* the end).
   *
   * @throws IllegalArgumentException if {@code n < 0}
   */
  public static BigInteger factorial(int n) {
    checkNonNegative("n", n);

    // If the factorial is small enough, just use LongMath to do it.
    if (n < LongMath.factorials.length) {
      return BigInteger.valueOf(LongMath.factorials[n]);
    }

    // Pre-allocate space for our list of intermediate BigIntegers.

<div class="termy">

```console
$ bash scripts/format.sh
```

</div>

Es sortiert auch alle Ihre Importe automatisch.

Damit es sie richtig sortiert, muss FastAPI lokal in Ihrer Umgebung installiert sein, mit dem Befehl vom obigen Abschnitt, welcher `-e` verwendet.

## Dokumentation

* Dla żądania `PUT` z ścieżką `/items/{item_id}`, odczyta treść żądania jako JSON:
    * Sprawdzi czy posiada wymagany atrybut `name`, który powinien być typu `str`.
    * Sprawdzi czy posiada wymagany atrybut `price`, który musi być typu `float`.
    * Sprawdzi czy posiada opcjonalny atrybut `is_offer`, który (jeżeli obecny) powinien być typu `bool`.
    * To wszystko będzie również działać dla głęboko zagnieżdżonych obiektów JSON.

    } catch (SecurityException expected) {
    }
    ClassPath classPath = ClassPath.from(getClass().getClassLoader());
    // ClassPath may contain resources from the boot class loader; just not from the class path.
    for (ResourceInfo resource : classPath.getResources()) {
      assertThat(resource.getResourceName()).doesNotContain("com/google/common/reflect/");
    }
  }

        };
    ListeningScheduledExecutorService service = listeningDecorator(delegate);
    ListenableFuture<Integer> future = service.schedule(Callables.returning(42), 1, MILLISECONDS);

    /*
     * Wait not just until the Future's value is set (as in future.get()) but
     * also until ListeningScheduledExecutorService's wrapper task is done
     * executing listeners, as detected by yielding control to afterExecute.
     */

   * package, that explicitly implements {@link Object#equals}. For a class {@code C}:
   *
   * <ul>
   *   <li>The visible constructor or visible static factory method with the most parameters is used
   *       to construct the sample instances. In case of tie, the candidate constructors or
   *       factories are tried one after another until one can be used to construct sample
   *       instances.

border-radius to keep list group items edge-to-edge. Most\n// useful within other components (e.g., cards).\n\n.list-group-flush {\n  @include border-radius(0);\n\n  > .list-group-item {\n    border-width: 0 0 $list-group-border-width;\n\n    &:last-child {\n      border-bottom-width: 0;\n    }\n  }\n}\n\n\n// Contextual variants\n//\n// Add modifier classes to change text and background color on individual items.\n// Organizationally, this must come after the `:hover` states.\n\n@each $color, $value...

     * requires us to define extra classes -- unfortunate under Android.) *Then* we could consider
     * lying about the fields below on the grounds that we always initialize them just after the
     * constructor -- an example of the kind of lying that our hypothetical bytecode rewriter would
     * already have to deal with, thanks to DI frameworks that perform field and method injection,

///

## Weitere Details zu `SecurityScopes`.

Sie können `SecurityScopes` an jeder Stelle und an mehreren Stellen verwenden, es muss sich nicht in der „Wurzel“-Abhängigkeit befinden.

```Python hl_lines="5-10  16  21" title="app/routers/items.py"
{!../../docs_src/bigger_applications/app/routers/items.py!}
```

Da der Pfad jeder *Pfadoperation* mit `/` beginnen muss, wie in:

```Python hl_lines="1"
@router.get("/{item_id}")
async def read_item(item_id: str):
    ...
```

... darf das Präfix kein abschließendes `/` enthalten.