// vol. 2, Knuth, 4.2.2, (16) to the two-variable case. We have two value series x_i and y_i.
    // We define the arithmetic means X_n = 1/n \sum_{i=1}^n x_i, and Y_n = 1/n \sum_{i=1}^n y_i.
    // We also define the sum of the products of the differences from the means
    //           C_n = \sum_{i=1}^n x_i y_i - n X_n Y_n
    // for all n >= 1. Then for all n > 1:

   * first decrementing to zero, and then removing. putIfAbsent or replace could observe the
   * intermediate zero-state. Ways we could deal with this are:
   *
   * - Don't define any of the ConcurrentMap operations. This is the current state of affairs.
   *
   * - Define putIfAbsent and replace as treating zero and absent identically (as currently
   *   implemented below). This is a bit surprising with putIfAbsent, which really becomes

    return requireLinks()[i];
  }

  private void setLink(int i, long value) {
    requireLinks()[i] = value;
  }

  /*
   * We don't define getPredecessor+getSuccessor and setPredecessor+setSuccessor here because
   * they're defined above -- including logic to add and subtract 1 to map between the values stored
   * in the predecessor/successor arrays and the indexes in the elements array that they identify.
   */

    SUBMULTISET,
    DESCENDING;

    @Override
    public Set<Feature<? super Void>> getImpliedFeatures() {
      return Collections.emptySet();
    }
  }

  /** Two bounds (from and to) define how to build a subMultiset. */
  enum Bound {
    INCLUSIVE,
    EXCLUSIVE,
    NO_BOUND;
  }

  List<TestSuite> createDerivedSuites(SortedMultisetTestSuiteBuilder<E> parentBuilder) {

    SUBMULTISET,
    DESCENDING;

    @Override
    public Set<Feature<? super Void>> getImpliedFeatures() {
      return Collections.emptySet();
    }
  }

  /** Two bounds (from and to) define how to build a subMultiset. */
  enum Bound {
    INCLUSIVE,
    EXCLUSIVE,
    NO_BOUND;
  }

  List<TestSuite> createDerivedSuites(SortedMultisetTestSuiteBuilder<E> parentBuilder) {

     * a given entry might not include null. The right fix for the header problems is probably to
     * define a separate MultimapLink interface with a separate "header" implementation, which
     * hopefully could avoid implementing Entry or ValueSetLink at all. (But note that that approach
     * requires us to define extra classes -- unfortunate under Android.) *Then* we could consider

    return requireLinks()[i];
  }

  private void setLink(int i, long value) {
    requireLinks()[i] = value;
  }

  /*
   * We don't define getPredecessor+getSuccessor and setPredecessor+setSuccessor here because
   * they're defined above -- including logic to add and subtract 1 to map between the values stored
   * in the predecessor/successor arrays and the indexes in the elements array that they identify.
   */

    return requireNonNull(predecessor);
  }

  private int[] requireSuccessors() {
    return requireNonNull(successor);
  }

  /*
   * We don't define getPredecessor+getSuccessor and setPredecessor+setSuccessor here because
   * they're defined above -- including logic to add and subtract 1 to map between the values stored
   * in the predecessor/successor arrays and the indexes in the elements array that they identify.
   */

    return requireNonNull(predecessor);
  }

  private int[] requireSuccessors() {
    return requireNonNull(successor);
  }

  /*
   * We don't define getPredecessor+getSuccessor and setPredecessor+setSuccessor here because
   * they're defined above -- including logic to add and subtract 1 to map between the values stored
   * in the predecessor/successor arrays and the indexes in the elements array that they identify.
   */

 * that associates each key with a collection of values. All methods of {@link Multimap} are
 * supported, including those specified as optional in the interface.
 *
 * <p>To implement a multimap, a subclass must define the method {@link #createCollection()}, which
 * creates an empty collection of values for a key.
 *
 * <p>The multimap constructor takes a map that has a single entry for each distinct key. When you