
from __future__ import annotations

from typing import Generic, TypeVar

lowercase__       =TypeVar('T')



class 		UpperCamelCase__  (       Generic[T]    ):
   def __init__(self :					Tuple					,				snake_case_ :					T   ):
    __a :  Optional[int]						=  data
    __a :  Optional[Any]						=  self
    __a :  int						=  0





class 		UpperCamelCase__  (       Generic[T]    ):
   def __init__(self :					List[Any]   ):
    # map from node name to the node object
    __a :  dict[T, DisjointSetTreeNode[T]]						=  {}
   def       lowerCAmelCase			(self :					Tuple					,				snake_case_ :					T   ):
    # create a new set with x as its member
    __a :  int						=  DisjointSetTreeNode(snake_case_   )
   def       lowerCAmelCase			(self :					int					,				snake_case_ :					T   ):
    # find the set x belongs to (with path-compression)
    __a :  Any						=  self.map[data]
    if elem_ref != elem_ref.parent:
     __a :  int						=  self.find_set(elem_ref.parent.data   )
    return elem_ref.parent
   def       lowerCAmelCase			(self :					Optional[int]					,				snake_case_ :					DisjointSetTreeNode[T]					,				snake_case_ :					DisjointSetTreeNode[T]   ):
    # helper function for union operation
    if nodea.rank > nodea.rank:
     __a :  Dict						=  nodea
    else:
     __a :  Tuple						=  nodea
     if nodea.rank == nodea.rank:
      nodea.rank += 1







   def       lowerCAmelCase			(self :					Optional[int]					,				snake_case_ :					T					,				snake_case_ :					T   ):
    # merge 2 disjoint sets
    self.link(self.find_set(snake_case_   )					,				self.find_set(snake_case_   )   )





class 		UpperCamelCase__  (       Generic[T]    ):
   def __init__(self :					Optional[Any]   ):
    # connections: map from the node to the neighbouring nodes (with weights)
    __a :  dict[T, dict[T, int]]						=  {}
   def       lowerCAmelCase			(self :					str					,				snake_case_ :					T   ):
    # add a node ONLY if its not present in the graph
    if node not in self.connections:
     __a :  int						=  {}
   def       lowerCAmelCase			(self :					Dict					,				snake_case_ :					T					,				snake_case_ :					T					,				snake_case_ :					int   ):
    # add an edge with the given weight
    self.add_node(snake_case_   )
    self.add_node(snake_case_   )
    __a :  Dict						=  weight
    __a :  List[str]						=  weight







   def       lowerCAmelCase			(self :					Optional[Any]   ):
    __a :  int						=  []
    __a :  Optional[int]						=  set()
    for start in self.connections:
     for end in self.connections[start]:
      if (start, end) not in seen:
       seen.add((end, start)   )
       edges.append((start, end, self.connections[start][end])   )
    edges.sort(key=lambda snake_case_   : x[2]   )

    # creating the disjoint set
    __a :  Optional[int]						=  DisjointSetTree[T]()
    for node in self.connections:
     disjoint_set.make_set(snake_case_   )

    # MST generation
    __a :  Tuple						=  0
    __a :  Tuple						=  0
    __a :  List[str]						=  GraphUndirectedWeighted[T]()
    while num_edges < len(self.connections   ) - 1:
     __a				,       __a				,       __a :  List[str]						=  edges[index]
     index += 1
     __a :  Dict						=  disjoint_set.find_set(snake_case_   )
     __a :  str						=  disjoint_set.find_set(snake_case_   )
     if parent_u != parent_v:
      num_edges += 1
      graph.add_edge(snake_case_					,				snake_case_					,				snake_case_   )
      disjoint_set.union(snake_case_					,				snake_case_   )
    return graph


import colorsys

from PIL import Image  # type: ignore




def    __UpperCamelCase     (				lowerCAmelCase__							:				float  ,   lowerCAmelCase__							:				float  ,   lowerCAmelCase__							:				int  ):
 __a :  Any						=  x
 __a :  List[Any]						=  y
 for step in range(lowerCAmelCase__  ):  # noqa: B007
  __a :  List[Any]						=  a * a - b * b + x
  __a :  Tuple						=  2 * a * b + y
  __a :  Optional[int]						=  a_new

  # divergence happens for all complex number with an absolute value
  # greater than 4
  if a * a + b * b > 4:
   break
 return step / (max_step - 1)




def    __UpperCamelCase     (				lowerCAmelCase__							:				float  ):
 if distance == 1:
  return (0, 0, 0)
 else:
  return (2_5_5, 2_5_5, 2_5_5)




def    __UpperCamelCase     (				lowerCAmelCase__							:				float  ):
 if distance == 1:
  return (0, 0, 0)
 else:
  return tuple(round(i * 2_5_5  ) for i in colorsys.hsv_to_rgb(lowerCAmelCase__  ,   1  ,   1  )  )




def    __UpperCamelCase     (				lowerCAmelCase__							:				int = 8_0_0  ,   lowerCAmelCase__							:				int = 6_0_0  ,   lowerCAmelCase__							:				float = -0.6  ,   lowerCAmelCase__							:				float = 0  ,   lowerCAmelCase__							:				float = 3.2  ,   lowerCAmelCase__							:				int = 5_0  ,   lowerCAmelCase__							:				bool = True  ,   ):
 __a :  int						=  Image.new('''RGB'''  ,   (image_width, image_height)  )
 __a :  Dict						=  img.load()

 # loop through the image-coordinates
 for image_x in range(lowerCAmelCase__  ):
  for image_y in range(lowerCAmelCase__  ):
   # determine the figure-coordinates based on the image-coordinates
   __a :  Optional[Any]						=  figure_width / image_width * image_height
   __a :  str						=  figure_center_x + (image_x / image_width - 0.5) * figure_width
   __a :  str						=  figure_center_y + (image_y / image_height - 0.5) * figure_height

   __a :  Tuple						=  get_distance(lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )

   # color the corresponding pixel based on the selected coloring-function
   if use_distance_color_coding:
    __a :  Optional[int]						=  get_color_coded_rgb(lowerCAmelCase__  )
   else:
    __a :  Optional[Any]						=  get_black_and_white_rgb(lowerCAmelCase__  )

 return img


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      # colored version, full figure
      lowercase__       =get_image()

      # uncomment for colored version, different section, zoomed in
      # img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
      # figure_width = 0.8)

      # uncomment for black and white version, full figure
      # img = get_image(use_distance_color_coding = False)

      # uncomment to save the image
      # img.save("mandelbrot.png")

      img.show()
