





"""simple docstring"""


def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					int:

 '''simple docstring'''






 snake_case__      							=			index
 snake_case__      							=			2 * index + 1
 snake_case__      							=			2 * index + 2
 if left_index < heap_size and unsorted[left_index] > unsorted[largest]:
  snake_case__      							=			left_index

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

 if largest != index:
  snake_case__							,				snake_case__      							=			unsorted[index], unsorted[largest]
  heapify(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)





def 							a__     (					_UpperCAmelCase		)      ->					Tuple:

 '''simple docstring'''






 snake_case__      							=			len(_UpperCAmelCase		)
 for i in range(n // 2 - 1		,       -1		,       -1		):
  heapify(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)
 for i in range(n - 1		,       0		,       -1		):
  snake_case__							,				snake_case__      							=			unsorted[i], unsorted[0]
  heapify(_UpperCAmelCase		,       0		,       _UpperCAmelCase		)
 return unsorted


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








"""simple docstring"""


from __future__ import annotations

from math import pi, pow





def 							a__     (					_UpperCAmelCase		)      ->					float:

 '''simple docstring'''






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





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       2		) * (3 * radius - height)





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       _UpperCAmelCase		)		)

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

 return vol_spherical_cap(_UpperCAmelCase		,       _UpperCAmelCase		) + vol_spherical_cap(_UpperCAmelCase		,       _UpperCAmelCase		)





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       _UpperCAmelCase		)		)

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





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					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 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					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 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					float:

 '''simple docstring'''






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





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					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 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					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 							a__     (					_UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       3		)





def 							a__     (					_UpperCAmelCase		)      ->					float:

 '''simple docstring'''






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





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       2		) * height * pi





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       2		) - pow(_UpperCAmelCase		,       2		)) * height





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					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(_UpperCAmelCase		,       2		) + pow(_UpperCAmelCase		,       2		) + radius_a * radius_a)
 )





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					float:

 '''simple docstring'''






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





def 							a__     (					)      ->					Union[str, Any]:

 '''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()

