





'''simple docstring'''
from math import factorial

class      snake_case     :




 """simple docstring"""



 def __init__(       self       :							List[str]							,	__A       :							Any							,	__A       :							Tuple	):
        __UpperCamelCase       =  real
        if isinstance(__A							,	__A	):
               __UpperCamelCase       =  [1] * rank
        else:
               __UpperCamelCase       =  rank






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






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






 def __add__(       self       :							List[Any]							,	__A       :							Any	):
        if not isinstance(__A							,	__A	):
               return Dual(self.real + other							,	self.duals	)
        __UpperCamelCase       =  self.duals.copy()
        __UpperCamelCase       =  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       =  []
        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_	:					Tuple					=__add__






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






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






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






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






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






def 				lowercase__   (   __lowercase						:  str				,  __lowercase						:  Optional[int]				,  __lowercase						:  List[str]     ) ->      Dict:



       """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       =  Dual(__lowercase				,  1     )
       __UpperCamelCase       =  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[int]     ) ->      List[Any]:



           """simple docstring"""






           return y**2 * y**4


    print(differentiate(f, 9, 2))




from __future__ import annotations




def    snake_case_     (  snake_case			,							snake_case     )  ->				bool:
       if len(snake_case     ) == 0:
              return False
       lowercase__:   Any  			=   len(snake_case     ) // 2
       if a_list[midpoint] == item:
              return True
       if item < a_list[midpoint]:
              return binary_search(a_list[:midpoint]			,							snake_case     )
       else:
              return binary_search(a_list[midpoint + 1 :]			,							snake_case     )


if __name__ == "__main__":
 __lowerCAmelCase		       =							input('''Enter numbers separated by comma:\n''').strip()
 __lowerCAmelCase		       =							[int(item.strip()) for item in user_input.split(''',''')]
 __lowerCAmelCase		       =							int(input('''Enter the number to be found in the list:\n''').strip())
 __lowerCAmelCase		       =							'''''' if binary_search(sequence, target) else '''not '''
 print(F'''{target} was {not_str}found in {sequence}''')


