1class Material:
  2    DENSITIES = {"Concrete": 2500, "Brick": 2000, "Stone": 1600, "Wood": 600, "Steel": 7700}
  3
  4    def __init__(self, mass):
  5        if not isinstance(mass, int):
  6            raise TypeError("Mass should be an integer.")
  7        self.mass = mass
  8        self.used = False
  9        self.components = [type(self).__name__]
 10
 11    @property
 12    def volume(self):
 13        return float(self.mass / self.density)
 14
 15
 16class Concrete(Material):
 17    density = Material.DENSITIES["Concrete"]
 18
 19
 20class Brick(Material):
 21    density = Material.DENSITIES["Brick"]
 22
 23
 24class Stone(Material):
 25    density = Material.DENSITIES["Stone"]
 26
 27
 28class Wood(Material):
 29    density = Material.DENSITIES["Wood"]
 30
 31
 32class Steel(Material):
 33    density = Material.DENSITIES["Steel"]
 34
 35
 36class Factory:
 37    ACCESS_CLASS = {"Concrete": Concrete, "Brick": Brick,
 38                    "Stone": Stone, "Wood": Wood, "Steel": Steel}
 39    dynamic_classes = {}
 40    all_materials = []
 41
 42    def __init__(self):
 43        self.materials = []
 44
 45    def __call__(self, *args, **kwargs):
 46        if (args and kwargs) or (not args and not kwargs):
 47            raise ValueError("Input error for factory arguments.")
 48        if kwargs:
 49            return self.create_materials_from_kwargs(kwargs)
 50        elif args:
 51            return self.create_alloy_from_args(args)
 52
 53    def create_materials_from_kwargs(self, kwargs):
 54        instance = []
 55        for class_name, mass in kwargs.items():
 56            if class_name not in self.ACCESS_CLASS:
 57                raise ValueError("Invalid material name.")
 58            cls = self.ACCESS_CLASS[class_name]
 59            material = cls(mass)
 60            instance.append(material)
 61            self.materials.append(material)
 62            self.all_materials.append(material)
 63        return tuple(instance)
 64
 65    def create_alloy_from_args(self, args):
 66        if any(arg.used for arg in args) or any(not isinstance(arg, Material) for arg in args):
 67            raise AssertionError("Materials have already been used or are invalid.")
 68
 69        used_materials = []
 70        for arg in args:
 71            if isinstance(arg, Material):
 72                for component in arg.components:
 73                    if "_" in component:
 74                        used_materials.extend(component.split("_"))
 75                    else:
 76                        used_materials.append(component)
 77            else:
 78                raise ValueError("Invalid argument type.")
 79            
 80        class_name = "_".join(sorted(set(used_materials)))
 81        mass = sum(arg.mass for arg in args)
 82
 83        if class_name not in self.dynamic_classes:
 84            all_densities = [self.ACCESS_CLASS[comp].density if comp in self.ACCESS_CLASS else self.dynamic_classes[comp].density
 85                             for comp in set(used_materials)]
 86            average_density = sum(all_densities) / len(all_densities)
 87            dynamic_class = type(class_name, (Material,), {'density': average_density})
 88            self.dynamic_classes[class_name] = dynamic_class
 89        else:
 90            dynamic_class = self.dynamic_classes[class_name]
 91
 92        new_material = dynamic_class(mass)
 93        self.materials.append(new_material)
 94        self.all_materials.append(new_material)
 95
 96        for arg in args:
 97            arg.used = True
 98
 99        return new_material
100
101    def can_build(self, required_volume):
102        return sum(material.volume for material in self.materials if not material.used) >= required_volume
103
104    @classmethod
105    def can_build_together(cls, required_volume):
106        return sum(material.volume for material in cls.all_materials if not material.used) >= required_volume