null
      * @param b  the second collection, must not be null
      * @param equator  the Equator used for testing equality
      * @return {@code true} iff the collections contain the same elements with the same cardinalities.
      * @throws NullPointerException if either collection or equator is null
      * @since 4.0
      */
     public static <E> boolean isEqualCollection(final Collection<? extends E> a,
                                                 final Collection<? extends E> b,
                                                 final Equator<? super E> equator) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         Objects.requireNonNull(equator, "equator");
 
         if (a.size() != b.size()) {
             return false;
         }
 
         @SuppressWarnings({ "unchecked", "rawtypes" })
         final Transformer<E, ?> transformer = input -> new EquatorWrapper(equator, input);
 
         return isEqualCollection(collect(a, transformer), collect(b, transformer));
     }
 
     /**
      * Returns true if no more elements can be added to the Collection.
      * <p>
      * This method uses the {@link BoundedCollection} interface to determine the
      * full status. If the collection does not implement this interface then
      * false is returned.
      * </p>
      * <p>
      * The collection does not have to implement this interface directly.
      * If the collection has been decorated using the decorators subpackage
      * then these will be removed to access the BoundedCollection.
      * </p>
      *
      * @param collection  the collection to check
      * @return true if the BoundedCollection is full
      * @throws NullPointerException if the collection is null
      */
     public static boolean isFull(final Collection<? extends Object> collection) {
         Objects.requireNonNull(collection, "collection");
         if (collection instanceof BoundedCollection) {
             return ((BoundedCollection<?>) collection).isFull();
         }
         try {
             final BoundedCollection<?> bcoll =
                     UnmodifiableBoundedCollection.unmodifiableBoundedCollection(collection);
             return bcoll.isFull();
         } catch (final IllegalArgumentException ex) {
             return false;
         }
     }
 
     /**
      * Null-safe check if the specified collection is not empty.
      * <p>
      * Null returns false.
      * </p>
      *
      * @param coll  the collection to check, may be null
      * @return true if non-null and non-empty
      * @since 3.2
      */
     public static boolean isNotEmpty(final Collection<?> coll) {
         return !isEmpty(coll);
     }
 
     /**
      * Returns {@code true} iff <i>a</i> is a <i>proper</i> sub-collection of <i>b</i>,
      * that is, iff the cardinality of <i>e</i> in <i>a</i> is less
      * than or equal to the cardinality of <i>e</i> in <i>b</i>,
      * for each element <i>e</i> in <i>a</i>, and there is at least one
      * element <i>f</i> such that the cardinality of <i>f</i> in <i>b</i>
      * is strictly greater than the cardinality of <i>f</i> in <i>a</i>.
      * <p>
      * The implementation assumes
      * </p>
      * <ul>
      *    <li>{@code a.size()} and {@code b.size()} represent the
      *    total cardinality of <i>a</i> and <i>b</i>, resp. </li>
      *    <li>{@code a.size() &lt; Integer.MAXVALUE}</li>
      * </ul>
      *
      * @param a  the first (sub?) collection, must not be null
      * @param b  the second (super?) collection, must not be null
      * @return {@code true} iff <i>a</i> is a <i>proper</i> sub-collection of <i>b</i>
      * @throws NullPointerException if either collection is null
      * @see #isSubCollection
      * @see Collection#containsAll
      */
     public static boolean isProperSubCollection(final Collection<?> a, final Collection<?> b) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         return a.size() < b.size() && CollectionUtils.isSubCollection(a, b);
     }
 
     /**
      * Returns {@code true} iff <i>a</i> is a sub-collection of <i>b</i>,
      * that is, iff the cardinality of <i>e</i> in <i>a</i> is less than or
      * equal to the cardinality of <i>e</i> in <i>b</i>, for each element <i>e</i>
      * in <i>a</i>.
      *
      * @param a the first (sub?) collection, must not be null
      * @param b the second (super?) collection, must not be null
      * @return {@code true} iff <i>a</i> is a sub-collection of <i>b</i>
      * @throws NullPointerException if either collection is null
      * @see #isProperSubCollection
      * @see Collection#containsAll
      */
     public static boolean isSubCollection(final Collection<?> a, final Collection<?> b) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         final CardinalityHelper<Object> helper = new CardinalityHelper<>(a, b);
         for (final Object obj : a) {
             if (helper.freqA(obj) > helper.freqB(obj)) {
                 return false;
             }
         }
         return true;
     }
 
