return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

            .size());

    // Almost force an overflow in the binomial coefficient calculation
    assertEquals(
        1391975640 /*C(34,14)*/,
        Collections2.orderedPermutations(concat(nCopies(20, 1), nCopies(14, 2))).size());
    // Do force an overflow in the binomial coefficient calculation
    assertEquals(
        Integer.MAX_VALUE,

        int m = (end + start) >>> 1;
        return listProduct(nums, start, m).multiply(listProduct(nums, m, end));
    }
  }

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, that is, {@code n! / (k! (n - k)!)}.
   *
   * <p><b>Warning:</b> the result can take as much as <i>O(k log n)</i> space.
   *

    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18 * 19 * 20
  };

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, or {@link Long#MAX_VALUE} if the result does not fit in a {@code long}.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0}, or {@code k > n}
   */

- **I/O Operations** (`org.codelibs.core.io`) - File handling, resource management, stream utilities, and traversal utilities for efficient resource processing
- **Reflection** (`org.codelibs.core.lang`) - Class loading, method/field access, type introspection utilities, and generics support

  }

  /**
   * A sensible, albeit inefficient, definition of {@link #size} in terms of {@link #entrySet}. If
   * you override {@link #entrySet}, you may wish to override {@link #size} to forward to this
   * implementation.
   *
   * @since 7.0
   */
  protected int standardSize() {
    return Multisets.linearTimeSizeImpl(this);
  }

  /**
   * A sensible, albeit inefficient, definition of {@link #equals} in terms of {@code

   * to this implementation.
   *
   * @since 7.0
   */
  protected void standardPutAll(Map<? extends K, ? extends V> map) {
    Maps.putAllImpl(this, map);
  }

  /**
   * A sensible, albeit inefficient, definition of {@link #remove} in terms of the {@code iterator}
   * method of {@link #entrySet}. If you override {@link #entrySet}, you may wish to override {@link
   * #remove} to forward to this implementation.
   *

@GwtCompatible
public final class Utf8 {
  /**
   * Returns the number of bytes in the UTF-8-encoded form of {@code sequence}. For a string, this
   * method is equivalent to {@code string.getBytes(UTF_8).length}, but is more efficient in both
   * time and space.
   *
   * @throws IllegalArgumentException if {@code sequence} contains ill-formed UTF-16 (unpaired
   *     surrogates)
   */
  public static int encodedLength(CharSequence sequence) {

          @Override
          protected char @Nullable [] escape(int cp) {
            return ('a' <= cp && cp <= 'z') ? new char[] {Character.toUpperCase((char) cp)} : null;
          }

          // Inefficient implementation that defines all letters as escapable.
          @Override
          protected int nextEscapeIndex(CharSequence csq, int index, int end) {