





"""simple docstring"""


from math import factorial



class   __SCREAMING_SNAKE_CASE     :







  '''simple docstring'''


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

  def __repr__(		self :							str						)		->					Union[str, Any]:
        return (
            F'''{self.real}+'''
            F'''{'+'.join(str(__a						)+'E'+str(n+1						)for n,dual in enumerate(self.duals						)						)}'''
        )

  def  __SCREAMING_SNAKE_CASE					(		self :							str						)		->					Any:
        _UpperCamelCase   :						Optional[Any]    =							self.duals.copy()
        while cur[-1] == 0:
              cur.pop(-1						)
        return Dual(self.real       , __a						)

  def __add__(		self :							Optional[int]       , __a :							Dict						)		->					Optional[int]:
        if not isinstance(__a       , __a						):
              return Dual(self.real + other       , self.duals						)
        _UpperCamelCase   :						Tuple    =							self.duals.copy()
        _UpperCamelCase   :						Tuple    =							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						))						)
        _UpperCamelCase   :						Optional[Any]    =							[]
        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 :							List[str]       , __a :							Tuple						)		->					int:
        return self + other * -1

  def __mul__(		self :							Union[str, Any]       , __a :							Optional[int]						)		->					int:
        if not isinstance(__a       , __a						):
              _UpperCamelCase   :						List[Any]    =							[]
              for i in self.duals:
                    new_duals.append(i * other						)
              return Dual(self.real * other       , __a						)
        _UpperCamelCase   :						Optional[int]    =							[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__				:str						  =       __mul__

  def __truediv__(		self :							str       , __a :							Union[str, Any]						)		->					List[str]:
        if not isinstance(__a       , __a						):
              _UpperCamelCase   :						str    =							[]
              for i in self.duals:
                    new_duals.append(i / other						)
              return Dual(self.real / other       , __a						)
        raise ValueError

  def __floordiv__(		self :							Tuple       , __a :							str						)		->					Optional[Any]:
        if not isinstance(__a       , __a						):
              _UpperCamelCase   :						Union[str, Any]    =							[]
              for i in self.duals:
                    new_duals.append(i // other						)
              return Dual(self.real // other       , __a						)
        raise ValueError


  def __pow__(		self :							Dict       , __a :							List[Any]						)		->					List[str]:
        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
        _UpperCamelCase   :						Optional[Any]    =							self
        for _ in range(n - 1						):
              x *= self
        return x





def        lowercase__     (       lowercase_		,lowercase_		,lowercase_      )       ->		Union[str, Any]:




      """simple docstring"""

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()




  def        lowercase__     (       lowercase_      )       ->		Optional[Any]:




        """simple docstring"""

        return y**2 * y**4

  print(differentiate(f, 9, 2))







"""simple docstring"""


import random
from typing import Any




def        lowercase__     (       lowercase_      )       ->		list[Any]:




      """simple docstring"""

      for _ in range(len(lowercase_      )      ):
            _UpperCamelCase   :						Dict    =							random.randint(0		,len(lowercase_      ) - 1      )
            _UpperCamelCase   :						str    =							random.randint(0		,len(lowercase_      ) - 1      )
            _UpperCamelCase,	_UpperCamelCase   :						Optional[Any]    =							data[b], data[a]
      return data


if __name__ == "__main__":
  lowerCamelCase__						= [0, 1, 2, 3, 4, 5, 6, 7]
  lowerCamelCase__						= ["python", "says", "hello", "!"]
  print("Fisher-Yates Shuffle:")
  print("List", integers, strings)
  print("FY Shuffle", fisher_yates_shuffle(integers), fisher_yates_shuffle(strings))
