


class  UpperCamelCase__ :






      def __init__(     self					:   Dict,		__lowerCamelCase					:   int   )  -> List[str]:
           UpperCamelCase__							:  Dict								=     data
           UpperCamelCase__							:  Optional[Any]								=     None
           UpperCamelCase__							:  List[str]								=     None






      def __str__(     self					:   List[Any]   )  -> Optional[Any]:
           return f'{self.data}'

class  UpperCamelCase__ :






      def __init__(     self					:   List[Any]   )  -> Optional[Any]:
           UpperCamelCase__							:  Optional[Any]								=     None
           UpperCamelCase__							:  str								=     None






      def __iter__(     self					:   str   )  -> List[str]:
           UpperCamelCase__							:  List[str]								=     self.head
           while node:
                yield node.data
                UpperCamelCase__							:  str								=     node.next






      def __str__(     self					:   Optional[int]   )  -> Dict:
           return "->".join([str(__lowerCamelCase   ) for item in self]   )






      def __len__(     self					:   Any   )  -> List[str]:
           return sum(1 for _ in self   )






      def 	__lowercase(     self					:   str,		__lowerCamelCase					:   int   )  -> int:
           self.insert_at_nth(0,		__lowerCamelCase   )






      def 	__lowercase(     self					:   str,		__lowerCamelCase					:   Optional[int]   )  -> int:
           self.insert_at_nth(len(self   ),		__lowerCamelCase   )






      def 	__lowercase(     self					:   Optional[Any],		__lowerCamelCase					:   int,		__lowerCamelCase					:   Any   )  -> List[Any]:
           UpperCamelCase__							:  List[str]								=     len(self   )

           if not 0 <= index <= length:
                raise IndexError('''list index out of range'''   )
           UpperCamelCase__							:  str								=     Node(__lowerCamelCase   )
           if self.head is None:
                UpperCamelCase__							:  Any								=     new_node
           elif index == 0:
                UpperCamelCase__							:  Any								=     new_node
                UpperCamelCase__							:  Any								=     self.head
                UpperCamelCase__							:  List[str]								=     new_node
           elif index == length:
                UpperCamelCase__							:  Dict								=     new_node
                UpperCamelCase__							:  Dict								=     self.tail
                UpperCamelCase__							:  List[Any]								=     new_node
           else:
                UpperCamelCase__							:  List[str]								=     self.head
                for _ in range(0,		__lowerCamelCase   ):
                     UpperCamelCase__							:  Union[str, Any]								=     temp.next
                UpperCamelCase__							:  Dict								=     new_node
                UpperCamelCase__							:  Any								=     temp.previous
                UpperCamelCase__							:  Optional[int]								=     temp
                UpperCamelCase__							:  List[Any]								=     new_node






      def 	__lowercase(     self					:   str   )  -> int:
           return self.delete_at_nth(0   )






      def 	__lowercase(     self					:   Any   )  -> str:
           return self.delete_at_nth(len(self   ) - 1   )






      def 	__lowercase(     self					:   List[Any],		__lowerCamelCase					:   int   )  -> Union[str, Any]:
           UpperCamelCase__							:  Tuple								=     len(self   )

           if not 0 <= index <= length - 1:
                raise IndexError('''list index out of range'''   )
           UpperCamelCase__							:  Tuple								=     self.head  # default first node
           if length == 1:
                UpperCamelCase__							:  Optional[int]								=     None
           elif index == 0:
                UpperCamelCase__							:  List[Any]								=     self.head.next
                UpperCamelCase__							:  List[str]								=     None
           elif index == length - 1:
                UpperCamelCase__							:  List[Any]								=     self.tail
                UpperCamelCase__							:  Optional[int]								=     self.tail.previous
                UpperCamelCase__							:  int								=     None
           else:
                UpperCamelCase__							:  Any								=     self.head
                for _ in range(0,		__lowerCamelCase   ):
                     UpperCamelCase__							:  Optional[Any]								=     temp.next
                UpperCamelCase__							:  Tuple								=     temp
                UpperCamelCase__							:  Tuple								=     temp.previous
                UpperCamelCase__							:  Any								=     temp.next
           return delete_node.data






