


'''simple docstring'''
def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	list:







     """simple docstring"""
     _A				=							int(__UpperCamelCase		)
     if n_element < 1:
          _A				=							ValueError('a should be a positive number'		)
          raise my_error

     _A				=							[1]
     _A		,				_A		,				_A				=							(0, 0, 0)
     _A				=							1
     while index < n_element:
          while hamming_list[i] * 2 <= hamming_list[-1]:
               i += 1
          while hamming_list[j] * 3 <= hamming_list[-1]:
               j += 1
          while hamming_list[k] * 5 <= hamming_list[-1]:
               k += 1
          hamming_list.append(
              min(hamming_list[i] * 2							,    hamming_list[j] * 3							,    hamming_list[k] * 5		)		)
          index += 1
     return hamming_list


if __name__ == "__main__":
    lowerCAmelCase						=					input("""Enter the last number (nth term) of the Hamming Number Series: """)
    print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
    lowerCAmelCase						=					hamming(int(n))
    print("""-----------------------------------------------------""")
    print(F'The list with nth numbers is: {hamming_numbers}')
    print("""-----------------------------------------------------""")









'''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()





