'''simple docstring'''

def snake_case_      (					)			->					list[list[int]]:
   return [list(range(1000 - i	,   -1000 - i	,   -1)) for i in range(1000)]


A_     :						str    							=generate_large_matrix()
A_     :						int    							=(
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)



def snake_case_      (					__snake_case  :							list[list[int]])			->					None:
   assert all(row == sorted(__snake_case	,   reverse=__snake_case) for row in grid)
   assert all(list(__snake_case) == sorted(__snake_case	,   reverse=__snake_case) for col in zip(*__snake_case))



def snake_case_      (					__snake_case  :							list[int])			->					int:
   lowerCAmelCase_			=      0
   lowerCAmelCase_			=      len(__snake_case) - 1

   # Edge cases such as no values or all numbers are negative.
   if not array or array[0] < 0:
      return 0

   while right + 1 > left:
      lowerCAmelCase_			=      (left + right) // 2
      lowerCAmelCase_			=      array[mid]

      # Num must be negative and the index must be greater than or equal to 0.
      if num < 0 and array[mid - 1] >= 0:
         return mid

      if num >= 0:
         lowerCAmelCase_			=      mid + 1
      else:
         lowerCAmelCase_			=      mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
   return len(__snake_case)



def snake_case_      (					__snake_case  :							list[list[int]])			->					int:
   lowerCAmelCase_			=      0
   lowerCAmelCase_			=      len(grid[0])

   for i in range(len(__snake_case)):
      lowerCAmelCase_			=      find_negative_index(grid[i][:bound])
      total += bound
   return (len(__snake_case) * len(grid[0])) - total



def snake_case_      (					__snake_case  :							list[list[int]])			->					int:
   return len([number for row in grid for number in row if number < 0])



def snake_case_      (					__snake_case  :							list[list[int]])			->					int:
   lowerCAmelCase_			=      0
   for row in grid:
      for i, number in enumerate(__snake_case):
         if number < 0:
            total += len(__snake_case) - i
            break
   return total



def snake_case_      (					)			->					None:
   from timeit import timeit

   print('''Running benchmarks''')
   lowerCAmelCase_			=      (
       '''from __main__ import count_negatives_binary_search, '''
       '''count_negatives_brute_force, count_negatives_brute_force_with_break, grid'''
   )
   for func in (
       "count_negatives_binary_search",  # took 0.7727 seconds
       "count_negatives_brute_force_with_break",  # took 4.6505 seconds
       "count_negatives_brute_force",  # took 12.8160 seconds
   ):
      lowerCAmelCase_			=      timeit(F'''{func}(grid=grid)'''	,   setup=__snake_case	,   number=500)
      print(F'''{func}() took {time:0.4f} seconds''')


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()






'''simple docstring'''

import colorsys

from PIL import Image  # type: ignore



def snake_case_      (					__snake_case  :							float	,   __snake_case  :							float	,   __snake_case  :							int)			->					float:
   lowerCAmelCase_			=      x
   lowerCAmelCase_			=      y
   for step in range(__snake_case):  # noqa: B007
      lowerCAmelCase_			=      a * a - b * b + x
      lowerCAmelCase_			=      2 * a * b + y
      lowerCAmelCase_			=      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 snake_case_      (					__snake_case  :							float)			->					tuple:
   if distance == 1:
      return (0, 0, 0)
   else:
      return (255, 255, 255)



def snake_case_      (					__snake_case  :							float)			->					tuple:
   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 snake_case_      (					__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	,   )			->					Image.Image:
   lowerCAmelCase_			=      Image.new('''RGB'''	,   (image_width, image_height))
   lowerCAmelCase_			=      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
         lowerCAmelCase_			=      figure_width / image_width * image_height
         lowerCAmelCase_			=      figure_center_x + (image_x / image_width - 0.5) * figure_width
         lowerCAmelCase_			=      figure_center_y + (image_y / image_height - 0.5) * figure_height

         lowerCAmelCase_			=      get_distance(__snake_case	,   __snake_case	,   __snake_case)

         # color the corresponding pixel based on the selected coloring-function
         if use_distance_color_coding:
            lowerCAmelCase_			=      get_color_coded_rgb(__snake_case)
         else:
            lowerCAmelCase_			=      get_black_and_white_rgb(__snake_case)

   return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 A_     :						List[str]    							=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()





