if user_id is None:
        return [{"item_id": "i1", "user_id": "u1"}, {"item_id": "i2", "user_id": "u2"}]
    else:
        return [{"item_id": "i2", "user_id": user_id}]


@item_router.get("/{item_id}")
def get_item(item_id: str, user_id: Optional[str] = None):
    if user_id is None:
        return {"item_id": item_id}
    else:
        return {"item_id": item_id, "user_id": user_id}

class User(BaseModel):
    username: str
    full_name: Union[str, None] = None


@app.put("/items/{item_id}")
async def update_item(
    item_id: int, item: Item, user: User, importance: Annotated[int, Body()]
):
    results = {"item_id": item_id, "item": item, "user": user, "importance": importance}

from datetime import datetime, time, timedelta
from typing import Annotated, Union
from uuid import UUID

from fastapi import Body, FastAPI

app = FastAPI()


@app.put("/items/{item_id}")
async def read_items(
    item_id: UUID,
    start_datetime: Annotated[datetime, Body()],
    end_datetime: Annotated[datetime, Body()],
    process_after: Annotated[timedelta, Body()],
    repeat_at: Annotated[Union[time, None], Body()] = None,
):

    )
    price: float = Field(gt=0, description="The price must be greater than zero")
    tax: float | None = None


@app.put("/items/{item_id}")
async def update_item(item_id: int, item: Annotated[Item, Body(embed=True)]):
    results = {"item_id": item_id, "item": item}

class User(BaseModel):
    username: str
    full_name: str | None = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Item,
    user: User,
    importance: Annotated[int, Body(gt=0)],
    q: str | None = None,
):
    results = {"item_id": item_id, "item": item, "user": user, "importance": importance}
    if q:
        results.update({"q": q})

class User(BaseModel):
    username: str
    full_name: Union[str, None] = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Item,
    user: User,
    importance: int = Body(gt=0),
    q: Union[str, None] = None,
):
    results = {"item_id": item_id, "item": item, "user": user, "importance": importance}
    if q:
        results.update({"q": q})

class User(BaseModel):
    username: str
    full_name: Union[str, None] = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Item,
    user: User,
    importance: Annotated[int, Body(gt=0)],
    q: Union[str, None] = None,
):
    results = {"item_id": item_id, "item": item, "user": user, "importance": importance}
    if q:
        results.update({"q": q})

class User(BaseModel):
    username: str
    full_name: Union[str, None] = None


@app.put("/items/{item_id}")
async def update_item(
    *,
    item_id: int,
    item: Item,
    user: User,
    importance: Annotated[int, Body(gt=0)],
    q: Union[str, None] = None,
):
    results = {"item_id": item_id, "item": item, "user": user, "importance": importance}
    if q:
        results.update({"q": q})

    except OwnerError as e:
        raise HTTPException(status_code=400, detail=f"Owner error: {e}")


@app.get("/items/{item_id}")
def get_item(item_id: str, username: str = Depends(get_username)):
    if item_id not in data:
        raise HTTPException(status_code=404, detail="Item not found")
    item = data[item_id]
    if item["owner"] != username:
        raise OwnerError(username)

    except OwnerError as e:
        raise HTTPException(status_code=400, detail=f"Owner error: {e}")


@app.get("/items/{item_id}")
def get_item(item_id: str, username: Annotated[str, Depends(get_username)]):
    if item_id not in data:
        raise HTTPException(status_code=404, detail="Item not found")
    item = data[item_id]
    if item["owner"] != username:
        raise OwnerError(username)