Keep in mind that JSON only supports `str` as keys.

But Pydantic has automatic data conversion.

This means that, even though your API clients can only send strings as keys, as long as those strings contain pure integers, Pydantic will convert them and validate them.

And the `dict` you receive as `weights` will actually have `int` keys and `float` values.

///

## Recap { #recap }

        BigInteger halfSquare = sqrtFloor.pow(2).add(sqrtFloor);
        /*
         * We wish to test whether or not x <= (sqrtFloor + 0.5)^2 = halfSquare + 0.25. Since both x
         * and halfSquare are integers, this is equivalent to testing whether or not x <=
         * halfSquare.
         */
        return (halfSquare.compareTo(x) >= 0) ? sqrtFloor : sqrtFloor.add(BigInteger.ONE);
    }
    throw new AssertionError();

   * default rounding mode: if the two nearest representable values are equally near, the one with
   * the least significant bit zero is chosen. (In such cases, both of the nearest representable
   * values are even integers; this method returns the one that is a multiple of a greater power of
   * two.)
   *
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}

```sh
export MINIO_ROOT_USER=<ACCESS_KEY>
export MINIO_ROOT_PASSWORD=<SECRET_KEY>
minio server http://host{1...n}/export{1...m}
```

> **NOTE:** In above example `n` and `m` represent positive integers, _do not copy paste and expect it work make the changes according to local deployment and setup_.

   * href="http://mathworld.wolfram.com/PrimeNumber.html">prime number</a>: an integer <i>greater
   * than one</i> that cannot be factored into a product of <i>smaller</i> positive integers.
   * Returns {@code false} if {@code n} is zero, one, or a composite number (one which <i>can</i> be
   * factored into smaller positive integers).
   *
   * <p>To test larger numbers, use {@link BigInteger#isProbablePrime}.
   *

*    product                integers, floats, complex values
/    quotient               integers, floats, complex values
%    remainder              integers

&    bitwise AND            integers
|    bitwise OR             integers
^    bitwise XOR            integers
&^   bit clear (AND NOT)    integers

<<   left shift             integer << integer >= 0

    Integer nullInt = (Integer) null;
    Ordering<@Nullable Iterable<@Nullable Integer>> example =
        Ordering.<Integer>natural()
            .<Integer>nullsFirst()
            .<@Nullable Integer>reverse()
            .<@Nullable Integer>lexicographical()
            .reverse()
            .<Iterable<@Nullable Integer>>nullsLast();
    List<@Nullable Integer> list1 = new ArrayList<>();

    Integer nullInt = (Integer) null;
    Ordering<@Nullable Iterable<@Nullable Integer>> example =
        Ordering.<Integer>natural()
            .<Integer>nullsFirst()
            .<@Nullable Integer>reverse()
            .<@Nullable Integer>lexicographical()
            .reverse()
            .<Iterable<@Nullable Integer>>nullsLast();
    List<@Nullable Integer> list1 = new ArrayList<>();

   * reached, but not the other, the shorter iterable is considered to be less than the longer one.
   * For example, a lexicographical natural ordering over integers considers {@code [] < [1] < [1,
   * 1] < [1, 2] < [2]}.
   *
   * <p>Note that {@code Collections.reverseOrder(lexicographical(comparator))} is not equivalent to

 *
 * @author mike nonemacher
 */

@NullUnmarked
public class PopulatedCachesTest extends TestCase {
  // we use integers as keys; make sure the range covers some values that ARE cached by
  // Integer.valueOf(int), and some that are not cached. (127 is the highest cached value.)
  static final int WARMUP_MIN = 120;
  static final int WARMUP_MAX = 135;