private transient int[] nextInBucketVToK;

  /** The "entry" of the first element in insertion order. */
  private transient int firstInInsertionOrder;

  /** The "entry" of the last element in insertion order. */
  private transient int lastInInsertionOrder;

  /** Maps an "entry" to the "entry" that precedes it in insertion order. */
  private transient int[] prevInInsertionOrder;

    copyIntoArray(other, 0);
    return other;
  }

  /** If this collection is backed by an array of its elements in insertion order, returns it. */
  @Nullable Object @Nullable [] internalArray() {
    return null;
  }

  /**
   * If this collection is backed by an array of its elements in insertion order, returns the offset
   * where this collection's elements start.
   */
  int internalArrayStart() {

 */
class PropertiesTest {

    @Nested
    class OrderPreservationTests {

        @Test
        void testPropertiesOrderPreservedInImmutableModel() {
            // Create properties with specific insertion order using LinkedHashMap
            Map<String, String> orderedMap = new LinkedHashMap<>();
            orderedMap.put("third", "3");
            orderedMap.put("first", "1");
            orderedMap.put("second", "2");

   * order described in the <a href="#iteration">class documentation</a>.
   */
  public static <K, V> ImmutableMultimap<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3) {
    return ImmutableListMultimap.of(k1, v1, k2, v2, k3, v3);
  }

  /**
   * Returns an immutable multimap containing the given entries, in the "key-grouped" insertion

   * order described in the <a href="#iteration">class documentation</a>.
   */
  public static <K, V> ImmutableMultimap<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3) {
    return ImmutableListMultimap.of(k1, v1, k2, v2, k3, v3);
  }

  /**
   * Returns an immutable multimap containing the given entries, in the "key-grouped" insertion

     * @param opType The operation type (CREATE, INDEX, etc.).
     * @return The IndexResponse from OpenSearch.
     * @throws OpenSearchAccessException if the insertion fails.
     * @throws CrawlingAccessException if there's a conflict during insertion.
     */
    protected IndexResponse insert(final Object target, final OpType opType) {
        final String url = getUrl(target);
        if (url == null) {

   * specified access policy.
   *
   * @param capacity the capacity of this queue
   * @param fair if {@code true} then queue accesses for threads blocked on insertion or removal,
   *     are processed in FIFO order; if {@code false} the access order is unspecified.
   * @throws IllegalArgumentException if {@code capacity} is less than 1
   */

        }
      };
    }

    /** Uses an insertion-ordered hash-based {@code Set} to store value collections. */
    public SetMultimapBuilder<K0, @Nullable Object> linkedHashSetValues() {
      return linkedHashSetValues(DEFAULT_EXPECTED_VALUES_PER_KEY);
    }

    /**
     * Uses an insertion-ordered hash-based {@code Set} to store value collections, initialized to

  /**
   * {@inheritDoc}
   *
   * <p>The iterator generated by the returned collection traverses the values in the order they
   * were added to the multimap. Because the values may have duplicates and follow the insertion
   * ordering, this method returns a {@link List}, instead of the {@link Collection} specified in
   * the {@link ListMultimap} interface.
   */
  @Override
  public List<V> values() {

   */
  public long approximateElementCount() {
    long bitSize = bits.bitSize();
    long bitCount = bits.bitCount();

    /*
     * Each insertion is expected to reduce the # of clear bits by a factor of
     * `numHashFunctions/bitSize`. So, after n insertions, expected bitCount is `bitSize * (1 - (1 -
     * numHashFunctions/bitSize)^n)`. Solving that for n, and approximating `ln x` as `x - 1` when x