};

  /**
   * 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}
   */
  public static long binomial(int n, int k) {
    checkNonNegative("n", n);

    /** Error code for request timeout. */
    public static final String ERROR_TIMEOUT = "timeout";

    /** Error code for context length exceeded. */
    public static final String ERROR_CONTEXT_LENGTH_EXCEEDED = "context_length_exceeded";

    /** Error code for model not found. */
    public static final String ERROR_MODEL_NOT_FOUND = "model_not_found";

    /** Error code for invalid response from the LLM provider. */

    return max;
  }

  /**
   * Returns the value nearest to {@code value} which is within the closed range {@code [min..max]}.
   *
   * <p>If {@code value} is within the range {@code [min..max]}, {@code value} is returned
   * unchanged. If {@code value} is less than {@code min}, {@code min} is returned, and if {@code
   * value} is greater than {@code max}, {@code max} is returned.
   *

An optional prefix sets a non-decimal base: <code>0b</code> or <code>0B</code>
for binary, <code>0</code>, <code>0o</code>, or <code>0O</code> for octal,
and <code>0x</code> or <code>0X</code> for hexadecimal
[<a href="#Go_1.13">Go 1.13</a>].
A single <code>0</code> is considered a decimal zero.
In hexadecimal literals, letters <code>a</code> through <code>f</code>
and <code>A</code> through <code>F</code> represent values 10 through 15.
</p>

  }

  /**
   * Returns {@code true} if {@code target} is present as an element anywhere in {@code array}. Note
   * that this always returns {@code false} when {@code target} is {@code NaN}.
   *
   * @param array an array of {@code double} values, possibly empty
   * @param target a primitive {@code double} value
   * @return {@code true} if {@code array[i] == target} for some value of {@code i}
   */

 *
 * <p>With method references it is more succinct: {@code comparing(Foo::aString)} for example.
 *
 * <p>Using {@link Comparator} avoids certain types of bugs, for example when you meant to write
 * {@code .compare(a.foo, b.foo)} but you actually wrote {@code .compare(a.foo, a.foo)} or {@code
 * .compare(a.foo, b.bar)}. {@code ComparisonChain} also has a potential performance problem that

   * the two equal instances {@code ImmutableSet.of(1, 2)} and {@code ImmutableSet.of(2, 1)}.
   *
   * <p><b>Warning:</b> as with all function types in this package, avoid depending on the specific
   * {@code equals}, {@code hashCode} or {@code toString} behavior of the returned function. A
   * future migration to {@code java.util.function} will not preserve this behavior.
   *

   * first over all the elements of {@code set1}, then over each element of {@code set2}, in order,
   * that is not contained in {@code set1}.
   *
   * <p>Results are undefined if {@code set1} and {@code set2} are sets based on different
   * equivalence relations, for example if {@code set1} is a {@link HashSet} and {@code set2} is a
   * {@link TreeSet} or the {@link Map#keySet} of an {@code IdentityHashMap}.
   */

 *
 * @since 17.0
 */
@GwtCompatible
public final class Verify {
  /**
   * Ensures that {@code expression} is {@code true}, throwing a {@code VerifyException} with no
   * message otherwise.
   *
   * @throws VerifyException if {@code expression} is {@code false}
   * @see Preconditions#checkState Preconditions.checkState()
   */
  public static void verify(boolean expression) {

   * its runtime check.
   *
   * <p>An example use case for this method is in implementing an {@code Iterator<T>} whose {@code
   * next} field is lazily initialized. The type of that field would be {@code @Nullable T}, and the
   * code would be responsible for populating a "real" {@code T} (which might still be the value