
from __future__ import annotations

from math import pi, pow



def      __UpperCAmelCase    (  snake_case_							:		int | float				):



	'''simple docstring'''



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



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		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(snake_case_				,					2				) * (3 * radius - height)



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				,					snake_case_							:		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(snake_case_				,					snake_case_				)				)

	UpperCAmelCase:					Union[str, Any] 						=     (
	    (radius_a - radius_a + centers_distance)
	    * (radius_a + radius_a - centers_distance)
	    / (2 * centers_distance)
	)
	UpperCAmelCase:					int 						=     (
	    (radius_a - radius_a + centers_distance)
	    * (radius_a + radius_a - centers_distance)
	    / (2 * centers_distance)
	)

	return vol_spherical_cap(snake_case_				,					snake_case_				) + vol_spherical_cap(snake_case_				,					snake_case_				)



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				,					snake_case_							:		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(snake_case_				,					snake_case_				)				)

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



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				,					snake_case_							:		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      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		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      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				):



	'''simple docstring'''



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



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		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      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		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      __UpperCAmelCase    (  snake_case_							:		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(snake_case_				,					3				)



def      __UpperCAmelCase    (  snake_case_							:		float				):



	'''simple docstring'''



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



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		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(snake_case_				,					2				) * height * pi



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				,					snake_case_							:		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(snake_case_				,					2				) - pow(snake_case_				,					2				)) * height



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				,					snake_case_							:		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(snake_case_				,					2				) + pow(snake_case_				,					2				) + radius_a * radius_a)
	)



def      __UpperCAmelCase    (  snake_case_							:		float				,					snake_case_							:		float				):



	'''simple docstring'''



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



def      __UpperCAmelCase    (  ):



	'''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)