     /**
      * Answers true if a predicate is true for every element of a
      * collection.
      *
      * <p>
      * A {@code null} predicate returns false.
      * </p>
      * <p>
      * A {@code null} or empty collection returns true.
      * </p>
      *
      * @param <C>  the type of object the {@link Iterable} contains
      * @param input  the {@link Iterable} to get the input from, may be null
      * @param predicate  the predicate to use, may be null
      * @return true if every element of the collection matches the predicate or if the
      * collection is empty, false otherwise
      * @since 4.0
      * @deprecated since 4.1, use {@link IterableUtils#matchesAll(Iterable, Predicate)} instead
      */
     @Deprecated
     public static <C> boolean matchesAll(final Iterable<C> input, final Predicate<? super C> predicate) {
         return predicate != null && IterableUtils.matchesAll(input, predicate);
     }
 
     /**
      * Gets the maximum number of elements that the Collection can contain.
      * <p>
      * This method uses the {@link BoundedCollection} interface to determine the
      * maximum size. If the collection does not implement this interface then
      * -1 is returned.
      * </p>
      * <p>
      * The collection does not have to implement this interface directly.
      * If the collection has been decorated using the decorators subpackage
      * then these will be removed to access the BoundedCollection.
      * </p>
      *
      * @param collection  the collection to check
      * @return the maximum size of the BoundedCollection, -1 if no maximum size
      * @throws NullPointerException if the collection is null
      */
     public static int maxSize(final Collection<? extends Object> collection) {
         Objects.requireNonNull(collection, "collection");
         if (collection instanceof BoundedCollection) {
             return ((BoundedCollection<?>) collection).maxSize();
         }
         try {
             final BoundedCollection<?> bcoll =
                     UnmodifiableBoundedCollection.unmodifiableBoundedCollection(collection);
             return bcoll.maxSize();
         } catch (final IllegalArgumentException ex) {
             return -1;
         }
     }
 
     /**
      * Returns a {@link Collection} of all the permutations of the input collection.
      * <p>
      * NOTE: the number of permutations of a given collection is equal to n!, where
      * n is the size of the collection. Thus, the resulting collection will become
      * <b>very</b> large for collections &gt; 10 (e.g. 10! = 3628800, 15! = 1307674368000).
      * </p>
      * <p>
      * For larger collections it is advised to use a {@link PermutationIterator} to
      * iterate over all permutations.
      * </p>
      *
      * @see PermutationIterator
      *
      * @param <E>  the element type
      * @param collection  the collection to create permutations for, must not be null
      * @return an unordered collection of all permutations of the input collection
      * @throws NullPointerException if collection is null
      * @since 4.0
      */
     public static <E> Collection<List<E>> permutations(final Collection<E> collection) {
         Objects.requireNonNull(collection, "collection");
         final PermutationIterator<E> it = new PermutationIterator<>(collection);
         final Collection<List<E>> result = new ArrayList<>();
         while (it.hasNext()) {
             result.add(it.next());
         }
         return result;
     }
 
     /**
      * Returns a predicated (validating) collection backed by the given collection.
      * <p>
      * Only objects that pass the test in the given predicate can be added to the collection.
      * Trying to add an invalid object results in an IllegalArgumentException.
      * It is important not to use the original collection after invoking this method,
      * as it is a backdoor for adding invalid objects.
      * </p>
      *
      * @param <C> the type of objects in the Collection.
      * @param collection  the collection to predicate, must not be null
      * @param predicate  the predicate for the collection, must not be null
      * @return a predicated collection backed by the given collection
      * @throws NullPointerException if the collection or predicate is null
      */
     public static <C> Collection<C> predicatedCollection(final Collection<C> collection,
                                                          final Predicate<? super C> predicate) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(predicate, "predicate");
         return PredicatedCollection.predicatedCollection(collection, predicate);
     }
 
