
'''simple docstring'''






from math import factorial

class  UpperCAmelCase__						:



    def __init__(	self      :       Optional[Any],__A      :       int,__A      :       List[Any]     ):
          _lowerCamelCase				:   Dict								=   real
          if isinstance(__A,__A     ):
                _lowerCamelCase				:   str								=   [1] * rank
          else:
                _lowerCamelCase				:   Union[str, Any]								=   rank



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



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



    def __add__(	self      :       int,__A      :       str     ):
          if not isinstance(__A,__A     ):
                return Dual(self.real + other,self.duals     )
          _lowerCamelCase				:   int								=   self.duals.copy()
          _lowerCamelCase				:   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     ))     )
          _lowerCamelCase				:   Tuple								=   []
          for i in range(len(__A     )     ):
                new_duals.append(s_dual[i] + o_dual[i]     )
          return Dual(self.real + other.real,__A     )

    lowerCAmelCase_				    =		__add__



    def __sub__(	self      :       Dict,__A      :       int     ):
          return self + other * -1



    def __mul__(	self      :       int,__A      :       Optional[int]     ):
          if not isinstance(__A,__A     ):
                _lowerCamelCase				:   str								=   []
                for i in self.duals:
                      new_duals.append(i * other     )
                return Dual(self.real * other,__A     )
          _lowerCamelCase				:   Any								=   [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     )

    lowerCAmelCase_				    =		__mul__



    def __truediv__(	self      :       List[str],__A      :       List[Any]     ):
          if not isinstance(__A,__A     ):
                _lowerCamelCase				:   Optional[int]								=   []
                for i in self.duals:
                      new_duals.append(i / other     )
                return Dual(self.real / other,__A     )
          raise ValueError



    def __floordiv__(	self      :       List[str],__A      :       Any     ):
          if not isinstance(__A,__A     ):
                _lowerCamelCase				:   Dict								=   []
                for i in self.duals:
                      new_duals.append(i // other     )
                return Dual(self.real // other,__A     )
          raise ValueError



    def __pow__(	self      :       Optional[Any],__A      :       Optional[Any]     ):
          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
          _lowerCamelCase				:   int								=   self
          for _ in range(n - 1     ):
                x *= self
          return x







def 		A_       (	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    str				,	_lowerCAmelCase   :    Any							):



      """simple docstring"""




      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"							)
      _lowerCamelCase				:   Optional[Any]								=   Dual(_lowerCAmelCase				,	1							)
      _lowerCamelCase				:   List[str]								=   func(_lowerCAmelCase							)
      if order == 0:
            return result.real
      return result.duals[order - 1] * factorial(_lowerCAmelCase							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()







 def 		A_       (	_lowerCAmelCase   :    Any							):



       """simple docstring"""




       return y**2 * y**4



 print(differentiate(f, 9, 2))

'''simple docstring'''






import random
from typing import Any







def 		A_       (	_lowerCAmelCase   :    list							):



      """simple docstring"""




      for _ in range(len(_lowerCAmelCase							)							):
            _lowerCamelCase				:   Any								=   random.randint(0				,	len(_lowerCAmelCase							) - 1							)
            _lowerCamelCase				:   List[str]								=   random.randint(0				,	len(_lowerCAmelCase							) - 1							)
            _lowerCamelCase						,		_lowerCamelCase				:   Union[str, Any]								=   data[b], data[a]
      return data


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