1class Material:
  2    def __init__(self, mass, density, materials_count = 1, factory = None):
  3        self.mass = mass
  4        self.density = density
  5        self.materials_count = materials_count
  6        self.is_valid = True
  7        self.factory = factory 
  8
  9    @property
 10    def volume(self):
 11        return float(self.mass / self.density)
 12
 13
 14class Concrete(Material):
 15    def __init__(self, mass):
 16        super().__init__(mass, density=2500)
 17
 18
 19class Brick(Material):
 20    def __init__(self, mass):
 21        super().__init__(mass, density=2000)
 22
 23
 24class Stone(Material):
 25    def __init__(self, mass):
 26        super().__init__(mass, density=1600)
 27
 28
 29class Wood(Material):
 30    def __init__(self, mass):
 31        super().__init__(mass, density=600)
 32
 33
 34class Steel(Material):
 35    def __init__(self, mass):
 36        super().__init__(mass, density=7700)
 37
 38class Factory:
 39    MATERIALS = {
 40        "Concrete": Concrete,
 41        "Brick": Brick,
 42        "Stone": Stone,
 43        "Wood": Wood,
 44        "Steel": Steel
 45    }
 46
 47    global_classes = {}
 48    all_created_materials = []
 49
 50    def __init__(self):
 51        self.classes = {}
 52        self.created_materials = []
 53
 54    def __call__(self, *args, **kwargs):
 55        if args and kwargs:
 56            raise ValueError("Unvalid calling of Factory with args and kwargs")
 57        
 58        if not args and not kwargs:
 59            raise ValueError("Unvalid calling of factory without any params")
 60
 61        if args:
 62            if not all(isinstance(arg, Material) for arg in args):
 63                raise ValueError("All positional arguments must be instances of Material.")
 64            if not all(arg.is_valid for arg in args):
 65                raise AssertionError("All positional arguments must be valid materials.") 
 66            # Generate class name
 67            material_names = sorted(arg.__class__.__name__ for arg in args)
 68            new_material_class_name = "_".join(material_names)
 69            new_materials_count = 0
 70            # If not already existing - calc avrg density and create new class
 71            if new_material_class_name not in Factory.global_classes:
 72                new_materials_count = sum(arg.materials_count for arg in args)
 73                total_density = sum(arg.density * arg.materials_count for arg in args)
 74                average_density = total_density / new_materials_count
 75
 76                class NewMaterial(Material):
 77                    def __init__(self, mass):
 78                        super().__init__(mass=mass, density=average_density, materials_count=new_materials_count)
 79                
 80                NewMaterial.__name__ = new_material_class_name
 81                Factory.global_classes[new_material_class_name] = NewMaterial
 82            # Mark the materials as already used and return instance of the new class
 83            for arg in args:
 84                arg.is_valid = False
 85            total_mass = sum(arg.mass for arg in args)
 86            new_instance = Factory.global_classes[new_material_class_name](total_mass)
 87            new_instance.factory = self
 88            self.created_materials.append(new_instance)
 89            Factory.all_created_materials.append(new_instance)
 90            return new_instance
 91
 92        if kwargs:
 93            instances = []
 94            for key, value in kwargs.items():
 95                if key not in self.MATERIALS and key not in Factory.global_classes:
 96                    raise ValueError("Invalid material name.")
 97                material_class = self.MATERIALS.get(key) or Factory.global_classes[key]
 98                instance = material_class(value)
 99                instance.factory = self
100                instances.append(instance)
101                self.created_materials.append(instance)
102                Factory.all_created_materials.append(instance)
103            return tuple(instances)
104        
105    def can_build(self, required_volume):
106        total_volume = sum(obj.volume for obj in self.created_materials if obj.is_valid)
107        return total_volume >= required_volume
108
109    @classmethod
110    def can_build_together(cls, required_volume):
111        total_volume = sum(obj.volume for obj in cls.all_created_materials if obj.is_valid)
112        return total_volume >= required_volume