






from __future__ import annotations

import math






def 	UpperCamelCase	(							snake_case__  : list						,snake_case__  : list	):




     '''simple docstring'''






     if len(snake_case__	) != 2 or len(a[0]	) != 2 or len(snake_case__	) != 2 or len(b[0]	) != 2:
          raise Exception("""Matrices are not 2x2"""	)
     __snake_case      :List[str] 							=    [
         [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
         [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
     ]
     return new_matrix






def 	UpperCamelCase	(							snake_case__  : list						,snake_case__  : list	):




     '''simple docstring'''






     return [
         [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]	)	)]
         for row in range(len(snake_case__	)	)
     ]






def 	UpperCamelCase	(							snake_case__  : list						,snake_case__  : list	):




     '''simple docstring'''






     return [
         [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]	)	)]
         for row in range(len(snake_case__	)	)
     ]






def 	UpperCamelCase	(							snake_case__  : list	):




     '''simple docstring'''






     if len(snake_case__	) % 2 != 0 or len(a[0]	) % 2 != 0:
          raise Exception("""Odd matrices are not supported!"""	)

     __snake_case      :Dict 							=    len(snake_case__	)
     __snake_case      :Dict 							=    matrix_length // 2

     __snake_case      :List[str] 							=    [[a[i][j] for j in range(snake_case__						,snake_case__	)] for i in range(snake_case__	)]
     __snake_case      :str 							=    [
         [a[i][j] for j in range(snake_case__						,snake_case__	)] for i in range(snake_case__						,snake_case__	)
     ]

     __snake_case      :Optional[Any] 							=    [[a[i][j] for j in range(snake_case__	)] for i in range(snake_case__	)]
     __snake_case      :List[Any] 							=    [[a[i][j] for j in range(snake_case__	)] for i in range(snake_case__						,snake_case__	)]

     return top_left, top_right, bot_left, bot_right






def 	UpperCamelCase	(							snake_case__  : list	):




     '''simple docstring'''






     return len(snake_case__	), len(matrix[0]	)






def 	UpperCamelCase	(							snake_case__  : list	):




     '''simple docstring'''






     print("""\n""".join(str(snake_case__	) for line in matrix	)	)






def 	UpperCamelCase	(							snake_case__  : list						,snake_case__  : list	):




     '''simple docstring'''






     if matrix_dimensions(snake_case__	) == (2, 2):
          return default_matrix_multiplication(snake_case__						,snake_case__	)

     __snake_case							,			__snake_case							,			__snake_case							,			__snake_case      :Any 							=    split_matrix(snake_case__	)
     __snake_case							,			__snake_case							,			__snake_case							,			__snake_case      :List[str] 							=    split_matrix(snake_case__	)

     __snake_case      :List[str] 							=    actual_strassen(snake_case__						,matrix_subtraction(snake_case__						,snake_case__	)	)
     __snake_case      :Dict 							=    actual_strassen(matrix_addition(snake_case__						,snake_case__	)						,snake_case__	)
     __snake_case      :List[str] 							=    actual_strassen(matrix_addition(snake_case__						,snake_case__	)						,snake_case__	)
     __snake_case      :Tuple 							=    actual_strassen(snake_case__						,matrix_subtraction(snake_case__						,snake_case__	)	)
     __snake_case      :Union[str, Any] 							=    actual_strassen(matrix_addition(snake_case__						,snake_case__	)						,matrix_addition(snake_case__						,snake_case__	)	)
     __snake_case      :Union[str, Any] 							=    actual_strassen(matrix_subtraction(snake_case__						,snake_case__	)						,matrix_addition(snake_case__						,snake_case__	)	)
     __snake_case      :Dict 							=    actual_strassen(matrix_subtraction(snake_case__						,snake_case__	)						,matrix_addition(snake_case__						,snake_case__	)	)

     __snake_case      :str 							=    matrix_addition(matrix_subtraction(matrix_addition(snake_case__						,snake_case__	)						,snake_case__	)						,snake_case__	)
     __snake_case      :str 							=    matrix_addition(snake_case__						,snake_case__	)
     __snake_case      :List[Any] 							=    matrix_addition(snake_case__						,snake_case__	)
     __snake_case      :int 							=    matrix_subtraction(matrix_subtraction(matrix_addition(snake_case__						,snake_case__	)						,snake_case__	)						,snake_case__	)