      def 	__lowercase(     self					:   Optional[int],		__lowerCamelCase					:   Any   )  -> str:
           UpperCamelCase__							:  Tuple								=     self.head

           while current.data != data:  # Find the position to delete
                if current.next:
                     UpperCamelCase__							:  Dict								=     current.next
                else:  # We have reached the end an no value matches
                     raise ValueError('''No data matching given value'''   )

           if current == self.head:
                self.delete_head()

           elif current == self.tail:
                self.delete_tail()

           else:  # Before: 1 <--> 2(current) <--> 3
                UpperCamelCase__							:  Optional[Any]								=     current.next  # 1 --> 3
                UpperCamelCase__							:  Dict								=     current.previous  # 1 <--> 3
           return data






      def 	__lowercase(     self					:   Union[str, Any]   )  -> Tuple:
           return len(self   ) == 0







def 						_lowercase       (     )  ->   None:





     '''simple docstring'''





     UpperCamelCase__							:  Tuple								=     DoublyLinkedList()
     assert linked_list.is_empty() is True
     assert str(__lowerCamelCase			) == ""

     try:
          linked_list.delete_head()
          raise AssertionError  # This should not happen.
     except IndexError:
          assert True  # This should happen.

     try:
          linked_list.delete_tail()
          raise AssertionError  # This should not happen.
     except IndexError:
          assert True  # This should happen.

     for i in range(10			):
          assert len(__lowerCamelCase			) == i
          linked_list.insert_at_nth(__lowerCamelCase		,i + 1			)
     assert str(__lowerCamelCase			) == "->".join(str(__lowerCamelCase			) for i in range(1		,11			)			)

     linked_list.insert_at_head(0			)
     linked_list.insert_at_tail(11			)
     assert str(__lowerCamelCase			) == "->".join(str(__lowerCamelCase			) for i in range(0		,12			)			)

     assert linked_list.delete_head() == 0
     assert linked_list.delete_at_nth(9			) == 10
     assert linked_list.delete_tail() == 11
     assert len(__lowerCamelCase			) == 9
     assert str(__lowerCamelCase			) == "->".join(str(__lowerCamelCase			) for i in range(1		,10			)			)


if __name__ == "__main__":
   from doctest import testmod

   testmod()








from __future__ import annotations

from math import pi, pow







def 						_lowercase       (     __lowerCamelCase			:					int | float			)  ->   float:





     '''simple docstring'''





     if side_length < 0:
          raise ValueError('''vol_cube() only accepts non-negative values'''			)
     return pow(__lowerCamelCase		,3			)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if height < 0 or radius < 0:
          raise ValueError('''vol_spherical_cap() only accepts non-negative values'''			)
     # Volume is 1/3 pi * height squared * (3 * radius - height)
     return 1 / 3 * pi * pow(__lowerCamelCase		,2			) * (3 * radius - height)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if radius_a < 0 or radius_a < 0 or centers_distance < 0:
          raise ValueError('''vol_spheres_intersect() only accepts non-negative values'''			)
     if centers_distance == 0:
          return vol_sphere(min(__lowerCamelCase		,__lowerCamelCase			)			)

     UpperCamelCase__							:  Dict								=     (
         (radius_a - radius_a + centers_distance)
         * (radius_a + radius_a - centers_distance)
         / (2 * centers_distance)
     )
     UpperCamelCase__							:  Tuple								=     (
         (radius_a - radius_a + centers_distance)
         * (radius_a + radius_a - centers_distance)
         / (2 * centers_distance)
     )

     return vol_spherical_cap(__lowerCamelCase		,__lowerCamelCase			) + vol_spherical_cap(__lowerCamelCase		,__lowerCamelCase			)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
          raise ValueError(
              '''vol_spheres_union() only accepts non-negative values, non-zero radius'''			)

     if centers_distance == 0:
          return vol_sphere(max(__lowerCamelCase		,__lowerCamelCase			)			)

     return (
         vol_sphere(__lowerCamelCase			)
         + vol_sphere(__lowerCamelCase			)
         - vol_spheres_intersect(__lowerCamelCase		,__lowerCamelCase		,__lowerCamelCase			)
     )







