1class Material:
  2    def __init__(self, mass):
  3        self.mass = mass
  4        self._used = False  
  5
  6    @property
  7    def volume(self):
  8        return self.mass / self._density
  9
 10    def mark_used(self):
 11        if self._used:
 12            raise AssertionError("Material already used.")
 13        self._used = True
 14
 15
 16class Concrete(Material):
 17    _density = 2500
 18
 19
 20class Brick(Material):
 21    _density = 2000
 22
 23
 24class Stone(Material):
 25    _density = 1600
 26
 27
 28class Wood(Material):
 29    _density = 600
 30
 31
 32class Steel(Material):
 33    _density = 7700
 34
 35
 36class Factory:
 37    _registry = { "Concrete": Concrete,
 38    "Brick": Brick,
 39    "Stone": Stone,
 40    "Wood": Wood,
 41    "Steel": Steel,}
 42
 43    _all_factories = []
 44
 45    def __init__(self):
 46        self.materials = []
 47        Factory._all_factories.append(self)
 48
 49    def __call__(self, *args, **kwargs): 
 50        if args and kwargs:
 51            raise ValueError("Cannot mix positional and keyword arguments.")
 52        if not args and not kwargs:
 53            raise ValueError("Must provide either positional or keyword arguments.")
 54
 55        if kwargs:
 56            return self._handle_named_args(kwargs)
 57        else:
 58            return self._handle_positional_args(args)
 59
 60    def _handle_named_args(self, kwargs):
 61        results = []
 62        for name, mass in kwargs.items():
 63            if name not in Factory._registry:
 64                raise ValueError(f"Invalid material name: {name}")
 65            material_class = Factory._registry[name]
 66            instance = material_class(mass)
 67            self.materials.append(instance)
 68            results.append(instance)
 69        return tuple(results)
 70
 71    def _handle_positional_args(self, args):
 72        for material in args:
 73            material.mark_used()
 74
 75        material_classes = []
 76        for material in args:
 77            if "_" in material.__class__.__name__:  
 78                material_classes.extend(material.__class__.__name__.split("_"))
 79            else:
 80                material_classes.append(material.__class__.__name__)
 81    
 82    
 83        class_name = "_".join(sorted(set(material_classes)))
 84
 85        if class_name not in Factory._registry:
 86            densities = [cls._density for cls in set(type(material) for material in args)]
 87            avg_density = sum(densities) / len(densities)
 88
 89            class DynamicMaterial(Material):
 90                _density = avg_density
 91
 92            DynamicMaterial.__name__ = class_name
 93            Factory._registry[class_name] = DynamicMaterial
 94
 95        new_material_class = Factory._registry[class_name]
 96        total_mass = sum(material.mass for material in args)
 97        instance = new_material_class(total_mass)
 98        self.materials.append(instance)
 99        return instance
100
101    def can_build(self, volume):
102        total_volume = sum(material.volume for material in self.materials if not material._used)
103        return total_volume >= volume
104
105    @classmethod
106    def can_build_together(cls, volume):
107        total_volume = sum(
108            material.volume
109            for factory in cls._all_factories 
110            for material in factory.materials
111            if not material._used
112        )
113        return total_volume >= volume