

def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      A_							       =		[]
      if len(__UpperCamelCase   ) == 1:
            return [nums.copy()]
      for _ in range(len(__UpperCamelCase   )   ):
            A_							       =		nums.pop(0   )
            A_							       =		permute(__UpperCamelCase   )
            for perm in permutations:
                  perm.append(__UpperCamelCase   )
            result.extend(__UpperCamelCase   )
            nums.append(__UpperCamelCase   )
      return result







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      def backtrack(SCREAMING_SNAKE_CASE   ):
            if start == len(__UpperCamelCase   ) - 1:
                  output.append(nums[:]   )
            else:
                  for i in range(__UpperCamelCase		,				len(__UpperCamelCase   )   ):
                        A_       ,A_							       =		nums[i], nums[start]
                        backtrack(start + 1   )
                        A_       ,A_							       =		nums[i], nums[start]  # backtrack

      A_							       =		[]
      backtrack(0   )
      return output


if __name__ == "__main__":
      import doctest

      # use res to print the data in permute2 function
      __lowercase				      =						permutea([1, 2, 3])
      print(res)
      doctest.testmod()









'''simple docstring'''
import colorsys

from PIL import Image  # type: ignore

def 					lowerCamelCase_ ( __UpperCamelCase					:       float							,    __UpperCamelCase					:       float							,    __UpperCamelCase					:       int		)					->	float:







     """simple docstring"""
     _A				=							x
     _A				=							y
     for step in range(__UpperCamelCase		):  # noqa: B007
          _A				=							a * a - b * b + x
          _A				=							2 * a * b + y
          _A				=							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 					lowerCamelCase_ ( __UpperCamelCase					:       float		)					->	tuple:







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

def 					lowerCamelCase_ ( __UpperCamelCase					:       float		)					->	tuple:







     """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 					lowerCamelCase_ ( __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							,    )					->	Image.Image:







     """simple docstring"""
     _A				=							Image.new('RGB'							,    (image_width, image_height)		)
     _A				=							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
               _A				=							figure_width / image_width * image_height
               _A				=							figure_center_x + (image_x / image_width - 0.5) * figure_width
               _A				=							figure_center_y + (image_y / image_height - 0.5) * figure_height

               _A				=							get_distance(__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase		)

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

     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()