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if width < 0 or height < 0 or length < 0:
          raise ValueError('''vol_cuboid() only accepts non-negative values'''			)
     return float(width * height * length			)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if height < 0 or area_of_base < 0:
          raise ValueError('''vol_cone() only accepts non-negative values'''			)
     return area_of_base * height / 3.0







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if height < 0 or radius < 0:
          raise ValueError('''vol_right_circ_cone() only accepts non-negative values'''			)
     return pi * pow(__lowerCamelCase		,2			) * height / 3.0







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if height < 0 or area_of_base < 0:
          raise ValueError('''vol_prism() only accepts non-negative values'''			)
     return float(area_of_base * height			)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if height < 0 or area_of_base < 0:
          raise ValueError('''vol_pyramid() only accepts non-negative values'''			)
     return area_of_base * height / 3.0







def 						_lowercase       (     __lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if radius < 0:
          raise ValueError('''vol_sphere() only accepts non-negative values'''			)
     # Volume is 4/3 * pi * radius cubed
     return 4 / 3 * pi * pow(__lowerCamelCase		,3			)







def 						_lowercase       (     __lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if radius < 0:
          raise ValueError('''vol_hemisphere() only accepts non-negative values'''			)
     # Volume is radius cubed * pi * 2/3
     return pow(__lowerCamelCase		,3			) * pi * 2 / 3







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if height < 0 or radius < 0:
          raise ValueError('''vol_circular_cylinder() only accepts non-negative values'''			)
     # Volume is radius squared * height * pi
     return pow(__lowerCamelCase		,2			) * height * pi







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if inner_radius < 0 or outer_radius < 0 or height < 0:
          raise ValueError(
              '''vol_hollow_circular_cylinder() only accepts non-negative values'''			)
     if outer_radius <= inner_radius:
          raise ValueError('''outer_radius must be greater than inner_radius'''			)
     return pi * (pow(__lowerCamelCase		,2			) - pow(__lowerCamelCase		,2			)) * height







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if radius_a < 0 or radius_a < 0 or height < 0:
          raise ValueError('''vol_conical_frustum() only accepts non-negative values'''			)
     return (
         1
         / 3
         * pi
         * height
         * (pow(__lowerCamelCase		,2			) + pow(__lowerCamelCase		,2			) + radius_a * radius_a)
     )







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





     if torus_radius < 0 or tube_radius < 0:
          raise ValueError('''vol_torus() only accepts non-negative values'''			)
     return 2 * pow(__lowerCamelCase		,2			) * torus_radius * pow(__lowerCamelCase		,2			)







def 						_lowercase       (     )  ->   Tuple:





     '''simple docstring'''





     print('''Volumes:'''			)
     print(F'Cube: {vol_cube(2			) = }'			)  # = 8
     print(F'Cuboid: {vol_cuboid(2		,2		,2			) = }'			)  # = 8
     print(F'Cone: {vol_cone(2		,2			) = }'			)  # ~= 1.33
     print(F'Right Circular Cone: {vol_right_circ_cone(2		,2			) = }'			)  # ~= 8.38
     print(F'Prism: {vol_prism(2		,2			) = }'			)  # = 4
     print(F'Pyramid: {vol_pyramid(2		,2			) = }'			)  # ~= 1.33
     print(F'Sphere: {vol_sphere(2			) = }'			)  # ~= 33.5
     print(F'Hemisphere: {vol_hemisphere(2			) = }'			)  # ~= 16.75
     print(F'Circular Cylinder: {vol_circular_cylinder(2		,2			) = }'			)  # ~= 25.1
     print(F'Torus: {vol_torus(2		,2			) = }'			)  # ~= 157.9
     print(F'Conical Frustum: {vol_conical_frustum(2		,2		,4			) = }'			)  # ~= 58.6
     print(F'Spherical cap: {vol_spherical_cap(1		,2			) = }'			)  # ~= 5.24
     print(F'Spheres intersetion: {vol_spheres_intersect(2		,2		,1			) = }'			)  # ~= 21.21
     print(F'Spheres union: {vol_spheres_union(2		,2		,1			) = }'			)  # ~= 45.81
     print(
         F'Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1		,2		,3			) = }'			)  # ~= 28.3


if __name__ == "__main__":
   main()




