






'''simple docstring'''
import colorsys

from PIL import Image  # type: ignore





def 	_a(					UpperCamelCase__			:  float,		UpperCamelCase__			:  float,		UpperCamelCase__			:  int							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Any													=x
      SCREAMING_SNAKE_CASE__       :			List[str]													=y
      for step in range(UpperCamelCase__							):  # noqa: B007
            SCREAMING_SNAKE_CASE__       :			str													=a * a - b * b + x
            SCREAMING_SNAKE_CASE__       :			List[str]													=2 * a * b + y
            SCREAMING_SNAKE_CASE__       :			List[Any]													=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 	_a(					UpperCamelCase__			:  float							):




      '''simple docstring'''






      if distance == 1:
            return (0, 0, 0)
      else:
            return (2_5_5, 2_5_5, 2_5_5)





def 	_a(					UpperCamelCase__			:  float							):




      '''simple docstring'''






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





def 	_a(					UpperCamelCase__			:  int = 8_0_0,		UpperCamelCase__			:  int = 6_0_0,		UpperCamelCase__			:  float = -0.6,		UpperCamelCase__			:  float = 0,		UpperCamelCase__			:  float = 3.2,		UpperCamelCase__			:  int = 5_0,		UpperCamelCase__			:  bool = True,		):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			List[str]													=Image.new('''RGB''',		(image_width, image_height)							)
      SCREAMING_SNAKE_CASE__       :			Any													=img.load()

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

                  SCREAMING_SNAKE_CASE__       :			Optional[int]													=get_distance(UpperCamelCase__,		UpperCamelCase__,		UpperCamelCase__							)

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

      return img


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # colored version, full figure
  a_					=	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()







'''simple docstring'''
from __future__ import annotations

import os
from collections.abc import Mapping

a_					=	tuple[int, int]






class        __SCREAMING_SNAKE_CASE :




 def __init__( self		:							Any   , __lowercase		:							set[int]   , __lowercase		:							Mapping[EdgeT, int] )		->  None:
       SCREAMING_SNAKE_CASE__       :			set[int]													=vertices
       SCREAMING_SNAKE_CASE__       :			dict[EdgeT, int]													={
           (min(__lowercase ), max(__lowercase )): weight for edge, weight in edges.items()
       }




 def        __magic_name__		( self		:							Union[str, Any]   , __lowercase		:							EdgeT   , __lowercase		:							int )		->  None:
       self.vertices.add(edge[0] )
       self.vertices.add(edge[1] )
       SCREAMING_SNAKE_CASE__       :			List[str]													=weight




 def        __magic_name__		( self		:							Optional[Any] )		->  Graph:
       SCREAMING_SNAKE_CASE__       :			Graph													=Graph({min(self.vertices )}   , {} )
       SCREAMING_SNAKE_CASE__       :			EdgeT
       SCREAMING_SNAKE_CASE__       :			int
       SCREAMING_SNAKE_CASE__       :			EdgeT
       SCREAMING_SNAKE_CASE__       :			int

       while len(subgraph.vertices ) < len(self.vertices ):
             SCREAMING_SNAKE_CASE__       :			Any													=max(self.edges.values() ) + 1
             for edge, weight in self.edges.items():
                   if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
                         if weight < min_weight:
                               SCREAMING_SNAKE_CASE__       :			List[str]													=edge
                               SCREAMING_SNAKE_CASE__       :			Any													=weight

             subgraph.add_edge(__lowercase   , __lowercase )

       return subgraph





def 	_a(					UpperCamelCase__			:  str = "p107_network.txt"							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			str													=os.path.abspath(os.path.dirname(UpperCamelCase__							)							)
      SCREAMING_SNAKE_CASE__       :			str													=os.path.join(UpperCamelCase__,		UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__       :			dict[EdgeT, int]													={}
      SCREAMING_SNAKE_CASE__       :			list[str]
      SCREAMING_SNAKE_CASE__       :			int
      SCREAMING_SNAKE_CASE__       :			int

      with open(UpperCamelCase__							) as f:
            SCREAMING_SNAKE_CASE__       :			Any													=f.read().strip().split('''\n'''							)

      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=[line.split(''','''							) for line in data]

      for edgea in range(1,		len(UpperCamelCase__							)							):
            for edgea in range(UpperCamelCase__							):
                  if adjaceny_matrix[edgea][edgea] != "-":
                        SCREAMING_SNAKE_CASE__       :			List[Any]													=int(adjaceny_matrix[edgea][edgea]							)

      SCREAMING_SNAKE_CASE__       :			Graph													=Graph(set(range(len(UpperCamelCase__							)							)							),		UpperCamelCase__							)

      SCREAMING_SNAKE_CASE__       :			Graph													=graph.prims_algorithm()

      SCREAMING_SNAKE_CASE__       :			int													=sum(graph.edges.values()							)
      SCREAMING_SNAKE_CASE__       :			int													=sum(subgraph.edges.values()							)

      return initial_total - optimal_total


if __name__ == "__main__":
  print(F'''{solution() = }''')