class SetsDict:
    def __init__(self):
        self._data: dict[str, set] = dict()

    def add(self, key, value):
        if key not in self._data: self._data[key] = set()
        if value not in self._data[key]: self._data[key].add(value)

    def delete(self, key, value):
        if self._data.get(key, None): self._data[key].remove(value)

    @property
    def index(self):
        res = set()
        for key, collection in self._data.items():
            for elem in collection:
                if elem not in res:
                    res.add(elem)
        return res

    def by_key(self, key):
        return self._data.get(key, None)

    @property
    def keys(self): return self._data.keys()