     /**
      * Removes the elements in {@code remove} from {@code collection}. That is, this
      * method returns a collection containing all the elements in {@code c}
      * that are not in {@code remove}. The cardinality of an element {@code e}
      * in the returned collection is the same as the cardinality of {@code e}
      * in {@code collection} unless {@code remove} contains {@code e}, in which
      * case the cardinality is zero. This method is useful if you do not wish to modify
      * the collection {@code c} and thus cannot call {@code collection.removeAll(remove);}.
      * <p>
      * This implementation iterates over {@code collection}, checking each element in
      * turn to see if it's contained in {@code remove}. If it's not contained, it's added
      * to the returned list. As a consequence, it is advised to use a collection type for
      * {@code remove} that provides a fast (e.g. O(1)) implementation of
      * {@link Collection#contains(Object)}.
      * </p>
      *
      * @param <E>  the type of object the {@link Collection} contains
      * @param collection  the collection from which items are removed (in the returned collection)
      * @param remove  the items to be removed from the returned {@code collection}
      * @return a {@code Collection} containing all the elements of {@code collection} except
      * any elements that also occur in {@code remove}.
      * @throws NullPointerException if either parameter is null
      * @since 4.0 (method existed in 3.2 but was completely broken)
      */
     public static <E> Collection<E> removeAll(final Collection<E> collection, final Collection<?> remove) {
         return ListUtils.removeAll(collection, remove);
     }
 
     /**
      * Removes all elements in {@code remove} from {@code collection}.
      * That is, this method returns a collection containing all the elements in
      * {@code collection} that are not in {@code remove}. The
      * cardinality of an element {@code e} in the returned collection is
      * the same as the cardinality of {@code e} in {@code collection}
      * unless {@code remove} contains {@code e}, in which case the
      * cardinality is zero. This method is useful if you do not wish to modify
      * the collection {@code c} and thus cannot call
      * {@code collection.removeAll(remove)}.
      * <p>
      * Moreover this method uses an {@link Equator} instead of
      * {@link Object#equals(Object)} to determine the equality of the elements
      * in {@code collection} and {@code remove}. Hence this method is
      * useful in cases where the equals behavior of an object needs to be
      * modified without changing the object itself.
      * </p>
      *
      * @param <E> the type of object the {@link Collection} contains
      * @param collection the collection from which items are removed (in the returned collection)
      * @param remove the items to be removed from the returned collection
      * @param equator the Equator used for testing equality
      * @return a {@code Collection} containing all the elements of {@code collection}
      * except any element that if equal according to the {@code equator}
      * @throws NullPointerException if any of the parameters is null
      * @since 4.1
      */
     public static <E> Collection<E> removeAll(final Iterable<E> collection,
                                               final Iterable<? extends E> remove,
                                               final Equator<? super E> equator) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(remove, "remove");
         Objects.requireNonNull(equator, "equator");
         final Transformer<E, EquatorWrapper<E>> transformer = input -> new EquatorWrapper<>(equator, input);
 
         final Set<EquatorWrapper<E>> removeSet =
                 collect(remove, transformer, new HashSet<>());
 
         final List<E> list = new ArrayList<>();
         for (final E element : collection) {
             if (!removeSet.contains(new EquatorWrapper<>(equator, element))) {
                 list.add(element);
             }
         }
         return list;
     }
 
     /**
      * Removes the specified number of elements from the start index in the collection and returns them.
      * This method modifies the input collections.
      *
      * @param <E>  the type of object the {@link Collection} contains
      * @param input  the collection will be operated, can't be null
      * @param startIndex  the start index (inclusive) to remove element, can't be less than 0
      * @param count  the specified number to remove, can't be less than 1
      * @return collection of elements that removed from the input collection
      * @throws NullPointerException if input is null
      * @since 4.5
      */
     public static <E> Collection<E> removeCount(final Collection<E> input, int startIndex, int count) {
         Objects.requireNonNull(input, "input");
         if (startIndex < 0) {
             throw new IndexOutOfBoundsException("The start index can't be less than 0.");
         }
         if (count < 0) {
             throw new IndexOutOfBoundsException("The count can't be less than 0.");
         }
         if (input.size() < startIndex + count) {
             throw new IndexOutOfBoundsException(
                     "The sum of start index and count can't be greater than the size of collection.");
         }
 
         final Collection<E> result = new ArrayList<>(count);
         final Iterator<E> iterator = input.iterator();
         while (count > 0) {
             if (startIndex > 0) {
                 startIndex -= 1;
                 iterator.next();
                 continue;
             }
             count -= 1;
             result.add(iterator.next());
             iterator.remove();
         }
         return result;
     }
 
