


from __future__ import annotations



def      _lowerCAmelCase  (							lowerCAmelCase_							:int							)->list[int]:
   '''simple docstring'''






   snake_case_         =   [0] * max_one

   for i in range(0						,  lowerCAmelCase_							):
      snake_case_         =   i

   for i in range(2						,  lowerCAmelCase_							):
      if totients[i] == i:
         for j in range(lowerCAmelCase_						,  lowerCAmelCase_						,  lowerCAmelCase_							):
            totients[j] -= totients[j] // i

   return totients



def      _lowerCAmelCase  (							lowerCAmelCase_							:int						,  lowerCAmelCase_							:int							)->bool:
   '''simple docstring'''






   return sorted(str(lowerCAmelCase_							)							) == sorted(str(lowerCAmelCase_							)							)



def      _lowerCAmelCase  (							lowerCAmelCase_							:int = 10_000_000							)->int:
   '''simple docstring'''






   snake_case_         =   1  # i
   snake_case_         =   0  # φ(i)
   snake_case_         =   get_totients(max_n + 1							)

   for i in range(2						,  max_n + 1							):
      snake_case_         =   totients[i]

      if i * min_denominator < min_numerator * t and has_same_digits(lowerCAmelCase_						,  lowerCAmelCase_							):
         snake_case_         =   i
         snake_case_         =   t

   return min_numerator


if __name__ == "__main__":
   print(F'''{solution() = }''')







import numpy as np
from cva import destroyAllWindows, imread, imshow, waitKey


class       __lowerCAmelCase       :






  """simple docstring"""





  def __init__(       self    :    Optional[Any]      ,			_lowerCAmelCase    :    Union[str, Any]      ,			_lowerCAmelCase    :    int					)				->	Tuple:




     """simple docstring"""
     snake_case_         =   0
     # max greyscale value for #FFFFFF
     snake_case_         =   int(self.get_greyscale(2_5_5      ,			2_5_5      ,			2_5_5					)					)

     if not self.min_threshold < threshold < self.max_threshold:
        snake_case_         =   F'''Factor value should be from 0 to {self.max_threshold}'''
        raise ValueError(_lowerCAmelCase					)

     snake_case_         =   input_img
     snake_case_         =   threshold
     snake_case_      ,      snake_case_         =   self.input_img.shape[1], self.input_img.shape[0]

     # error table size (+4 columns and +1 row) greater than input image because of
     # lack of if statements
     snake_case_         =   [
         [0 for _ in range(self.height + 4					)] for __ in range(self.width + 1					)
     ]
     snake_case_         =   np.ones((self.width, self.height, 3)      ,			np.uinta					) * 2_5_5



  @classmethod
  def    lowerCAmelCase__					(       cls    :    Optional[Any]      ,			_lowerCAmelCase    :    int      ,			_lowerCAmelCase    :    int      ,			_lowerCAmelCase    :    int					)				->	float:




     """simple docstring"""
     return 0.114 * blue + 0.587 * green + 0.2_126 * red



  def    lowerCAmelCase__					(       self    :    Union[str, Any]					)				->	None:




     """simple docstring"""
     for y in range(self.height					):
        for x in range(self.width					):
           snake_case_         =   int(self.get_greyscale(*self.input_img[y][x]					)					)
           if self.threshold > greyscale + self.error_table[y][x]:
              snake_case_         =   (0, 0, 0)
              snake_case_         =   greyscale + self.error_table[x][y]
           else:
              snake_case_         =   (2_5_5, 2_5_5, 2_5_5)
              snake_case_         =   greyscale + self.error_table[x][y] - 2_5_5
           self.error_table[y][x + 1] += int(8 / 3_2 * current_error					)
           self.error_table[y][x + 2] += int(4 / 3_2 * current_error					)
           self.error_table[y + 1][x] += int(8 / 3_2 * current_error					)
           self.error_table[y + 1][x + 1] += int(4 / 3_2 * current_error					)
           self.error_table[y + 1][x + 2] += int(2 / 3_2 * current_error					)
           self.error_table[y + 1][x - 1] += int(4 / 3_2 * current_error					)
           self.error_table[y + 1][x - 2] += int(2 / 3_2 * current_error					)


if __name__ == "__main__":
   # create Burke's instances with original images in greyscale
   SCREAMING_SNAKE_CASE		:Dict											=       [
       Burkes(imread('''image_data/lena.jpg''', 1), threshold)
       for threshold in (1, 1_26, 1_30, 1_40)
   ]

   for burkes in burkes_instances:
      burkes.process()

   for burkes in burkes_instances:
      imshow(
          F'''Original image with dithering threshold: {burkes.threshold}''',
          burkes.output_img,
      )

   waitKey(0)
   destroyAllWindows()




