






"""simple docstring"""



def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->Optional[Any]:
 UpperCAmelCase__ 						=				index
 UpperCAmelCase__ 						=				2 * index + 1
 UpperCAmelCase__ 						=				2 * index + 2
 if left_index < heap_size and unsorted[left_index] > unsorted[largest]:
  UpperCAmelCase__ 						=				left_index

 if right_index < heap_size and unsorted[right_index] > unsorted[largest]:
  UpperCAmelCase__ 						=				right_index

 if largest != index:
  UpperCAmelCase__						,	UpperCAmelCase__ 						=				unsorted[index], unsorted[largest]
  heapify(_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->Optional[Any]:
 UpperCAmelCase__ 						=				len(_SCREAMING_SNAKE_CASE			)
 for i in range(n // 2 - 1       ,	-1       ,	-1			):
  heapify(_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)
 for i in range(n - 1       ,	0       ,	-1			):
  UpperCAmelCase__						,	UpperCAmelCase__ 						=				unsorted[i], unsorted[0]
  heapify(_SCREAMING_SNAKE_CASE       ,	0       ,	_SCREAMING_SNAKE_CASE			)
 return unsorted


if __name__ == "__main__":
 a  :						int					       =							input('''Enter numbers separated by a comma:\n''').strip()
 a  :						Union[str, Any]					       =							[int(item) for item in user_input.split(''',''')]
 print(heap_sort(unsorted))











"""simple docstring"""



from __future__ import annotations

from math import pi, pow




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->float:
 if side_length < 0:
  raise ValueError("""vol_cube() only accepts non-negative values"""			)
 return pow(_SCREAMING_SNAKE_CASE       ,	3			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 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(_SCREAMING_SNAKE_CASE       ,	2			) * (3 * radius - height)




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 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(_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)			)

 UpperCAmelCase__ 						=				(
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )
 UpperCAmelCase__ 						=				(
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )

 return vol_spherical_cap(_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			) + vol_spherical_cap(_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:

 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(_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)			)

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




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 if width < 0 or height < 0 or length < 0:
  raise ValueError("""vol_cuboid() only accepts non-negative values"""			)
 return float(width * height * length			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 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       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 if height < 0 or radius < 0:
  raise ValueError("""vol_right_circ_cone() only accepts non-negative values"""			)
 return pi * pow(_SCREAMING_SNAKE_CASE       ,	2			) * height / 3.0




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 if height < 0 or area_of_base < 0:
  raise ValueError("""vol_prism() only accepts non-negative values"""			)
 return float(area_of_base * height			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 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       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->float:
 if radius < 0:
  raise ValueError("""vol_sphere() only accepts non-negative values"""			)
 # Volume is 4/3 * pi * radius cubed
 return 4 / 3 * pi * pow(_SCREAMING_SNAKE_CASE       ,	3			)




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->float:
 if radius < 0:
  raise ValueError("""vol_hemisphere() only accepts non-negative values"""			)
 # Volume is radius cubed * pi * 2/3
 return pow(_SCREAMING_SNAKE_CASE       ,	3			) * pi * 2 / 3




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 if height < 0 or radius < 0:
  raise ValueError("""vol_circular_cylinder() only accepts non-negative values"""			)
 # Volume is radius squared * height * pi
 return pow(_SCREAMING_SNAKE_CASE       ,	2			) * height * pi




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 # Volume - (outer_radius squared - inner_radius squared) * pi * height
 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(_SCREAMING_SNAKE_CASE       ,	2			) - pow(_SCREAMING_SNAKE_CASE       ,	2			)) * height




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 # Volume is 1/3 * pi * height *
 #           (radius_1 squared + radius_2 squared + radius_1 * radius_2)
 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(_SCREAMING_SNAKE_CASE       ,	2			) + pow(_SCREAMING_SNAKE_CASE       ,	2			) + radius_a * radius_a)
 )




def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->float:
 if torus_radius < 0 or tube_radius < 0:
  raise ValueError("""vol_torus() only accepts non-negative values"""			)
 return 2 * pow(_SCREAMING_SNAKE_CASE       ,	2			) * torus_radius * pow(_SCREAMING_SNAKE_CASE       ,	2			)




def       snake_case__		(   )    ->str:
 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()