     /**
      * Removes elements whose index are between startIndex, inclusive and endIndex,
      * exclusive in the collection and returns them.
      * This method modifies the input collections.
      *
      * @param <E>  the type of object the {@link Collection} contains
      * @param input  the collection will be operated, must not be null
      * @param startIndex  the start index (inclusive) to remove element, must not be less than 0
      * @param endIndex  the end index (exclusive) to remove, must not be less than startIndex
      * @return collection of elements that removed from the input collection
      * @throws NullPointerException if input is null
      * @since 4.5
      */
     public static <E> Collection<E> removeRange(final Collection<E> input, final int startIndex, final int endIndex) {
         Objects.requireNonNull(input, "input");
         if (endIndex < startIndex) {
             throw new IllegalArgumentException("The end index can't be less than the start index.");
         }
         if (input.size() < endIndex) {
             throw new IndexOutOfBoundsException("The end index can't be greater than the size of collection.");
         }
         return CollectionUtils.removeCount(input, startIndex, endIndex - startIndex);
     }
 
     /**
      * Returns a collection containing all the elements in {@code collection}
      * that are also in {@code retain}. The cardinality of an element {@code e}
      * in the returned collection is the same as the cardinality of {@code e}
      * in {@code collection} unless {@code retain} does not contain {@code e}, in which
      * case the cardinality is zero. This method is useful if you do not wish to modify
      * the collection {@code c} and thus cannot call {@code c.retainAll(retain);}.
      * <p>
      * This implementation iterates over {@code collection}, checking each element in
      * turn to see if it's contained in {@code retain}. If it's contained, it's added
      * to the returned list. As a consequence, it is advised to use a collection type for
      * {@code retain} that provides a fast (e.g. O(1)) implementation of
      * {@link Collection#contains(Object)}.
      * </p>
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection whose contents are the target of the #retailAll operation
      * @param retain  the collection containing the elements to be retained in the returned collection
      * @return a {@code Collection} containing all the elements of {@code collection}
      * that occur at least once in {@code retain}.
      * @throws NullPointerException if either parameter is null
      * @since 3.2
      */
     public static <C> Collection<C> retainAll(final Collection<C> collection, final Collection<?> retain) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(retain, "retain");
         return ListUtils.retainAll(collection, retain);
     }
 
     /**
      * Returns a collection containing all the elements in
      * {@code collection} that are also in {@code retain}. The
      * cardinality of an element {@code e} in the returned collection is
      * the same as the cardinality of {@code e} in {@code collection}
      * unless {@code retain} does not contain {@code e}, in which case
      * the cardinality is zero. This method is useful if you do not wish to
      * modify the collection {@code c} and thus cannot call
      * {@code c.retainAll(retain);}.
      * <p>
      * Moreover this method uses an {@link Equator} instead of
      * {@link Object#equals(Object)} to determine the equality of the elements
      * in {@code collection} and {@code retain}. Hence this method is
      * useful in cases where the equals behavior of an object needs to be
      * modified without changing the object itself.
      * </p>
      *
      * @param <E> the type of object the {@link Collection} contains
      * @param collection the collection whose contents are the target of the {@code retainAll} operation
      * @param retain the collection containing the elements to be retained in the returned collection
      * @param equator the Equator used for testing equality
      * @return a {@code Collection} containing all the elements of {@code collection}
      * that occur at least once in {@code retain} according to the {@code equator}
      * @throws NullPointerException if any of the parameters is null
      * @since 4.1
      */
     public static <E> Collection<E> retainAll(final Iterable<E> collection,
                                               final Iterable<? extends E> retain,
                                               final Equator<? super E> equator) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(retain, "retain");
         Objects.requireNonNull(equator, "equator");
         final Transformer<E, EquatorWrapper<E>> transformer = input -> new EquatorWrapper<>(equator, input);
 
         final Set<EquatorWrapper<E>> retainSet =
                 collect(retain, transformer, new HashSet<>());
 
         final List<E> list = new ArrayList<>();
         for (final E element : collection) {
             if (retainSet.contains(new EquatorWrapper<>(equator, element))) {
                 list.add(element);
             }
         }
         return list;
     }
 
