1class Material:
  2    DENSITY = None
  3    def __init__(self, mass):
  4        self.mass = mass
  5       
  6    @property    
  7    def volume(self):
  8        return self.mass / self.DENSITY
  9    
 10
 11class Concrete(Material):
 12    DENSITY = 2500
 13
 14
 15class Brick(Material):
 16    DENSITY = 2000
 17
 18
 19class Stone(Material):
 20    DENSITY = 1600
 21
 22
 23class Wood(Material):
 24    DENSITY = 600
 25
 26
 27class Steel(Material):
 28    DENSITY = 7700
 29
 30
 31class Factory:
 32    material_classes = {
 33            "Concrete": Concrete,
 34            "Brick": Brick,
 35            "Stone": Stone,
 36            "Wood": Wood,
 37            "Steel": Steel,
 38        }  # Shared across all factories, and here we also add the new created classes
 39    _invalid_instances = set()  # Shared across all factories
 40    _materials_created = []  # Tracks materials created by all factories
 41
 42    def __init__(self):
 43        self.local_materials = []  # Tracks materials created by this factory
 44
 45    def __call__(self, *args, **kwargs):
 46        if args and kwargs:
 47            raise ValueError("Cannot mix positional and named arguments.")
 48
 49        if not args and not kwargs:
 50            raise ValueError("No arguments provided.")
 51
 52        if kwargs:
 53            new_materials = self._handle_named_arguments(kwargs)
 54            # Register created materials
 55            self.local_materials.extend(new_materials)
 56            Factory._materials_created.extend(new_materials)
 57            
 58        else:
 59            new_materials = self._handle_positional_arguments(args)
 60            # Register created materials
 61            self.local_materials.append(new_materials)
 62            Factory._materials_created.append(new_materials)
 63
 64        return new_materials
 65
 66    def _handle_named_arguments(self, kwargs):
 67        result = []
 68        for name, mass in kwargs.items():
 69            not_in_material_classes = name not in Factory.material_classes
 70            
 71
 72            if not_in_material_classes:
 73                raise ValueError(f"Invalid material name: {name}")
 74
 75            material_class = self.material_classes.get(name) 
 76
 77            if material_class is None:
 78                material_class = Factory.material_classes[name]
 79            
 80            result.append(material_class(mass))
 81        return tuple(result)
 82
 83    def _handle_positional_arguments(self, args):
 84        for arg in args:
 85            if arg in Factory._invalid_instances:
 86                raise AssertionError("This material has already been used and is now invalid.")
 87
 88        all_material_names = [
 89            mat_name 
 90            for arg in args 
 91            for mat_name in arg.__class__.__name__.split('_')
 92        ]
 93        all_material_names.sort()
 94        class_name = "_".join(mat_name for mat_name in all_material_names)
 95
 96        if class_name not in Factory.material_classes:
 97            densities = [arg.DENSITY for arg in args]
 98            DENSITY = sum(densities) / len(densities)
 99
100            DynamicMaterial = type(
101                class_name,  
102                (Material,),  
103                {"DENSITY": DENSITY},  
104            )
105            Factory.material_classes[class_name] = DynamicMaterial
106
107        new_class = Factory.material_classes[class_name]
108        total_mass = sum(arg.mass for arg in args)
109
110        # Mark used materials as invalid
111        Factory._invalid_instances.update(args)
112
113        return new_class(total_mass)
114
115    def can_build(self, volume: int) -> bool:
116        total_volume = sum(
117            material.volume 
118            for material in self.local_materials 
119            if material not in Factory._invalid_instances
120        )
121        return total_volume >= volume
122
123    @classmethod
124    def can_build_together(cls, volume: int) -> bool:
125        total_volume = sum(
126            material.volume 
127            for material in cls._materials_created 
128            if material not in cls._invalid_instances
129        )
130        return total_volume >= volume