


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	)	)

	a_     			=   (
	    (radius_a - radius_a + centers_distance)
	    * (radius_a + radius_a - centers_distance)
	    / (2 * centers_distance)
	)
	a_     			=   (
	    (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		(		)     ->	List[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()



def 			__SCREAMING_SNAKE_CASE		(		UpperCamelCase		:      int     ,					UpperCamelCase		:      list[tuple[int, int, int]]	)     ->	list[tuple[int, int, int]]:



	"""simple docstring"""






	a_     			=   sorted(UpperCamelCase     ,					key=lambda UpperCamelCase	: edge[2]	)

	a_     			=   list(range(UpperCamelCase	)	)

	def find_parent(UpperCamelCase		:      Any	):
		if i != parent[i]:
			a_     			=   find_parent(parent[i]	)
		return parent[i]

	a_     			=   0
	a_     			=   []

	for edge in edges:
		a_     			=   find_parent(edge[0]	)
		a_     			=   find_parent(edge[1]	)
		if parent_a != parent_b:
			minimum_spanning_tree_cost += edge[2]
			minimum_spanning_tree.append(UpperCamelCase	)
			a_     			=   parent_b

	return minimum_spanning_tree


if __name__ == "__main__":  # pragma: no cover
			_A     ,				_A							     =       list(map(int, input().strip().split()))
			_A							     =       []

			for _ in range(num_edges):
						_A     ,				_A     ,				_A							     =       (int(x) for x in input().strip().split())
						edges.append((nodea, nodea, cost))

			kruskal(num_nodes, edges)