     # construct the new matrix from our 4 quadrants
     __snake_case      :Optional[Any] 							=    []
     for i in range(len(snake_case__	)	):
          new_matrix.append(top_left[i] + top_right[i]	)
     for i in range(len(snake_case__	)	):
          new_matrix.append(bot_left[i] + bot_right[i]	)
     return new_matrix






def 	UpperCamelCase	(							snake_case__  : list						,snake_case__  : list	):




     '''simple docstring'''






     if matrix_dimensions(snake_case__	)[1] != matrix_dimensions(snake_case__	)[0]:
          __snake_case      :Optional[Any] 							=    (
              """Unable to multiply these matrices, please check the dimensions.\n"""
              f'''Matrix A: {matrixa}\n'''
              f'''Matrix B: {matrixa}'''
          )
          raise Exception(snake_case__	)
     __snake_case      :Union[str, Any] 							=    matrix_dimensions(snake_case__	)
     __snake_case      :Tuple 							=    matrix_dimensions(snake_case__	)

     if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
          return [matrixa, matrixa]

     __snake_case      :Tuple 							=    max(*snake_case__						,*snake_case__	)
     __snake_case      :Tuple 							=    int(math.pow(2						,math.ceil(math.loga(snake_case__	)	)	)	)
     __snake_case      :int 							=    matrixa
     __snake_case      :Tuple 							=    matrixa

     # Adding zeros to the matrices so that the arrays dimensions are the same and also
     # power of 2
     for i in range(0						,snake_case__	):
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]						,snake_case__	):
                    new_matrixa[i].append(0	)
          else:
               new_matrixa.append([0] * maxim	)
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]						,snake_case__	):
                    new_matrixa[i].append(0	)
          else:
               new_matrixa.append([0] * maxim	)

     __snake_case      :Union[str, Any] 							=    actual_strassen(snake_case__						,snake_case__	)

     # Removing the additional zeros
     for i in range(0						,snake_case__	):
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]						,snake_case__	):
                    final_matrix[i].pop()
          else:
               final_matrix.pop()
     return final_matrix


if __name__ == "__main__":
     lowerCamelCase__       		=  [
         [2, 3, 4, 5],
         [6, 4, 3, 1],
         [2, 3, 6, 7],
         [3, 1, 2, 4],
         [2, 3, 4, 5],
         [6, 4, 3, 1],
         [2, 3, 6, 7],
         [3, 1, 2, 4],
         [2, 3, 4, 5],
         [6, 2, 3, 1],
     ]
     lowerCamelCase__       		=  [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
     print(strassen(matrixa, matrixa))










import colorsys

from PIL import Image  # type: ignore






def 	UpperCamelCase	(							snake_case__  : float						,snake_case__  : float						,snake_case__  : int	):




     '''simple docstring'''






     __snake_case      :List[Any] 							=    x
     __snake_case      :str 							=    y
     for step in range(snake_case__	):  # noqa: B007
          __snake_case      :Tuple 							=    a * a - b * b + x
          __snake_case      :Dict 							=    2 * a * b + y
          __snake_case      :str 							=    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	(							snake_case__  : float	):




     '''simple docstring'''






     if distance == 1:
          return (0, 0, 0)
     else:
          return (255, 255, 255)






def 	UpperCamelCase	(							snake_case__  : float	):




     '''simple docstring'''






     if distance == 1:
          return (0, 0, 0)
     else:
          return tuple(round(i * 255	) for i in colorsys.hsv_to_rgb(snake_case__						,1						,1	)	)






def 	UpperCamelCase	(							snake_case__  : int = 800						,snake_case__  : int = 600						,snake_case__  : float = -0.6						,snake_case__  : float = 0						,snake_case__  : float = 3.2						,snake_case__  : int = 50						,snake_case__  : bool = True						,):




     '''simple docstring'''






     __snake_case      :Tuple 							=    Image.new("""RGB"""						,(image_width, image_height)	)
     __snake_case      :Dict 							=    img.load()

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

               __snake_case      :Tuple 							=    get_distance(snake_case__						,snake_case__						,snake_case__	)

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

     return img


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     # colored version, full figure
     lowerCamelCase__       		=  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()


