
"""simple docstring"""




from math import factorial



class 	lowerCAmelCase_						:


				"""simple docstring"""



				def __init__(self   ,       SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    )					->		int:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Any           =   real
											if isinstance(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    ):
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   [1] * rank
											else:
																		SCREAMING_SNAKE_CASE__						:       int           =   rank



				def __repr__(self    )					->		Optional[int]:



											"""simple docstring"""




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



				def 	__magic_name__    (self    )					->		List[str]:



											"""simple docstring"""




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



				def __add__(self   ,       SCREAMING_SNAKE_CASE__    )					->		Optional[Any]:



											"""simple docstring"""




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

				__UpperCamelCase      :						int					       =   __add__



				def __sub__(self   ,       SCREAMING_SNAKE_CASE__    )					->		Dict:



											"""simple docstring"""




											return self + other * -1



				def __mul__(self   ,       SCREAMING_SNAKE_CASE__    )					->		int:



											"""simple docstring"""




											if not isinstance(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    ):
																		SCREAMING_SNAKE_CASE__						:       Optional[int]           =   []
																		for i in self.duals:
																									new_duals.append(i * other    )
																		return Dual(self.real * other   ,       SCREAMING_SNAKE_CASE__    )
											SCREAMING_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   ,       SCREAMING_SNAKE_CASE__    )

				__UpperCamelCase      :						Any					       =   __mul__



				def __truediv__(self   ,       SCREAMING_SNAKE_CASE__    )					->		List[Any]:



											"""simple docstring"""




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



				def __floordiv__(self   ,       SCREAMING_SNAKE_CASE__    )					->		List[str]:



											"""simple docstring"""




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



				def __pow__(self   ,       SCREAMING_SNAKE_CASE__    )					->		List[str]:



											"""simple docstring"""




											if n < 0 or isinstance(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    ):
																		raise ValueError("""power must be a positive integer"""    )
											if n == 0:
																		return 1
											if n == 1:
																		return self
											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self
											for _ in range(n - 1    ):
																		x *= self
											return x






def lowercase_  (   _snake_case   ,_snake_case   ,_snake_case						):
							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"""						)
							SCREAMING_SNAKE_CASE__						:       Any           =   Dual(_snake_case   ,1						)
							SCREAMING_SNAKE_CASE__						:       Optional[int]           =   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						):
												return y**2 * y**4

					print(differentiate(f, 9, 2))






"""simple docstring"""




def lowercase_  (   _snake_case   ,_snake_case						):

							if not (isinstance(_snake_case   ,_snake_case						) and isinstance(_snake_case   ,_snake_case						)):
														raise ValueError("""longest_common_substring() takes two strings for inputs"""						)

							SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   len(_snake_case						)
							SCREAMING_SNAKE_CASE__						:       int           =   len(_snake_case						)

							SCREAMING_SNAKE_CASE__						:       Dict           =   [[0] * (texta_length + 1) for _ in range(texta_length + 1						)]
							SCREAMING_SNAKE_CASE__						:       List[Any]           =   0
							SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   0

							for i in range(1   ,texta_length + 1						):
														for j in range(1   ,texta_length + 1						):
																					if texta[i - 1] == texta[j - 1]:
																												SCREAMING_SNAKE_CASE__						:       int           =   1 + dp[i - 1][j - 1]
																												if dp[i][j] > ans_length:
																																			SCREAMING_SNAKE_CASE__						:       List[Any]           =   i
																																			SCREAMING_SNAKE_CASE__						:       List[str]           =   dp[i][j]

							return texta[ans_index - ans_length : ans_index]


if __name__ == "__main__":
					import doctest

					doctest.testmod()




