public final <S extends @Nullable T> Equivalence<Iterable<S>> pairwise() {
    // Ideally, the returned equivalence would support Iterable<? extends T>. However,
    // the need for this is so rare that it's not worth making callers deal with the ugly wildcard.
    return new PairwiseEquivalence<>(this);
  }

  /**
   * Returns a predicate that evaluates to true if and only if the input is equivalent to {@code

   *
   * if (guardExpression) {
   *    throw new BadException(badMsg(...));
   * }
   *
   * The alternative natural refactorings into void or Exception-returning methods are much slower.
   * This is a big deal - we're talking factors of 2-8 in microbenchmarks, not just 10-20%. (This is
   * a hotspot optimizer bug, which should be fixed, but that's a separate, big project).
   *

     * handling not just {@code Iterable<S>} instances, but also any {@code
     * Iterable<? extends S>}. However, the need for this comes up so rarely
     * that it doesn't justify making everyone else deal with the very ugly
     * wildcard.
     */
    return new LexicographicalOrdering<S>(this);
  }

  // Regular instance methods

  @Override

      // It's a weird formula, but tests prove it works.
      int adjust = size() - 1;
      for (int i = 0; i < axes.size(); i++) {
        adjust *= 31;
        adjust = ~~adjust;
        // in GWT, we have to deal with integer overflow carefully
      }
      int hash = 1;
      for (Set<E> axis : axes) {
        hash = 31 * hash + (size() / axis.size() * axis.hashCode());

        hash = ~~hash;
      }

   * k <= i < n}.
   *
   * <p>After this method returns, {@code elements} will contain no duplicates, but {@code elements}
   * may be the real array backing the returned set, so do not modify it further.
   *
   * <p>{@code elements} may contain only values of type {@code E}.
   *

  public int hashCode() {
    int hashCode = 1;
    int n = size();
    for (int i = 0; i < n; i++) {
      hashCode = 31 * hashCode + get(i).hashCode();

      hashCode = ~~hashCode;
      // needed to deal with GWT integer overflow
    }
    return hashCode;
  }

  /*
   * Serializes ImmutableLists as their logical contents. This ensures that