     /**
      * Reverses the order of the given array.
      *
      * @param array  the array to reverse
      */
     public static void reverseArray(final Object[] array) {
         Objects.requireNonNull(array, "array");
         int i = 0;
         int j = array.length - 1;
         Object tmp;
 
         while (j > i) {
             tmp = array[j];
             array[j] = array[i];
             array[i] = tmp;
             j--;
             i++;
         }
     }
 
     /**
      * Selects all elements from input collection which match the given
      * predicate into an output collection.
      * <p>
      * A {@code null} predicate matches no elements.
      * </p>
      *
      * @param <O>  the type of object the {@link Iterable} contains
      * @param inputCollection  the collection to get the input from, may not be null
      * @param predicate  the predicate to use, may be null
      * @return the elements matching the predicate (new list)
      */
     public static <O> Collection<O> select(final Iterable<? extends O> inputCollection,
                                            final Predicate<? super O> predicate) {
         int size = 0;
         if (null != inputCollection) {
             size = inputCollection instanceof Collection<?> ? ((Collection<?>) inputCollection).size() : 0;
         }
         final Collection<O> answer = size == 0 ? new ArrayList<>() : new ArrayList<>(size);
         return select(inputCollection, predicate, answer);
     }
 
     /**
      * Selects all elements from input collection which match the given
      * predicate and adds them to outputCollection.
      * <p>
      * If the input collection or predicate is null, there is no change to the
      * output collection.
      * </p>
      *
      * @param <O>  the type of object the {@link Iterable} contains
      * @param <R>  the type of the output {@link Collection}
      * @param inputCollection  the collection to get the input from, may be null
      * @param predicate  the predicate to use, may be null
      * @param outputCollection  the collection to output into, may not be null if the inputCollection
      *   and predicate or not null
      * @return the outputCollection
      */
     public static <O, R extends Collection<? super O>> R select(final Iterable<? extends O> inputCollection,
             final Predicate<? super O> predicate, final R outputCollection) {
 
         if (inputCollection != null && predicate != null) {
             for (final O item : inputCollection) {
                 if (predicate.evaluate(item)) {
                     outputCollection.add(item);
                 }
             }
         }
         return outputCollection;
     }
 
     /**
      * Selects all elements from inputCollection into an output and rejected collection,
      * based on the evaluation of the given predicate.
      * <p>
      * Elements matching the predicate are added to the {@code outputCollection},
      * all other elements are added to the {@code rejectedCollection}.
      * </p>
      * <p>
      * If the input predicate is {@code null}, no elements are added to
      * {@code outputCollection} or {@code rejectedCollection}.
      * </p>
      * <p>
      * Note: calling the method is equivalent to the following code snippet:
      * </p>
      * <pre>
      *   select(inputCollection, predicate, outputCollection);
      *   selectRejected(inputCollection, predicate, rejectedCollection);
      * </pre>
      *
      * @param <O>  the type of object the {@link Iterable} contains
      * @param <R>  the type of the output {@link Collection}
      * @param inputCollection  the collection to get the input from, may be null
      * @param predicate  the predicate to use, may be null
      * @param outputCollection  the collection to output selected elements into, may not be null if the
      *   inputCollection and predicate are not null
      * @param rejectedCollection  the collection to output rejected elements into, may not be null if the
      *   inputCollection or predicate are not null
      * @return the outputCollection
      * @since 4.1
      */
     public static <O, R extends Collection<? super O>> R select(final Iterable<? extends O> inputCollection,
             final Predicate<? super O> predicate, final R outputCollection, final R rejectedCollection) {
 
         if (inputCollection != null && predicate != null) {
             for (final O element : inputCollection) {
                 if (predicate.evaluate(element)) {
                     outputCollection.add(element);
                 } else {
                     rejectedCollection.add(element);
                 }
             }
         }
         return outputCollection;
     }
 
