
def 						__magic_name__			(   __a      :	str						):



     '''simple docstring'''




     UpperCamelCase__				=    [0 for i in range(len(__a						)						)]

     # initialize interval's left pointer and right pointer
     UpperCamelCase__		,	UpperCamelCase__				=    0, 0

     for i in range(1	,		len(__a						)						):
          # case when current index is inside the interval
          if i <= right_pointer:
               UpperCamelCase__				=    min(right_pointer - i + 1	,		z_result[i - left_pointer]						)
               UpperCamelCase__				=    min_edge

          while go_next(__a	,		__a	,		__a						):
               z_result[i] += 1

          # if new index's result gives us more right interval,
          # we've to update left_pointer and right_pointer
          if i + z_result[i] - 1 > right_pointer:
               UpperCamelCase__		,	UpperCamelCase__				=    i, i + z_result[i] - 1

     return z_result






def 						__magic_name__			(   __a      :	int	,		__a      :	list[int]	,		__a      :	str						):



     '''simple docstring'''




     return i + z_result[i] < len(__a						) and s[z_result[i]] == s[i + z_result[i]]






def 						__magic_name__			(   __a      :	str	,		__a      :	str						):



     '''simple docstring'''




     UpperCamelCase__				=    0
     # concatenate 'pattern' and 'input_str' and call z_function
     # with concatenated string
     UpperCamelCase__				=    z_function(pattern + input_str						)

     for val in z_result:
          # if value is greater then length of the pattern string
          # that means this index is starting position of substring
          # which is equal to pattern string
          if val >= len(__a						):
               answer += 1

     return answer


if __name__ == "__main__":
    import doctest

    doctest.testmod()







from PIL import Image






def 						__magic_name__			(   __a      :	Image						):



     '''simple docstring'''




     UpperCamelCase__		,	UpperCamelCase__				=    image.size
     UpperCamelCase__				=    0
     UpperCamelCase__				=    image.load()
     for i in range(__a						):
          for j in range(__a						):
               UpperCamelCase__				=    pixels[j, i]
               mean += pixel
     mean //= width * height

     for j in range(__a						):
          for i in range(__a						):
               UpperCamelCase__				=    255 if pixels[i, j] > mean else 0
     return image


if __name__ == "__main__":
    lowerCamelCase_						     =					mean_threshold(Image.open('''path_to_image''').convert('''L'''))
    image.save('''output_image_path''')





