




from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__					,			__magic_name__						:						Union[str, Any]										=analyze_text(lowerCamelCase )
				__magic_name__						:						List[Any]										=list(""" """ + ascii_lowercase )
				# what is our total sum of probabilities.
				__magic_name__						:						Union[str, Any]										=sum(single_char_strings.values() )

				# one length string
				__magic_name__						:						Optional[int]										=0
				# for each alpha we go in our dict and if it is in it we calculate entropy
				for ch in my_alphas:
								if ch in single_char_strings:
												__magic_name__						:						str										=single_char_strings[ch]
												__magic_name__						:						Dict										=my_str / all_sum
												my_fir_sum += prob * math.loga(lowerCamelCase )  # entropy formula.

    # print entropy
				print(F"{round(-1 * my_fir_sum ):.1f}" )

				# two len string
				__magic_name__						:						Optional[Any]										=sum(two_char_strings.values() )
				__magic_name__						:						int										=0
				# for each alpha (two in size) calculate entropy.
				for cha in my_alphas:
								for cha in my_alphas:
												__magic_name__						:						List[str]										=cha + cha
												if sequence in two_char_strings:
																__magic_name__						:						str										=two_char_strings[sequence]
																__magic_name__						:						Union[str, Any]										=int(lowerCamelCase ) / all_sum
																my_sec_sum += prob * math.loga(lowerCamelCase )

    # print second entropy
				print(F"{round(-1 * my_sec_sum ):.1f}" )

				# print the difference between them
				print(F"{round((-1 * my_sec_sum) - (-1 * my_fir_sum) ):.1f}" )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Tuple										=Counter()  # type: ignore
				__magic_name__						:						int										=Counter()  # type: ignore
				single_char_strings[text[-1]] += 1

				# first case when we have space at start.
				two_char_strings[" " + text[0]] += 1
				for i in range(0						,  len(lowerCamelCase ) - 1 ):
								single_char_strings[text[i]] += 1
								two_char_strings[text[i : i + 2]] += 1
				return single_char_strings, two_char_strings




def 		lowerCAmelCase_ (						):
				import doctest

				doctest.testmod()
				# text = (
				#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
				#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
				#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
				#     "beloved evident through no service elderly is. Blind there if every no so "
				#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
				#     "of message cottage windows do besides against uncivil.  Delightful "
				#     "unreserved impossible few estimating men favourable see entreaties. She "
				#     "propriety immediate was improving. He or entrance humoured likewise "
				#     "moderate. Much nor game son say feel. Fat make met can must form into "
				#     "gate. Me we offending prevailed discovery. "
				# )

				# calculate_prob(text)


if __name__ == "__main__":
							main()








'''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()