     /**
      * Selects all elements from inputCollection which don't match the given
      * predicate into an output collection.
      * <p>
      * If the input predicate is {@code null}, the result is an empty
      * list.
      * </p>
      *
      * @param <O>  the type of object the {@link Iterable} contains
      * @param inputCollection  the collection to get the input from, may not be null
      * @param predicate  the predicate to use, may be null
      * @return the elements <b>not</b> matching the predicate (new list)
      */
     public static <O> Collection<O> selectRejected(final Iterable<? extends O> inputCollection,
                                                    final Predicate<? super O> predicate) {
         int size = 0;
         if (null != inputCollection) {
             size = inputCollection instanceof Collection<?> ? ((Collection<?>) inputCollection).size() : 0;
         }
         final Collection<O> answer = size == 0 ? new ArrayList<>() : new ArrayList<>(size);
         return selectRejected(inputCollection, predicate, answer);
     }
 
     /**
      * Selects all elements from inputCollection which don't match the given
      * predicate and adds them to outputCollection.
      * <p>
      * If the input predicate is {@code null}, no elements are added to
      * {@code outputCollection}.
      * </p>
      *
      * @param <O>  the type of object the {@link Iterable} contains
      * @param <R>  the type of the output {@link Collection}
      * @param inputCollection  the collection to get the input from, may be null
      * @param predicate  the predicate to use, may be null
      * @param outputCollection  the collection to output into, may not be null if the inputCollection
      *   and predicate or not null
      * @return outputCollection
      */
     public static <O, R extends Collection<? super O>> R selectRejected(final Iterable<? extends O> inputCollection,
             final Predicate<? super O> predicate, final R outputCollection) {
 
         if (inputCollection != null && predicate != null) {
             for (final O item : inputCollection) {
                 if (!predicate.evaluate(item)) {
                     outputCollection.add(item);
                 }
             }
         }
         return outputCollection;
     }
 
     /**
      * Gets the size of the collection/iterator specified.
      * <p>
      * This method can handles objects as follows
      * </p>
      * <ul>
      * <li>Collection - the collection size
      * <li>Map - the map size
      * <li>Array - the array size
      * <li>Iterator - the number of elements remaining in the iterator
      * <li>Enumeration - the number of elements remaining in the enumeration
      * </ul>
      *
      * @param object  the object to get the size of, may be null
      * @return the size of the specified collection or 0 if the object was null
      * @throws IllegalArgumentException thrown if object is not recognized
      * @since 3.1
      */
     public static int size(final Object object) {
         if (object == null) {
             return 0;
         }
         int total = 0;
         if (object instanceof Map<?, ?>) {
             total = ((Map<?, ?>) object).size();
         } else if (object instanceof Collection<?>) {
             total = ((Collection<?>) object).size();
         } else if (object instanceof Iterable<?>) {
             total = IterableUtils.size((Iterable<?>) object);
         } else if (object instanceof Object[]) {
             total = ((Object[]) object).length;
         } else if (object instanceof Iterator<?>) {
             total = IteratorUtils.size((Iterator<?>) object);
         } else if (object instanceof Enumeration<?>) {
             final Enumeration<?> it = (Enumeration<?>) object;
             while (it.hasMoreElements()) {
                 total++;
                 it.nextElement();
             }
         } else {
             try {
                 total = Array.getLength(object);
             } catch (final IllegalArgumentException ex) {
                 throw new IllegalArgumentException("Unsupported object type: " + object.getClass().getName());
             }
         }
         return total;
     }
 
