

from math import factorial







class 					lowercase							:




				def __init__(   self ,  snake_case ,  snake_case			):
											snake_case_     							=       real
											if isinstance(snake_case ,  snake_case			):
																		snake_case_     							=       [1] * rank
											else:
																		snake_case_     							=       rank




				def __repr__(   self			):
											return (
											    F'''{self.real}+'''
											    F'''{"+".join(str(snake_case			)+"E"+str(n+1			)for n,dual in enumerate(self.duals			)			)}'''
											)




				def        a				(   self			):
											snake_case_     							=       self.duals.copy()
											while cur[-1] == 0:
																		cur.pop(-1			)
											return Dual(self.real ,  snake_case			)




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

				__SCREAMING_SNAKE_CASE   :					Union[str, Any]			     =     __add__




				def __sub__(   self ,  snake_case			):
											return self + other * -1




				def __mul__(   self ,  snake_case			):
											if not isinstance(snake_case ,  snake_case			):
																		snake_case_     							=       []
																		for i in self.duals:
																									new_duals.append(i * other			)
																		return Dual(self.real * other ,  snake_case			)
											snake_case_     							=       [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 ,  snake_case			)

				__SCREAMING_SNAKE_CASE   :					str			     =     __mul__




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




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




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





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






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


if __name__ == "__main__":
					import doctest

					doctest.testmod()





					def    __lowerCamelCase      (					UpperCamelCase__ ):







												'''simple docstring'''






												return y**2 * y**4


					print(differentiate(f, 9, 2))







_UpperCAmelCase						:  Any									=			6_5521





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''simple docstring'''






							snake_case_     							=       1
							snake_case_     							=       0
							for plain_chr in plain_text:
														snake_case_     							=       (a + ord(UpperCamelCase__ )) % MOD_ADLER
														snake_case_     							=       (b + a) % MOD_ADLER
							return (b << 16) | a




