1class Material:
  2    """Parent class for defining a material."""
  3
  4    _DENSITY = 1
  5    made_of = None
  6
  7    def __init__(self, mass):
  8        self.mass = mass
  9        self.is_valid = True
 10
 11    @property
 12    def volume(self):
 13        return self.mass / self._DENSITY
 14
 15    def invalidate(self):
 16        self.is_valid = False
 17
 18
 19class Concrete(Material):
 20    """Define the material concrete."""
 21
 22    _DENSITY = 2500
 23    made_of = ("Concrete",)
 24
 25
 26class Brick(Material):
 27    """Define the material brick."""
 28
 29    _DENSITY = 2000
 30    made_of = ("Brick",)
 31
 32
 33class Stone(Material):
 34    """Define the material stone."""
 35
 36    _DENSITY = 1600
 37    made_of = ("Stone",)
 38
 39
 40class Wood(Material):
 41    """Define the material wood."""
 42
 43    _DENSITY = 600
 44    made_of = ("Wood",)
 45
 46
 47class Steel(Material):
 48    """Define the material steel."""
 49
 50    _DENSITY = 7700
 51    made_of = ("Steel",)
 52
 53
 54class Factory:
 55    """Factory for material production."""
 56
 57    allowed_materials = {
 58        "Concrete": Concrete,
 59        "Brick": Brick,
 60        "Stone": Stone,
 61        "Wood": Wood,
 62        "Steel": Steel
 63    }
 64
 65    all_created_materials = []
 66
 67    def __init__(self):
 68        self.created_materials = []
 69
 70    def __call__(self, *args, **kwargs):
 71        if args and kwargs:
 72            raise ValueError("Both arguments and keyword arguments cannot be provided.")
 73
 74        if not args and not kwargs:
 75            raise ValueError("What are you trying to do without materials?!")
 76
 77        if kwargs:
 78            try:
 79                materials = tuple(
 80                    self.allowed_materials[name](mass) for name, mass in kwargs.items()
 81                )
 82                self.created_materials.extend(list(materials))
 83                Factory.all_created_materials.extend(list(materials))
 84            except KeyError:
 85                raise ValueError("Material not found!")
 86            return materials
 87
 88        if args:
 89            if not all(isinstance(arg, tuple(self.allowed_materials.values()))
 90                       for arg in args):
 91                raise ValueError("All arguments must be instances of existing materials.")
 92            if not all(arg.is_valid for arg in args):
 93                raise AssertionError("All materials must be unused.")
 94
 95            for arg in args:
 96                arg.invalidate()
 97
 98            material_names = set()
 99            for arg in args:
100                material_names.update(type(arg).made_of)
101            material_names_inorder = sorted(list(material_names))
102            class_name = "_".join(material_names_inorder)
103
104            if class_name in Factory.allowed_materials:
105                alloy_class = Factory.allowed_materials[class_name]
106            else:
107                densities = [self.allowed_materials[name]._DENSITY
108                             for name in material_names]
109                avg_density = sum(densities) / len(densities)
110                class_attributes = {
111                    'made_of': tuple(material_names),
112                    '_DENSITY': avg_density
113                }
114                alloy_class = type(class_name, (Material,), class_attributes)
115                Factory.allowed_materials[class_name] = alloy_class
116
117            new_material = alloy_class(sum(arg.mass for arg in args))
118            self.created_materials.append(new_material)
119            Factory.all_created_materials.append(new_material)
120            return new_material
121
122    def can_build(self, volume):
123        """Check if enough valid materials have been created to build a wall."""
124        total_volume = sum(material.volume for material in self.created_materials
125                           if material.is_valid)
126        return total_volume >= volume
127
128    @classmethod
129    def can_build_together(cls, volume):
130        """Check if enough valid materials have been created across all factories."""
131        total_volume = sum(material.volume for material in cls.all_created_materials
132                           if material.is_valid)
133        return total_volume >= volume