

from math import pi, sqrt, tan







def 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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   :					Tuple        =    (height**2 + (radius_a - radius_a) ** 2) ** 0.5
     return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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(SCREAMING_SNAKE_CASE		,							2				) * torus_radius * tube_radius







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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   :					List[str]        =    (sidea + sidea + sidea) / 2
     _lowerCAmelCase   :					Optional[Any]        =    sqrt(
         semi_perimeter
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)				)
     return area







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







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







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      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 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      float:

     """simple docstring"""







     if not isinstance(SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				) 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(1_0, 2_0) = }''')
  print(f'''Square: {area_square(1_0) = }''')
  print(f'''Triangle: {area_triangle(1_0, 1_0) = }''')
  print(f'''Triangle: {area_triangle_three_sides(5, 1_2, 1_3) = }''')
  print(f'''Parallelogram: {area_parallelogram(1_0, 2_0) = }''')
  print(f'''Rhombus: {area_rhombus(1_0, 2_0) = }''')
  print(f'''Trapezium: {area_trapezium(1_0, 2_0, 3_0) = }''')
  print(f'''Circle: {area_circle(2_0) = }''')
  print(f'''Ellipse: {area_ellipse(1_0, 2_0) = }''')
  print('\nSurface Areas of various geometric shapes: \n')
  print(f'''Cube: {surface_area_cube(2_0) = }''')
  print(f'''Cuboid: {surface_area_cuboid(1_0, 2_0, 3_0) = }''')
  print(f'''Sphere: {surface_area_sphere(2_0) = }''')
  print(f'''Hemisphere: {surface_area_hemisphere(2_0) = }''')
  print(f'''Cone: {surface_area_cone(1_0, 2_0) = }''')
  print(f'''Conical Frustum: {surface_area_conical_frustum(1_0, 2_0, 3_0) = }''')
  print(f'''Cylinder: {surface_area_cylinder(1_0, 2_0) = }''')
  print(f'''Torus: {surface_area_torus(2_0, 1_0) = }''')
  print(f'''Equilateral Triangle: {area_reg_polygon(3, 1_0) = }''')
  print(f'''Square: {area_reg_polygon(4, 1_0) = }''')
  print(f'''Reqular Pentagon: {area_reg_polygon(5, 1_0) = }''')









from __future__ import annotations







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      List[Any]:

     """simple docstring"""







     print(f'''Vertex\tShortest Distance from vertex {src}'''				)
     for i, d in enumerate(SCREAMING_SNAKE_CASE				):
          print(f'''{i}\t\t{d}'''				)







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      Tuple:

     """simple docstring"""







     for j in range(SCREAMING_SNAKE_CASE				):
          _lowerCAmelCase      ,			_lowerCAmelCase      ,			_lowerCAmelCase   :					Any        =    (graph[j][k] for k in ["src", "dst", "weight"])
          if distance[u] != float("inf"				) and distance[u] + w < distance[v]:
               return True
     return False







def 	_snake_case		(    SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)       ->      list[float]:

     """simple docstring"""







     _lowerCAmelCase   :					Tuple        =    [float("inf"				)] * vertex_count
     _lowerCAmelCase   :					int        =    0.0

     for _ in range(vertex_count - 1				):
          for j in range(SCREAMING_SNAKE_CASE				):
               _lowerCAmelCase      ,			_lowerCAmelCase      ,			_lowerCAmelCase   :					int        =    (graph[j][k] for k in ["src", "dst", "weight"])

               if distance[u] != float("inf"				) and distance[u] + w < distance[v]:
                    _lowerCAmelCase   :					List[str]        =    distance[u] + w

     _lowerCAmelCase   :					int        =    check_negative_cycle(SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE		,							SCREAMING_SNAKE_CASE				)
     if negative_cycle_exists:
          raise Exception("Negative cycle found"				)

     return distance


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  __UpperCAmelCase    				=     int(input('Enter number of vertices: ').strip())
  __UpperCAmelCase    				=     int(input('Enter number of edges: ').strip())

  __UpperCAmelCase    				=     [{} for _ in range(E)]

  for i in range(E):
    print('Edge ', i + 1)
    __UpperCAmelCase				,__UpperCAmelCase				,__UpperCAmelCase    				=     (
        int(x)
        for x in input('Enter source, destination, weight: ').strip().split(' ')
    )
    __UpperCAmelCase    				=     {'src': src, 'dst': dest, 'weight': weight}

  __UpperCAmelCase    				=     int(input('\nEnter shortest path source:').strip())
  __UpperCAmelCase    				=     bellman_ford(graph, V, E, source)
  print_distance(shortest_distance, 0)