     /**
      * Checks if the specified collection/array/iterator is empty.
      * <p>
      * This method can handles objects as follows
      * </p>
      * <ul>
      * <li>Collection - via collection isEmpty
      * <li>Map - via map isEmpty
      * <li>Array - using array size
      * <li>Iterator - via hasNext
      * <li>Enumeration - via hasMoreElements
      * </ul>
      * <p>
      * Note: This method is named to avoid clashing with
      * {@link #isEmpty(Collection)}.
      * </p>
      *
      * @param object  the object to get the size of, may be null
      * @return true if empty or null
      * @throws IllegalArgumentException thrown if object is not recognized
      * @since 3.2
      */
     public static boolean sizeIsEmpty(final Object object) {
         if (object == null) {
             return true;
         }
         if (object instanceof Collection<?>) {
             return ((Collection<?>) object).isEmpty();
         }
         if (object instanceof Iterable<?>) {
             return IterableUtils.isEmpty((Iterable<?>) object);
         }
         if (object instanceof Map<?, ?>) {
             return ((Map<?, ?>) object).isEmpty();
         }
         if (object instanceof Object[]) {
             return ((Object[]) object).length == 0;
         }
         if (object instanceof Iterator<?>) {
             return !((Iterator<?>) object).hasNext();
         }
         if (object instanceof Enumeration<?>) {
             return !((Enumeration<?>) object).hasMoreElements();
         }
         try {
             return Array.getLength(object) == 0;
         } catch (final IllegalArgumentException ex) {
             throw new IllegalArgumentException("Unsupported object type: " + object.getClass().getName());
         }
     }
 
     /**
      * Returns a new {@link Collection} containing {@code <i>a</i> - <i>b</i>}.
      * The cardinality of each element <i>e</i> in the returned {@link Collection}
      * will be the cardinality of <i>e</i> in <i>a</i> minus the cardinality
      * of <i>e</i> in <i>b</i>, or zero, whichever is greater.
      *
      * @param a  the collection to subtract from, must not be null
      * @param b  the collection to subtract, must not be null
      * @param <O> the generic type that is able to represent the types contained
      *        in both input collections.
      * @return a new collection with the results
      * @see Collection#removeAll
      */
     public static <O> Collection<O> subtract(final Iterable<? extends O> a, final Iterable<? extends O> b) {
         final Predicate<O> p = TruePredicate.truePredicate();
         return subtract(a, b, p);
     }
 
     /**
      * Returns a new {@link Collection} containing <i>a</i> minus a subset of
      * <i>b</i>.  Only the elements of <i>b</i> that satisfy the predicate
      * condition, <i>p</i> are subtracted from <i>a</i>.
      *
      * <p>
      * The cardinality of each element <i>e</i> in the returned {@link Collection}
      * that satisfies the predicate condition will be the cardinality of <i>e</i> in <i>a</i>
      * minus the cardinality of <i>e</i> in <i>b</i>, or zero, whichever is greater.
      * </p>
      * <p>
      * The cardinality of each element <i>e</i> in the returned {@link Collection} that does <b>not</b>
      * satisfy the predicate condition will be equal to the cardinality of <i>e</i> in <i>a</i>.
      * </p>
      *
      * @param a  the collection to subtract from, must not be null
      * @param b  the collection to subtract, must not be null
      * @param p  the condition used to determine which elements of <i>b</i> are
      *        subtracted.
      * @param <O> the generic type that is able to represent the types contained
      *        in both input collections.
      * @return a new collection with the results
      * @throws NullPointerException if either collection or p is null
      * @since 4.0
      * @see Collection#removeAll
      */
     public static <O> Collection<O> subtract(final Iterable<? extends O> a,
                                              final Iterable<? extends O> b,
                                              final Predicate<O> p) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         Objects.requireNonNull(p, "p");
         final ArrayList<O> list = new ArrayList<>();
         final HashBag<O> bag = new HashBag<>();
         for (final O element : b) {
             if (p.evaluate(element)) {
                 bag.add(element);
             }
         }
         for (final O element : a) {
             if (!bag.remove(element, 1)) {
                 list.add(element);
             }
         }
         return list;
     }
 
     /**
      * Returns a synchronized collection backed by the given collection.
      * <p>
      * You must manually synchronize on the returned buffer's iterator to
      * avoid non-deterministic behavior:
      * </p>
      * <pre>
      * Collection c = CollectionUtils.synchronizedCollection(myCollection);
      * synchronized (c) {
      *     Iterator i = c.iterator();
      *     while (i.hasNext()) {
      *         process (i.next());
      *     }
      * }
      * </pre>
      * <p>
      * This method uses the implementation in the decorators subpackage.
      * </p>
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection to synchronize, must not be null
      * @return a synchronized collection backed by the given collection
      * @throws NullPointerException if the collection is null
      * @deprecated since 4.1, use {@link java.util.Collections#synchronizedCollection(Collection)} instead
      */
     @Deprecated
     public static <C> Collection<C> synchronizedCollection(final Collection<C> collection) {
         Objects.requireNonNull(collection, "collection");
         return SynchronizedCollection.synchronizedCollection(collection);
     }
 
