




from math import pi, sqrt, tan







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if side_length < 0:
								raise ValueError('surface_area_cube() only accepts non-negative values'      )
				return 6 * side_length**2







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if length < 0 or breadth < 0 or height < 0:
								raise ValueError('surface_area_cuboid() only accepts non-negative values'      )
				return 2 * ((length * breadth) + (breadth * height) + (length * height))







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius < 0:
								raise ValueError('surface_area_sphere() only accepts non-negative values'      )
				return 4 * pi * radius**2







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius < 0:
								raise ValueError('surface_area_hemisphere() only accepts non-negative values'      )
				return 3 * pi * radius**2







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius < 0 or height < 0:
								raise ValueError('surface_area_cone() only accepts non-negative values'      )
				return pi * radius * (radius + (height**2 + radius**2) ** 0.5)







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius_a < 0 or radius_a < 0 or height < 0:
								raise ValueError(
								    'surface_area_conical_frustum() only accepts non-negative values'      )
				__lowerCamelCase		       =    (height**2 + (radius_a - radius_a) ** 2) ** 0.5
				return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius < 0 or height < 0:
								raise ValueError('surface_area_cylinder() only accepts non-negative values'      )
				return 2 * pi * radius * (height + radius)







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if torus_radius < 0 or tube_radius < 0:
								raise ValueError('surface_area_torus() only accepts non-negative values'      )
				if torus_radius < tube_radius:
								raise ValueError(
								    'surface_area_torus() does not support spindle or self intersecting tori'      )
				return 4 * pow(UpperCamelCase__ ,     2      ) * torus_radius * tube_radius







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if length < 0 or width < 0:
								raise ValueError('area_rectangle() only accepts non-negative values'      )
				return length * width







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if side_length < 0:
								raise ValueError('area_square() only accepts non-negative values'      )
				return side_length**2







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if base < 0 or height < 0:
								raise ValueError('area_triangle() only accepts non-negative values'      )
				return (base * height) / 2







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if sidea < 0 or sidea < 0 or sidea < 0:
								raise ValueError('area_triangle_three_sides() only accepts non-negative values'      )
				elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
								raise ValueError('Given three sides do not form a triangle'      )
				__lowerCamelCase		       =    (sidea + sidea + sidea) / 2
				__lowerCamelCase		       =    sqrt(
				    semi_perimeter
				    * (semi_perimeter - sidea)
				    * (semi_perimeter - sidea)
				    * (semi_perimeter - sidea)      )
				return area







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if base < 0 or height < 0:
								raise ValueError('area_parallelogram() only accepts non-negative values'      )
				return base * height







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if basea < 0 or basea < 0 or height < 0:
								raise ValueError('area_trapezium() only accepts non-negative values'      )
				return 1 / 2 * (basea + basea) * height







def 			lowerCamelCase_		(       UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius < 0:
								raise ValueError('area_circle() only accepts non-negative values'      )
				return pi * radius**2







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if radius_x < 0 or radius_y < 0:
								raise ValueError('area_ellipse() only accepts non-negative values'      )
				return pi * radius_x * radius_y







def 			lowerCamelCase_		(       UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if diagonal_a < 0 or diagonal_a < 0:
								raise ValueError('area_rhombus() only accepts non-negative values'      )
				return 1 / 2 * diagonal_a * diagonal_a







def 			lowerCamelCase_		(       UpperCamelCase__				:      int ,     UpperCamelCase__				:      float      )     ->       float:





				"""simple docstring"""


				if not isinstance(UpperCamelCase__ ,     UpperCamelCase__      ) or sides < 3:
								raise ValueError(
								    'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'      )
				elif length < 0:
								raise ValueError(
								    'area_reg_polygon() only accepts non-negative values as \
length of a side'      )
				return (sides * length**2) / (4 * tan(pi / sides      ))
				return (sides * length**2) / (4 * tan(pi / sides      ))


if __name__ == "__main__":
					import doctest

					doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

					print("[DEMO] Areas of various geometric shapes: \n")
					print(f'''Rectangle: {area_rectangle(10, 20) = }''')
					print(f'''Square: {area_square(10) = }''')
					print(f'''Triangle: {area_triangle(10, 10) = }''')
					print(f'''Triangle: {area_triangle_three_sides(5, 12, 13) = }''')
					print(f'''Parallelogram: {area_parallelogram(10, 20) = }''')
					print(f'''Rhombus: {area_rhombus(10, 20) = }''')
					print(f'''Trapezium: {area_trapezium(10, 20, 30) = }''')
					print(f'''Circle: {area_circle(20) = }''')
					print(f'''Ellipse: {area_ellipse(10, 20) = }''')
					print("\nSurface Areas of various geometric shapes: \n")
					print(f'''Cube: {surface_area_cube(20) = }''')
					print(f'''Cuboid: {surface_area_cuboid(10, 20, 30) = }''')
					print(f'''Sphere: {surface_area_sphere(20) = }''')
					print(f'''Hemisphere: {surface_area_hemisphere(20) = }''')
					print(f'''Cone: {surface_area_cone(10, 20) = }''')
					print(f'''Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }''')
					print(f'''Cylinder: {surface_area_cylinder(10, 20) = }''')
					print(f'''Torus: {surface_area_torus(20, 10) = }''')
					print(f'''Equilateral Triangle: {area_reg_polygon(3, 10) = }''')
					print(f'''Square: {area_reg_polygon(4, 10) = }''')
					print(f'''Reqular Pentagon: {area_reg_polygon(5, 10) = }''')









from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       )      ->				list[list[int]]:
   __snake_case							       =   []
   __snake_case							       =   []
   __snake_case							       =   0
   __snake_case							       =   sum(snake_case_       )
   create_state_space_tree(snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       )
   return result






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       ,      snake_case_	:  int       ,      snake_case_	:  list[int]       ,      snake_case_	:  list[list[int]]       ,      snake_case_	:  int       ,      )      ->				None:
   if sum(snake_case_       ) > max_sum or (remaining_nums_sum + sum(snake_case_       )) < max_sum:
      return
   if sum(snake_case_       ) == max_sum:
      result.append(snake_case_       )
      return
   for index in range(snake_case_       ,      len(snake_case_       )       ):
      create_state_space_tree(
          snake_case_       ,      snake_case_       ,      index + 1       ,      [*path, nums[index]]       ,      snake_case_       ,      remaining_nums_sum - nums[index]       ,      )
snake_case_				=			[3, 34, 4, 12, 5, 2]
snake_case_				=			9
snake_case_				=			generate_sum_of_subsets_soln(nums, max_sum)







print(*result)

