* Returns every possible list that can be formed by choosing one element from each of the given
   * lists in order; the "n-ary <a href="http://en.wikipedia.org/wiki/Cartesian_product">Cartesian
   * product</a>" of the lists. For example:
   *
   * <pre>{@code
   * Lists.cartesianProduct(ImmutableList.of(
   *     ImmutableList.of(1, 2),
   *     ImmutableList.of("A", "B", "C")))
   * }</pre>
   *

System Libraries, or general-purpose tools or generally available free
programs which are used unmodified in performing those activities but
which are not part of the work.  For example, Corresponding Source
includes interface definition files associated with source files for
the work, and the source code for shared libraries and dynamically
linked subprograms that the work is specifically designed to require,

class Item(BaseModel):
    name: str
    description: Union[str, None] = None
    price: float
    tax: Union[float, None] = None

    model_config = {
        "json_schema_extra": {
            "examples": [
                {
                    "name": "Foo",
                    "description": "A very nice Item",
                    "price": 35.4,
                    "tax": 3.2,
                }
            ]

//  	CanonicalizedResource;
//
// CanonicalizedResource = [ SlashSeparator + Bucket ] +
//  	<HTTP-Request-URI, from the protocol name up to the query string> +
//  	[ subresource, if present. For example "?acl", "?location", "?logging", or "?torrent"];
//
// CanonicalizedProtocolHeaders = <described below>

// doesSignV2Match - Verify authorization header with calculated header in accordance with

app = FastAPI()


class Item(BaseModel):
    name: str
    description: Union[str, None] = None
    price: float
    tax: Union[float, None] = None

    class Config:
        schema_extra = {
            "examples": [
                {
                    "name": "Foo",
                    "description": "A very nice Item",
                    "price": 35.4,
                    "tax": 3.2,
                }
            ]

    price: float
    tax: Union[float, None] = None


@app.put("/items/{item_id}")
async def update_item(
    item_id: int,
    item: Annotated[
        Item,
        Body(
            examples=[
                {
                    "name": "Foo",
                    "description": "A very nice Item",
                    "price": 35.4,
                    "tax": 3.2,
                }
            ],

```Python hl_lines="6-7"
{!../../docs_src/path_params/tutorial001.py!}
```

The value of the path parameter `item_id` will be passed to your function as the argument `item_id`.

So, if you run this example and go to <a href="http://127.0.0.1:8000/items/foo" class="external-link" target="_blank">http://127.0.0.1:8000/items/foo</a>, you will see a response of:

```JSON
{"item_id":"foo"}
```

## Path parameters with types

    price: float
    tax: Union[float, None] = None


@app.put("/items/{item_id}")
async def update_item(
    item_id: int,
    item: Annotated[
        Item,
        Body(
            examples=[
                {
                    "name": "Foo",
                    "description": "A very nice Item",
                    "price": 35.4,
                    "tax": 3.2,
                }
            ],

///

### Before and after the `response`

You can add code to be run with the `request`,  before any *path operation* receives it.

And also after the `response` is generated, before returning it.

For example, you could add a custom header `X-Process-Time` containing the time in seconds that it took to process the request and generate a response:

```Python hl_lines="10  12-13"
{!../../docs_src/middleware/tutorial001.py!}
```

    price: float
    tax: Union[float, None] = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Annotated[
        Item,
        Body(
            examples=[
                {
                    "name": "Foo",
                    "description": "A very nice Item",
                    "price": 35.4,
                    "tax": 3.2,
                },
                {