from math import pi, sqrt, tan




def       __lowerCAmelCase      (						A_   : float					)    ->  float:
  if side_length < 0:
    raise ValueError("surface_area_cube() only accepts non-negative values"					)
  return 6 * side_length**2




def       __lowerCAmelCase      (						A_   : float						,	A_   : float						,	A_   : float					)    ->  float:
  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      (						A_   : float					)    ->  float:
  if radius < 0:
    raise ValueError("surface_area_sphere() only accepts non-negative values"					)
  return 4 * pi * radius**2




def       __lowerCAmelCase      (						A_   : float					)    ->  float:
  if radius < 0:
    raise ValueError("surface_area_hemisphere() only accepts non-negative values"					)
  return 3 * pi * radius**2




def       __lowerCAmelCase      (						A_   : float						,	A_   : float					)    ->  float:
  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      (						A_   : float						,	A_   : float						,	A_   : float					)    ->  float:
  if radius_a < 0 or radius_a < 0 or height < 0:
    raise ValueError(
        "surface_area_conical_frustum() only accepts non-negative values"					)
  __UpperCAmelCase						    =       (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      (						A_   : float						,	A_   : float					)    ->  float:
  if radius < 0 or height < 0:
    raise ValueError("surface_area_cylinder() only accepts non-negative values"					)
  return 2 * pi * radius * (height + radius)




def       __lowerCAmelCase      (						A_   : float						,	A_   : float					)    ->  float:
  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(A_						,	2					) * torus_radius * tube_radius




def       __lowerCAmelCase      (						A_   : float						,	A_   : float					)    ->  float:
  if length < 0 or width < 0:
    raise ValueError("area_rectangle() only accepts non-negative values"					)
  return length * width




def       __lowerCAmelCase      (						A_   : float					)    ->  float:
  if side_length < 0:
    raise ValueError("area_square() only accepts non-negative values"					)
  return side_length**2




def       __lowerCAmelCase      (						A_   : float						,	A_   : float					)    ->  float:
  if base < 0 or height < 0:
    raise ValueError("area_triangle() only accepts non-negative values"					)
  return (base * height) / 2




def       __lowerCAmelCase      (						A_   : float						,	A_   : float						,	A_   : float					)    ->  float:
  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"					)
  __UpperCAmelCase						    =       (sidea + sidea + sidea) / 2
  __UpperCAmelCase						    =       sqrt(
      semi_perimeter
      * (semi_perimeter - sidea)
      * (semi_perimeter - sidea)
      * (semi_perimeter - sidea)					)
  return area




def       __lowerCAmelCase      (						A_   : float						,	A_   : float					)    ->  float:
  if base < 0 or height < 0:
    raise ValueError("area_parallelogram() only accepts non-negative values"					)
  return base * height




def       __lowerCAmelCase      (						A_   : float						,	A_   : float						,	A_   : float					)    ->  float:
  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      (						A_   : float					)    ->  float:
  if radius < 0:
    raise ValueError("area_circle() only accepts non-negative values"					)
  return pi * radius**2




def       __lowerCAmelCase      (						A_   : float						,	A_   : float					)    ->  float:
  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      (						A_   : float						,	A_   : float					)    ->  float:
  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      (						A_   : int						,	A_   : float					)    ->  float:
  if not isinstance(A_						,	A_					) 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) = }")




def       __lowerCAmelCase      (						A_   : str					)    ->  Any:
  if not head:
    return True
  # split the list to two parts
  __UpperCAmelCase    ,		__UpperCAmelCase						    =       head.next, head
  while fast and fast.next:
    __UpperCAmelCase						    =       fast.next.next
    __UpperCAmelCase						    =       slow.next
  __UpperCAmelCase						    =       slow.next
  __UpperCAmelCase						    =       None  # Don't forget here! But forget still works!
  # reverse the second part
  __UpperCAmelCase						    =       None
  while second:
    __UpperCAmelCase						    =       second.next
    __UpperCAmelCase						    =       node
    __UpperCAmelCase						    =       second
    __UpperCAmelCase						    =       nxt
  # compare two parts
  # second part has the same or one less node
  while node:
    if node.val != head.val:
      return False
    __UpperCAmelCase						    =       node.next
    __UpperCAmelCase						    =       head.next
  return True




def       __lowerCAmelCase      (						A_   : Optional[Any]					)    ->  Optional[Any]:
  if not head or not head.next:
    return True

  # 1. Get the midpoint (slow)
  __UpperCAmelCase						    =       __UpperCAmelCase						    =       __UpperCAmelCase						    =       head
  while fast and fast.next:
    __UpperCAmelCase    ,		__UpperCAmelCase						    =       fast.next.next, slow.next

  # 2. Push the second half into the stack
  __UpperCAmelCase						    =       [slow.val]
  while slow.next:
    __UpperCAmelCase						    =       slow.next
    stack.append(slow.val					)

  # 3. Comparison
  while stack:
    if stack.pop() != cur.val:
      return False
    __UpperCAmelCase						    =       cur.next

  return True





def       __lowerCAmelCase      (						A_   : int					)    ->  Optional[int]:
  if not head or not head.next:
    return True
  __UpperCAmelCase						    =       {}
  __UpperCAmelCase						    =       0
  while head:
    if head.val in d:
      d[head.val].append(A_					)
    else:
      __UpperCAmelCase						    =       [pos]
    __UpperCAmelCase						    =       head.next
    pos += 1
  __UpperCAmelCase						    =       pos - 1
  __UpperCAmelCase						    =       0
  for v in d.values():
    if len(A_					) % 2 != 0:
      middle += 1
    else:
      __UpperCAmelCase						    =       0
      for i in range(0						,	len(A_					)					):
        if v[i] + v[len(A_					) - 1 - step] != checksum:
          return False
        step += 1
    if middle > 1:
      return False
  return True