     /**
      * Transform the collection by applying a Transformer to each element.
      * <p>
      * If the input collection or transformer is null, there is no change made.
      * </p>
      * <p>
      * This routine is best for Lists, for which set() is used to do the
      * transformations "in place." For other Collections, clear() and addAll()
      * are used to replace elements.
      * </p>
      * <p>
      * If the input collection controls its input, such as a Set, and the
      * Transformer creates duplicates (or are otherwise invalid), the collection
      * may reduce in size due to calling this method.
      * </p>
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the {@link Collection} to get the input from, may be null
      * @param transformer  the transformer to perform, may be null
      */
     public static <C> void transform(final Collection<C> collection,
                                      final Transformer<? super C, ? extends C> transformer) {
 
         if (collection != null && transformer != null) {
             if (collection instanceof List<?>) {
                 final List<C> list = (List<C>) collection;
                 for (final ListIterator<C> it = list.listIterator(); it.hasNext();) {
                     it.set(transformer.transform(it.next()));
                 }
             } else {
                 final Collection<C> resultCollection = collect(collection, transformer);
                 collection.clear();
                 collection.addAll(resultCollection);
             }
         }
     }
 
     /**
      * Returns a transformed bag backed by the given collection.
      * <p>
      * Each object is passed through the transformer as it is added to the
      * Collection. It is important not to use the original collection after invoking this
      * method, as it is a backdoor for adding untransformed objects.
      * </p>
      * <p>
      * Existing entries in the specified collection will not be transformed.
      * If you want that behavior, see {@link TransformedCollection#transformedCollection}.
      * </p>
      *
      * @param <E> the type of object the {@link Collection} contains
      * @param collection  the collection to predicate, must not be null
      * @param transformer  the transformer for the collection, must not be null
      * @return a transformed collection backed by the given collection
      * @throws NullPointerException if the collection or transformer is null
      */
     public static <E> Collection<E> transformingCollection(final Collection<E> collection,
             final Transformer<? super E, ? extends E> transformer) {
         Objects.requireNonNull(collection, "collection");
         Objects.requireNonNull(transformer, "transformer");
         return TransformedCollection.transformingCollection(collection, transformer);
     }
 
     /**
      * Returns a {@link Collection} containing the union of the given
      * {@link Iterable}s.
      * <p>
      * The cardinality of each element in the returned {@link Collection} will
      * be equal to the maximum of the cardinality of that element in the two
      * given {@link Iterable}s.
      * </p>
      *
      * @param a the first collection, must not be null
      * @param b the second collection, must not be null
      * @param <O> the generic type that is able to represent the types contained
      *        in both input collections.
      * @return the union of the two collections
      * @throws NullPointerException if either collection is null
      * @see Collection#addAll
      */
     public static <O> Collection<O> union(final Iterable<? extends O> a, final Iterable<? extends O> b) {
         Objects.requireNonNull(a, "a");
         Objects.requireNonNull(b, "b");
         final SetOperationCardinalityHelper<O> helper = new SetOperationCardinalityHelper<>(a, b);
         for (final O obj : helper) {
             helper.setCardinality(obj, helper.max(obj));
         }
         return helper.list();
     }
 
     /**
      * Returns an unmodifiable collection backed by the given collection.
      * <p>
      * This method uses the implementation in the decorators subpackage.
      * </p>
      *
      * @param <C>  the type of object the {@link Collection} contains
      * @param collection  the collection to make unmodifiable, must not be null
      * @return an unmodifiable collection backed by the given collection
      * @throws NullPointerException if the collection is null
      * @deprecated since 4.1, use {@link java.util.Collections#unmodifiableCollection(Collection)} instead
      */
     @Deprecated
     public static <C> Collection<C> unmodifiableCollection(final Collection<? extends C> collection) {
         Objects.requireNonNull(collection, "collection");
         return UnmodifiableCollection.unmodifiableCollection(collection);
     }
 
     /**
      * Don't allow instances.
      */
     private CollectionUtils() {}
 }