


'''simple docstring'''

from __future__ import annotations

from math import pi, pow



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int | float )		->       float:





   '''simple docstring'''







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



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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(_UpperCamelCase     ,		2 ) * (3 * radius - height)



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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(_UpperCamelCase     ,		_UpperCamelCase ) )

   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(_UpperCamelCase     ,		_UpperCamelCase ) + vol_spherical_cap(_UpperCamelCase     ,		_UpperCamelCase )



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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(_UpperCamelCase     ,		_UpperCamelCase ) )

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



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float )		->       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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					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(_UpperCamelCase     ,		3 )



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					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(_UpperCamelCase     ,		3 ) * pi * 2 / 3



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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(_UpperCamelCase     ,		2 ) * height * pi



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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(_UpperCamelCase     ,		2 ) - pow(_UpperCamelCase     ,		2 )) * height



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					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(_UpperCamelCase     ,		2 ) + pow(_UpperCamelCase     ,		2 ) + radius_a * radius_a)
   )



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					float     ,		_UpperCamelCase   :					float )		->       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 							SCREAMING_SNAKE_CASE__(		)		->       int:





   '''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()



'''simple docstring'''

from __future__ import annotations



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					list[list[int]]     ,		_UpperCamelCase   :					list[list[int]] )		->       list[int]:





   '''simple docstring'''







   assert len(_UpperCamelCase ) == len(_UpperCamelCase )

   UpperCamelCase__			    =    len(_UpperCamelCase )
   UpperCamelCase__			    =    list(range(_UpperCamelCase ) )
   UpperCamelCase__			    =    [-1] * n  # who the donor has donated to
   UpperCamelCase__			    =    [-1] * n  # who the recipient has received from
   UpperCamelCase__			    =    [0] * n

   while unmatched_donors:
      UpperCamelCase__			    =    unmatched_donors[0]
      UpperCamelCase__			    =    donor_pref[donor]
      UpperCamelCase__			    =    donor_preference[num_donations[donor]]
      num_donations[donor] += 1
      UpperCamelCase__			    =    recipient_pref[recipient]
      UpperCamelCase__			    =    rec_record[recipient]

      if prev_donor != -1:
         if rec_preference.index(_UpperCamelCase ) > rec_preference.index(_UpperCamelCase ):
            UpperCamelCase__			    =    donor
            UpperCamelCase__			    =    recipient
            unmatched_donors.append(_UpperCamelCase )
            unmatched_donors.remove(_UpperCamelCase )
      else:
         UpperCamelCase__			    =    donor
         UpperCamelCase__			    =    recipient
         unmatched_donors.remove(_UpperCamelCase )
   return donor_record