1class Material:
  2    """
  3    Define a material with a given mass and calculate its volume using a predefined density.
  4    """
  5    def __init__(self, mass):
  6        self.mass = mass
  7 
  8    @property
  9    def volume(self):
 10        return self.mass / self.DENSITY
 11 
 12 
 13class Concrete(Material):
 14    DENSITY = 2500
 15 
 16 
 17class Brick(Material):
 18    DENSITY = 2000
 19 
 20 
 21class Stone(Material):
 22    DENSITY = 1600
 23 
 24 
 25class Wood(Material):
 26    DENSITY = 600
 27 
 28 
 29class Steel(Material):
 30    DENSITY = 7700
 31 
 32 
 33class Factory:
 34    """
 35    Manage the creation and combination of materials while enforcing reuse and uniqueness rules.
 36    """
 37    _used_instances = []
 38 
 39    _dynamic_classes = {}
 40 
 41    _all_factories = []
 42 
 43    _all_base_materials = {
 44        "Concrete": Concrete,
 45        "Brick": Brick,
 46        "Stone": Stone,
 47        "Wood": Wood,
 48        "Steel": Steel,
 49    }
 50 
 51    def __init__(self):
 52        self._created_materials = []
 53        self._all_factories.append(self) 
 54 
 55    def __call__(self, *args, **kwargs):
 56        if not args and not kwargs:
 57            raise ValueError("Cannot have an instance without an argument or arguments.")
 58        if args and kwargs:
 59            raise ValueError("There cannot be an instance with a mixture of positional and named arguments.")
 60 
 61        if args:
 62            return self._create_from_args(*args)
 63        return self._create_from_kwargs(**kwargs)
 64 
 65    def _create_from_args(self, *args):
 66        if not self._validate_unused_materials(args):
 67            raise AssertionError("One or more materials have been used.")
 68        self._used_instances.extend(args)
 69 
 70        components = {}
 71 
 72        for material in args:
 73            material_name = material.__class__.__name__
 74            if material_name in self._all_base_materials.keys():
 75                components[material_name] = self._all_base_materials[material_name]
 76            else:
 77                class_components = material.__class__.__name__.split("_")
 78                for component_name in class_components:
 79                    components[component_name] = self._all_base_materials[component_name]
 80 
 81        class_name = "_".join(sorted(components.keys()))
 82 
 83        if class_name not in self._dynamic_classes.keys():
 84            self._create_dynamic_material(class_name, components)
 85 
 86        total_mass = 0
 87        for material in args:
 88            total_mass += material.mass
 89        new_material = self._dynamic_classes[class_name](total_mass)
 90        self._created_materials.append(new_material)
 91        return new_material
 92 
 93    def _create_from_kwargs(self, **kwargs):
 94        created_instances = []
 95        for name, mass in kwargs.items():
 96            if not self._validate_material_name(name):
 97                raise ValueError("Invalid material name")
 98            if name in self._all_base_materials:
 99                material_class = self._all_base_materials[name](mass)
100                created_instances.append(material_class)
101            elif name in self._dynamic_classes:
102                material_class = self._dynamic_classes[name](mass)
103                created_instances.append(material_class)
104 
105        self._created_materials.extend(created_instances)
106        return tuple(created_instances)
107 
108    def _create_dynamic_material(self, name, components):
109        total_density = 0
110        for current in components.values():
111            total_density += current.DENSITY
112 
113        if len(components):
114            num_components = len(components)
115        else:
116            num_components = 1
117        average_density = total_density / num_components
118
119        dynamic_material = type(name,
120                                (Material,), 
121                                {
122                                    'DENSITY': average_density 
123                                }
124                            )
125        self._dynamic_classes[name] = dynamic_material
126 
127    def _validate_unused_materials(self, materials):
128        return all(material not in self._used_instances for material in materials)
129 
130    def _validate_material_name(self, name):
131        return name in self._all_base_materials or name in self._dynamic_classes
132 
133    def can_build(self, wall_volume):
134        current_volume = 0
135        for material in self._created_materials:
136            if material not in self._used_instances:
137                current_volume += material.volume
138        return current_volume >= wall_volume
139 
140    @classmethod
141    def can_build_together(cls, wall_volume):
142        total_volume = 0
143        for factory in cls._all_factories:
144            for material in factory._created_materials:
145                if material not in cls._used_instances:
146                    total_volume += material.volume
147        return total_volume >= wall_volume
148