You are given a simple hierarchy where Director extends Cast. Implement a robust, testable solution that avoids common Python pitfalls and demonstrates correct use of @property, @classmethod, and @staticmethod. Starting point: class Cast: def __init__(self, actors: list[str]): self.actors = list(actors) class Director(Cast): def __init__(self, name: str, actors: list[str], movies: list[str]): super().__init__(actors) self.name = name self.movies = list(movies) self._awards: list[tuple[str,int]] = [] # (award_name, year) Tasks: 1) Implement add_award(award_name: str, year: int) that appends a new (award_name, year) pair only if it does not already exist for this director (idempotent). Ensure no mutable-default arguments and that self._awards cannot be mutated from outside the class. 2) Add a property awards that returns an immutable, chronologically sorted view of awards; add a property latest_award that returns Optional[tuple[str,int]]. 3) Add a @staticmethod validate_award(award_name: str, year: int) that raises ValueError for empty names or years outside [1900, current_year]. Use it inside add_award. 4) Add a @classmethod from_filmography(cls, name: str, filmography: dict) that constructs a Director from {'actors': [...], 'movies': [...]}. Show how subclassing would work if you later create an AwardWinningDirector that adds fields like guild_membership. 5) Implement __eq__ and __hash__ so that two Director instances with the same name compare equal. Explain the trade-offs of this choice. 6) Provide a short doctest-style example demonstrating creation, adding duplicate awards, and the latest_award property.