






from math import factorial


class 					_snake_case						:






	def __init__(		self					,UpperCamelCase					,UpperCamelCase       )						->    List[Any]:
					snake_case__      :Any         =   real
					if isinstance(UpperCamelCase					,UpperCamelCase       ):
									snake_case__      :Union[str, Any]         =   [1] * rank
					else:
									snake_case__      :Tuple         =   rank






	def __repr__(		self       )						->    List[str]:
					return (
					    f'{self.real}+'
					    f'{"+".join(str(UpperCamelCase       )+"E"+str(n+1       )for n,dual in enumerate(self.duals       )       )}'
					)






	def    lowerCAmelCase_							(		self       )						->    int:
					snake_case__      :str         =   self.duals.copy()
					while cur[-1] == 0:
									cur.pop(-1       )
					return Dual(self.real					,UpperCamelCase       )






	def __add__(		self					,UpperCamelCase       )						->    Dict:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									return Dual(self.real + other					,self.duals       )
					snake_case__      :Union[str, Any]         =   self.duals.copy()
					snake_case__      :Dict         =   other.duals.copy()
					if len(UpperCamelCase       ) > len(UpperCamelCase       ):
									o_dual.extend([1] * (len(UpperCamelCase       ) - len(UpperCamelCase       ))       )
					elif len(UpperCamelCase       ) < len(UpperCamelCase       ):
									s_dual.extend([1] * (len(UpperCamelCase       ) - len(UpperCamelCase       ))       )
					snake_case__      :Dict         =   []
					for i in range(len(UpperCamelCase       )       ):
									new_duals.append(s_dual[i] + o_dual[i]       )
					return Dual(self.real + other.real					,UpperCamelCase       )

	_A          =   __add__






	def __sub__(		self					,UpperCamelCase       )						->    List[Any]:
					return self + other * -1






	def __mul__(		self					,UpperCamelCase       )						->    Any:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									snake_case__      :Any         =   []
									for i in self.duals:
													new_duals.append(i * other       )
									return Dual(self.real * other					,UpperCamelCase       )
					snake_case__      :List[str]         =   [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					,UpperCamelCase       )

	_A          =   __mul__






	def __truediv__(		self					,UpperCamelCase       )						->    Optional[int]:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									snake_case__      :Tuple         =   []
									for i in self.duals:
													new_duals.append(i / other       )
									return Dual(self.real / other					,UpperCamelCase       )
					raise ValueError






	def __floordiv__(		self					,UpperCamelCase       )						->    int:
					if not isinstance(UpperCamelCase					,UpperCamelCase       ):
									snake_case__      :int         =   []
									for i in self.duals:
													new_duals.append(i // other       )
									return Dual(self.real // other					,UpperCamelCase       )
					raise ValueError






	def __pow__(		self					,UpperCamelCase       )						->    Dict:
					if n < 0 or isinstance(UpperCamelCase					,UpperCamelCase       ):
									raise ValueError("power must be a positive integer"       )
					if n == 0:
									return 1
					if n == 1:
									return self
					snake_case__      :Tuple         =   self
					for _ in range(n - 1       ):
									x *= self
					return x





def 					lowercase_ (    __snake_case     :							List[str]	,	__snake_case     :							List[Any]	,	__snake_case     :							Optional[int]      )     -> Union[str, Any]:





				'''simple docstring'''


				if not callable(__snake_case      ):
								raise ValueError("differentiate() requires a function as input for func"      )
				if not isinstance(__snake_case	,	(float, int)      ):
								raise ValueError("differentiate() requires a float as input for position"      )
				if not isinstance(__snake_case	,	__snake_case      ):
								raise ValueError("differentiate() requires an int as input for order"      )
				snake_case__      :str         =   Dual(__snake_case	,	1      )
				snake_case__      :Optional[Any]         =   func(__snake_case      )
				if order == 0:
								return result.real
				return result.duals[order - 1] * factorial(__snake_case      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()





	def 					lowercase_ (    __snake_case     :							str      )     -> Optional[int]:





					'''simple docstring'''


					return y**2 * y**4
	print(differentiate(f, 9, 2))







import os

try:
	from .build_directory_md import good_file_paths
except ImportError:
	from build_directory_md import good_file_paths  # type: ignore

__UpperCAmelCase							:   List[Any]							=  list(good_file_paths())
assert filepaths, "good_file_paths() failed!"

__UpperCAmelCase							:   int							=  [file for file in filepaths if file != file.lower()]
if upper_files:
	print(F'''{len(upper_files)} files contain uppercase characters:''')
	print("\n".join(upper_files) + "\n")

__UpperCAmelCase							:   Any							=  [file for file in filepaths if " " in file]
if space_files:
	print(F'''{len(space_files)} files contain space characters:''')
	print("\n".join(space_files) + "\n")

__UpperCAmelCase							:   str							=  [file for file in filepaths if "-" in file]
if hyphen_files:
	print(F'''{len(hyphen_files)} files contain hyphen characters:''')
	print("\n".join(hyphen_files) + "\n")

__UpperCAmelCase							:   Dict							=  [file for file in filepaths if os.sep not in file]
if nodir_files:
	print(F'''{len(nodir_files)} files are not in a directory:''')
	print("\n".join(nodir_files) + "\n")

__UpperCAmelCase							:   int							=  len(upper_files + space_files + hyphen_files + nodir_files)
if bad_files:
	import sys

	sys.exit(bad_files)