





def     a_       (					lowerCAmelCase_ :     Union[str, Any]      ):



   if isinstance(__A,      __A      ):
      raise TypeError('\'float\' object cannot be interpreted as an integer'      )
   if isinstance(__A,      __A      ):
      raise TypeError('\'str\' object cannot be interpreted as an integer'      )

   if num == 0:
      return "0b0"

   __lowerCAmelCase				      =      False

   if num < 0:
      __lowerCAmelCase				      =      True
      __lowerCAmelCase				      =      -num

   __lowerCAmelCase				      =      []
   while num > 0:
      binary.insert(0,      num % 2      )
      num >>= 1

   if negative:
      return "-0b" + "".join(str(__A      ) for e in binary      )

   return "0b" + "".join(str(__A      ) for e in binary      )


if __name__ == "__main__":
     import doctest

     doctest.testmod()






'''simple docstring'''





def lowerCAmelCase    (__A):



     """simple docstring"""



     if not isinstance(__A    ,      __A):
          raise ValueError('''multiplicative_persistence() only accepts integral values''')
     if num < 0:
          raise ValueError('''multiplicative_persistence() does not accept negative values''')

     _a           =    0
     _a           =    str(__A)

     while len(__A) != 1:
          _a           =    [int(__A) for i in num_string]

          _a           =    1
          for i in range(0    ,      len(__A)):
               total *= numbers[i]

          _a           =    str(__A)

          steps += 1
     return steps




def lowerCAmelCase    (__A):



     """simple docstring"""



     if not isinstance(__A    ,      __A):
          raise ValueError('''additive_persistence() only accepts integral values''')
     if num < 0:
          raise ValueError('''additive_persistence() does not accept negative values''')

     _a           =    0
     _a           =    str(__A)

     while len(__A) != 1:
          _a           =    [int(__A) for i in num_string]

          _a           =    0
          for i in range(0    ,      len(__A)):
               total += numbers[i]

          _a           =    str(__A)

          steps += 1
     return steps


if __name__ == "__main__":
  import doctest

  doctest.testmod()



