
"""simple docstring"""


from math import pow






def    _snake_case					(		snake_case__ :  int						,   snake_case__ :  int						,   snake_case__ :  int						,   snake_case__ :  int						,   snake_case__ :  int						,   ):
	if current_sum == needed_sum:
		# If the sum of the powers is equal to needed_sum, then we have a solution.
		solutions_count += 1
		return current_sum, solutions_count

	A     = int(pow(snake_case__						,   snake_case__  )  )
	if current_sum + i_to_n <= needed_sum:
		# If the sum of the powers is less than needed_sum, then continue adding powers.
		current_sum += i_to_n
		A ,   A     = backtrack(
		    snake_case__						,   snake_case__						,   current_number + 1						,   snake_case__						,   snake_case__  )
		current_sum -= i_to_n
	if i_to_n < needed_sum:
		# If the power of i is less than needed_sum, then try with the next power.
		A ,   A     = backtrack(
		    snake_case__						,   snake_case__						,   current_number + 1						,   snake_case__						,   snake_case__  )
	return current_sum, solutions_count






def    _snake_case					(		snake_case__ :  int						,   snake_case__ :  int  ):
	if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
		raise ValueError(
		    'Invalid input\n'
		    'needed_sum must be between 1 and 1000, power between 2 and 10.'  )

	return backtrack(snake_case__						,   snake_case__						,   1						,   0						,   0  )[1]  # Return the solutions_count


if __name__ == "__main__":
		import doctest

		doctest.testmod()

from PIL import Image


def    a      ( a	)     ->Image:




			'''simple docstring'''


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

			for j in range(a	):
						for i in range(a	):
									SCREAMING_SNAKE_CASE     						= 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')