






"""simple docstring"""






from math import factorial





class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					A__							 =       real
					if isinstance(__a  ,					__a						):
									A__							 =       [1] * rank
					else:
									A__							 =       rank


	def __repr__(      self						):


					"""simple docstring"""

					return (
					    f'''{self.real}+'''
					    f'''{'+'.join(str(__a						)+'E'+str(n+1						)for n,dual in enumerate(self.duals						)						)}'''
					)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					A__							 =       self.duals.copy()
					while cur[-1] == 0:
									cur.pop(-1						)
					return Dual(self.real  ,					__a						)


	def __add__(      self  ,					__a						):


					"""simple docstring"""

					if not isinstance(__a  ,					__a						):
									return Dual(self.real + other  ,					self.duals						)
					A__							 =       self.duals.copy()
					A__							 =       other.duals.copy()
					if len(__a						) > len(__a						):
									o_dual.extend([1] * (len(__a						) - len(__a						))						)
					elif len(__a						) < len(__a						):
									s_dual.extend([1] * (len(__a						) - len(__a						))						)
					A__							 =       []
					for i in range(len(__a						)						):
									new_duals.append(s_dual[i] + o_dual[i]						)
					return Dual(self.real + other.real  ,					__a						)

	SCREAMING_SNAKE_CASE_:							Union[str, Any]   			=					__add__


	def __sub__(      self  ,					__a						):


					"""simple docstring"""

					return self + other * -1


	def __mul__(      self  ,					__a						):


					"""simple docstring"""

					if not isinstance(__a  ,					__a						):
									A__							 =       []
									for i in self.duals:
													new_duals.append(i * other						)
									return Dual(self.real * other  ,					__a						)
					A__							 =       [0] * (len(self.duals						) + len(other.duals						) + 1)
					for i, item in enumerate(self.duals						):
									for j, jtem in enumerate(other.duals						):
													new_duals[i + j + 1] += item * jtem
					for k in range(len(self.duals						)						):
									new_duals[k] += self.duals[k] * other.real
					for index in range(len(other.duals						)						):
									new_duals[index] += other.duals[index] * self.real
					return Dual(self.real * other.real  ,					__a						)

	SCREAMING_SNAKE_CASE_:							List[Any]   			=					__mul__


	def __truediv__(      self  ,					__a						):


					"""simple docstring"""

					if not isinstance(__a  ,					__a						):
									A__							 =       []
									for i in self.duals:
													new_duals.append(i / other						)
									return Dual(self.real / other  ,					__a						)
					raise ValueError


	def __floordiv__(      self  ,					__a						):


					"""simple docstring"""

					if not isinstance(__a  ,					__a						):
									A__							 =       []
									for i in self.duals:
													new_duals.append(i // other						)
									return Dual(self.real // other  ,					__a						)
					raise ValueError






	def __pow__(      self  ,					__a						):


					"""simple docstring"""

					if n < 0 or isinstance(__a  ,					__a						):
									raise ValueError('power must be a positive integer'						)
					if n == 0:
									return 1
					if n == 1:
									return self
					A__							 =       self
					for _ in range(n - 1						):
									x *= self
					return x





def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__				):
				if not callable(lowerCAmelCase__				):
								raise ValueError('differentiate() requires a function as input for func'				)
				if not isinstance(lowerCAmelCase__       ,(float, int)				):
								raise ValueError('differentiate() requires a float as input for position'				)
				if not isinstance(lowerCAmelCase__       ,lowerCAmelCase__				):
								raise ValueError('differentiate() requires an int as input for order'				)
				A__							 =       Dual(lowerCAmelCase__       ,1				)
				A__							 =       func(lowerCAmelCase__				)
				if order == 0:
								return result.real
				return result.duals[order - 1] * factorial(lowerCAmelCase__				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()



					def  __lowerCamelCase					(					lowerCAmelCase__				):
									return y**2 * y**4







					print(differentiate(f, 9, 2))










"""simple docstring"""






from PIL import Image



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

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


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


